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Download the following FREE pdf e-Books ( Chapter wise / Topic wise solutions, Written by Prof. Subhashish Chattopadhyay SKMClasses Bangalore )
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IIT-JEE, NCERT / CBSE, I.Sc., PU, Board exam, EAMCET, BITS Physics Books with lots of Examples ( Free pdf download of Physics Books, Chapter wise / Topic wise Questions and Solutions )
27 ] CBSE & IIT-JEE Physics Survival Guide – Thermal Properties of Solids, or Thermal Properties of Material, Thermal Conductivity etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Thermal Properties of Solids, or Thermal Properties of Material, Thermal Conductivity Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Thermal Properties of Solids, or Thermal Properties of Material, Thermal Conductivity Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Thermal Properties of Solids, or Thermal Properties of Material, Thermal Conductivity Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-thermal-properties-of-solids-by-prof-subhashish-chattopadhyay
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26 ] CBSE & IIT-JEE Physics Survival Guide – Buoyant Force, Buoyancy, Discussions on Layer of Liquid below the Object etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Buoyant Force, Buoyancy, Discussions on Layer of Liquid below the Object Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Buoyant Force, Buoyancy, Discussions on Layer of Liquid below the Object Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Buoyant Force, Buoyancy, Discussions on Layer of Liquid below the Object Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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25 ] CBSE & IIT-JEE Physics Survival Guide – Mechanical Properties of Material, Mechanical Properties of Solids, Young ‘s Modulus, Bulk Modulus, Poisson ‘s Ratio, Shear Stress, Strain, Energy Stored in elongated wire etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Mechanical Properties of Material, Mechanical Properties of Solids, Young ‘s Modulus, Bulk Modulus, Poisson ‘s Ratio, Shear Stress, Strain, Energy Stored in elongated wire Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Mechanical Properties of Material, Mechanical Properties of Solids, Young ‘s Modulus, Bulk Modulus, Poisson ‘s Ratio, Shear Stress, Strain, Energy Stored in elongated wire Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Mechanical Properties of Material, Mechanical Properties of Solids, Young ‘s Modulus, Bulk Modulus, Poisson ‘s Ratio, Shear Stress, Strain, Energy Stored in elongated wire Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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24 ] CBSE & IIT-JEE Physics Survival Guide – Kinetic Theory of Gases etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Kinetic Theory of Gases Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Kinetic Theory of Gases Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Kinetic Theory of Gases Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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23 ] CBSE & IIT-JEE Physics Survival Guide – Vectors & Scalars etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Vectors & Scalars Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Vectors & Scalars Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Vectors & Scalars Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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22 ] CBSE & IIT-JEE Physics Survival Guide – Units, Dimensions, Measurements & Errors etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Units, Dimensions, Measurements & Errors Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Units, Dimensions, Measurements & Errors Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Units, Dimensions, Measurements & Errors Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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21 ] CBSE & IIT-JEE Physics Survival Guide – Kinematics, Dynamics or Kinetics, Circular Motion & Projectile Motion etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Kinematics, Dynamics or Kinetics, Circular Motion & Projectile Motion Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Kinematics, Dynamics or Kinetics, Circular Motion & Projectile Motion Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Kinematics, Dynamics or Kinetics, Circular Motion & Projectile Motion, Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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20 ] CBSE & IIT-JEE Physics Survival Guide – Measuring Speed of Light, Various Methods etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Measuring Speed of Light, Various Methods by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Measuring Speed of Light, Various Methods etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Measuring Speed of Light, Various Methods etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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19 ] CBSE & IIT-JEE Physics Survival Guide – Maxwell ‘s Equations, Electromagnetic Waves etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Maxwell ‘s Equations, Electromagnetic Waves by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Maxwell ‘s Equations, Electromagnetic Waves etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Maxwell ‘s Equations & Electromagnetic Waves etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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18 ] CBSE & IIT-JEE Physics Survival Guide – Magnetism History etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Magnetism History by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Magnetism History etc by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Magnetism History etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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17 ] CBSE & IIT-JEE Physics Survival Guide – Magnetic Induction, Voltage Produced etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Magnetic Induction, Voltage Produced by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Magnetic Induction, Voltage Produced by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Magnetic Induction, Voltage Produced etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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16 ] CBSE & IIT-JEE Physics Survival Guide – Magnetic Effects of Current etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Magnetic Effects of Current by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Magnetic Effects of Current by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Magnetic Effects of Current, Various Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-magnetic-effect-of-current-by-prof-subhashish-chattopadhyay
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15 ] CBSE & IIT-JEE Physics Survival Guide – Capacitance Dielectrics & Circuits etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Capacitance Dielectrics & Circuits by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Capacitance Dielectrics & Circuits by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Capacitance, Trick Circuits, Combinations of Dielectrics, Various Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
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14 ] CBSE & IIT-JEE Physics Survival Guide – Electrostatics & Gauss Theorem etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Electrostatics & Gauss Theorem by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Electrostatics & Gauss Theorem by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Electrostatics, Gauss Theorem, Various Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-electrostatics-gauss-theorem-by-prof-subhashish-chattopadhyay
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13 ] CBSE & IIT-JEE Physics Survival Guide – Center of Mass etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Center of Mass by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Center of Mass by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Center of Mass, Various Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-center-of-mass-by-prof-subhashish-chattopadhyay
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12 ] CBSE & IIT-JEE Physics Survival Guide – Work Power Energy Variable Force Leaking Bucket etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Work Power Energy Variable Force Leaking Bucket by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Work Power Energy Variable Force Leaking Bucket by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Work Power Energy Variable Force Leaking Bucket, Various Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-work-power-energy-by-prof-subhashish-chattopadhyay
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11 ] CBSE & IIT-JEE Physics Survival Guide – Moment of Inertia, Solid Bodies Angular Momentum etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Moment of Inertia of Solid Bodies by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Moment of Inertia of Solid Bodies by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Moment of Inertia, Solid Bodies Angular Momentum, Rotational Energy, Derivations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-moment-of-inertia-by-prof-subhashish-chattopadhyay
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10 ] CBSE & IIT-JEE Physics Survival Guide – Circular Motion, Conical Pendulum etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Circular Motion, Conical Pendulum etc and many complicated Problems by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Circular Motion by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Circular Motion. Conical Pendulum etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-circular-motion-by-prof-subhashish-chattopadhyay
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9 ] CBSE & IIT-JEE Physics Survival Guide – Solutions to Irodov Problems, by Subhashish Sir, and Other Professors.
cbse-iit-jee-physics-survival-guide-irodov-problems-solutions-by-prof-subhashish-others
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8 ] CBSE & IIT-JEE Physics Survival Guide – Electrical Circuits, Delta to Star Conversion, Current Source, Trick Circuits, Unbalanced Wheatstone Bridge, Steps and Techniques of Solving Electrical Circuits etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Electrical Circuits, Delta to Star Conversion, Current Source, Trick Circuits, Unbalanced Wheatstone Bridge, Steps and Techniques of Solving Electrical Circuits etc and many complicated Problems by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Gravitation by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Electrical Circuits, including Inductance & Capacitance, internal Resistance etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-electrical-circuits-by-prof-subhashish-chattopadhyay
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7 ] CBSE & IIT-JEE Physics Survival Guide – Gravitation, Contrasting Comparisons of Gravitational Potential and Electrostatic Potential, Contrasting Comparisons of Gravitational Field and Electrostatic Field, Escape Velocity, Height attended by a mass thrown at various speeds etc – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Gravitation, Contrasting Comparisons of Gravitational Potential and Electrostatic Potential, Contrasting Comparisons of Gravitational Field and Electrostatic Field, Escape Velocity, Height attended by a mass thrown at various speeds etc and many complicated Problems by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Gravitation by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Gravitation, Field, Potential, escape velocity etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-gravitation-by-prof-subhashish-chattopadhyay
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6 ] CBSE & IIT-JEE Physics Survival Guide – SHM Periodic Motion, Harmonic Oscillations with Solid Objects, Approximate Simple Harmonic Motions – by Professor Subhashish Chattopadhyay, Bangalore.
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – SHM ( Simple Harmonic Motion ) and many complicated Problems by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – SHM by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of SHM Approximate Oscillations etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
cbse-iit-jee-physics-survival-guide-shm-harmonic-oscillations-or-periodic-motion-by-prof-subhashish
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5 ] CBSE & IIT-JEE Physics Survival Guide – Sound Waves, Doppler Effect, Standing waves in Open Tube, Closed Tube, Rods or Bars by Professor Subhashish Chattopadhyay, Bangalore
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Sound Waves, Doppler Effect, Standing waves in Open Tube, Closed Tube, Rods or Bars by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Sound Waves, Oscillations in Wires by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Sound Waves, Doppler effect, Standing waves and Propagating Waves, Oscillations in Wires, Bars, Tubes ( both Open Tube and Closed Tube ) etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. Regarding the latest developments I wrote … “ GUT [ General Unified Theory ] is being modified to introduce a 5th fundamental force, because some heavy particles have been observed at CERN and various other experiments and Producing Gravitational waves at will, without mass, Madala Bosons to explain Dark Matter ”
cbse-iit-jee-physics-survival-guide-waves-and-sound-by-prof-subhashish
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4 ] CBSE & IIT-JEE Physics Survival Guide – Radio activity and Modern Physics by Professor Subhashish Chattopadhyay, Bangalore
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Radio activity and Modern Physics by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Radio activity and Modern Physics by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Radioactivity and Modern Physics. LASERS, Dirac Equation, Particle Physics, Diode, Triode, Transistor, Quantum Mechanics etc are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE & IIT-JEE Physics Survival Guide-Radio activity and Modern Physics by Prof. Subhashish
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3 ] CBSE & IIT-JEE Physics Survival Guide – Mirrors Lenses Slabs Prisms Ray Diagram Problems – Optics by Professor Subhashish Chattopadhyay, Bangalore
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Mirrors Lenses Slabs Prisms Ray Diagram Problems Optics by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Mirrors Lenses Slabs Prisms Ray Diagram Problems Optics by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Mirror Slab Prism Lenses Ray Diagram Problems & Solutions Optics. Silvered Slab, Silvered Lenses, Silvered prisms are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
In this eBook I wrote about my Personal Choice of, ” List of Best Experiments ” …
Michelson–Morley experiment proving there was no Aether, Moseley ‘s experiment with X-Rays to discover Protons, Jagadish chandra Bose demonstrating controlled emission / transmission and receiving of Radio waves, Casimir experiments to show Casimir forces of virtual particles, Eddington measuring bending of light, Flying atomic clocks in planes and confirming slowing down of time at high speeds, Victor Hess measured Radiation level variation at ground and high up in the atmosphere, Soviet physicist Sergey Vernov was the first to use radiosondes to perform cosmic ray readings with an instrument carried to high altitude by a balloon at heights up to 13.6 km, The proof of time dilation by Muon decay, Measurement of Space-time curvature near Earth and thereby the stress–energy tensor (which is related to the distribution and the motion of matter in space) in and near Earth , Detecting Gravitational Waves.
CBSE & IIT-JEE Physics Survival Guide-Mirrors Prisms Lens Slabs Optics by Prof. Subhashish
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2 ] CBSE & IIT-JEE Physics Survival Guide – Wave Optics by Professor Subhashish Chattopadhyay, Bangalore
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Wave Optics by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide- Wave Optics by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Wave Optics. Slabs, Silvered Slab, Lenses, Silvered Lenses, Prisms, Silvered prisms are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE & IIT-JEE Physics Survival Guide-Wave Optics by Prof. Subhashish
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1 ] CBSE & IIT-JEE Physics Survival Guide – Ray or Geometrical Optics by Professor Subhashish Chattopadhyay, Bangalore
Description – “ Spoon Feeding CBSE & IIT-JEE Physics Survival Guide – Ray or Geometrical Optics by Professor Subhashish Chattopadhyay ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Physics Survival Guide – CBSE & IIT-JEE Physics Survival Guide – Ray or Geometrical Optics by Professor Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II COMED-K CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Ray or Geometrical Optics. Slabs, Silvered Slab, Lenses, Silvered Lenses, Prisms, Silvered prisms are also covered. There are many kinds of Problems which are NOT covered in Professor H C Verma ‘s books ( Concepts of Physics ) or Irodov, or ” Resnick & Halliday “. Some examples being split Lenses, Fresnel’s Biprism, Polytropic Processes, Silvered lenses, Slab with a lens like hole or filled with liquids, Cylindrical lenses, isodiaphers, Spallation Reaction, Magic Numbers, Doubly Magic Numbers, Metamaterials with Negative Refractive Index etc. All these kinds of Questions which have been asked in various exams are covered in eBooks of Professor Subhashish Chattopadhyay. Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, COMED-K etc with CBSE, CEE, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE & IIT-JEE Physics Survival Guide-Ray or Geometrical Optics by Prof. Subhashish
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Nima Arkani-Hamed has written a beautiful paper on ” The Future of Fundamental Physics “
We are too used to see ‘daily news ‘ which changes everyday. Often many of us start thinking or imagining Progress in Science and / or technology will also happen at that speed. Searching the net for future trends, every hour, actually wastes time, rather than teaching us anything. Slow long term prediction is difficult to do. These predictions does not change much. It needs very deep understanding of the present trends, to write about future.
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IIT-JEE, NCERT / CBSE, I.Sc., PU, Board exam, EAMCET, BITS Chemistry Books with lots of Examples ( Free pdf download of Chemistry Books, Chapter wise / Topic wise Questions and Solutions )
8 ] CBSE 12 & IIT-JEE Chemistry Survival Guide – Stoichiometry Titration by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Stoichiometry Titration ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chemistry Survival Guide – Stoichiometry Titration by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers several examples of Stoichiometry Titrations, Heating effects in several salts, colours or colors of the precipitates, Empirical formulae calculation, Limiting reagents, Titration examples, Equivalent weight, milli-equivalent weight, What mass or moles is reacting with how much ? How much is oxidised ? How much is Reduced ? Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-Stoichiometry Titration by Prof. Subhashish
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7 ] CBSE 12 & IIT-JEE Chemistry Survival Guide – Redox Reactions by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Redox Reactions ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chemistry Survival Guide – Redox Reactions by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers more than 60 examples of Redox Reactions, Several Complicated examples and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-Redox Reactions by Prof. Subhashish
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6 ] CBSE 12 & IIT-JEE Chemistry Survival Guide – Electrochemistry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Electrochemistry ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chemistry Survival Guide – Electrochemistry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers Electrochemistry, Oxidation Potential, Reduction Potential, Electrode Potential, Reactivity Series, Battery, Nernst Equation, Variation of Voltage with concentration, Electrolyte, Electrolysis, Salt Bridge, Daniel Cell, Primary Cell, Secondary Cell, Galvanic Cell, Electrolytic Cell, Conductivity, Kohlrausch ’s Law and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-ElectroChemistry by Prof. Subhashish
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5 ] CBSE 12 & IIT-JEE Organic Chemistry Survival Guide – Reduction Methods by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Reduction Methods ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Organic Chemistry Survival Guide – Reduction Methods by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers Various kinds of Reduction Methods in Organic Chemistry. Covers Gilmann ’s Reagent, Grignard Reagent, Trimethyl Silyl Iodide, Silyl Wittig Reaction, Hydrogen with Ni, Zn, Pd Palladium, Bakers Yeast, Wolf Kishner, Wilkinson ’s Catalyst, Birch Reduction, Lindlar ’s Catalyst, Benkeser Reduction, Reduction with HCO2H, Sodium Boro Hydride NaBH4, Veils Meier Reaction, Luche ’s Reagent, Super Hydride, Sodium Cyno boro hydride, Dibal H, Adams Catalyst, Rosen Mund Reduction, Various Lithium Aluminium Hydrides, NaNH2, and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Organic Chem Survival Guide-Reduction methods by Prof. Subhashish
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4 ] CBSE 12 & IIT-JEE Organic Chemistry Survival Guide – Oxidation Methods by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Oxidation Methods ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Organic Chemistry Survival Guide – Oxidation Methods by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers Various kinds of Oxidation Methods in Organic Chemistry. Covers Sarett ’s Reagent, PCC, Chromium Oxide, Osmium Oxide, Manganese Oxide, Silver oxides, Ruthenium Oxide, Hydrogen Peroxide, Selenium dioxide, KMnO4, Jones, Julia Colonna, DCC, Corey ’s, Moffats, Ley Oxidation, MPV, Fetizon, Fremy ’s Salt, Elbs Persulphate Oxidation, Sodiumperiodate, Palladium Chloride, Copper Chloride, Sharpless epoxidation, and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Organic Chem Survival Guide-Oxidation methods by Prof. Subhashish
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3 ] CBSE 12 & IIT-JEE Chem Survival Guide – Bonds & Structure by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Bonds & Structures ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chem Survival Guide – Bonds & Structures by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers Various kinds of Bonds and Structures in Chemistry. Covers Sigma, Pi, Delta, Back Bonding, Coordinate or Dative Bond, Eta Bond, Hydrogen Bond, London forces, and many more, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-Bonds & Structure by Prof. Subhashish
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2 ] CBSE 12 & IIT-JEE Chem Survival Guide – Elements & Properties by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Elements & Properties ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chem Survival Guide – Elements & Properties by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers Elements & Their Properties in Chemistry. Covers the discoveries by spectral Analysis, Named after smell, places, people etc. Various compounds, tests, properties, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-Elements & Properties by Prof. Subhashish
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1 ] CBSE 12 & IIT-JEE Chem Survival Guide – Empirical Formulae by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Empirical Formulae ” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Chem Survival Guide – Empirical Formulae by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CEE COMED-K IGCSE IB AP-Chemistry, CET, VIT, Manipal, SRM and other exams.
This e-Book covers various kinds of Empirical Equations in Chemistry. These equations are formed by experiments, and graph plotting. In some rare cases the Theory was developed later. Covers Slater’s rule, Shielding, Finding Electronegativity values by Allred and Rochow ’s empirical formula, Moseley’s Law, Trouton ’s law, Einstein-Debey equation (Dulong & Petit), Reynolds number, Raoult’s law, Variation of viscosity with temperature, Arrhenius model, Williams-Landel-Ferry model, Masuko and Magill model, Walther formula, Wright model, Seeton model, Variation of surface tension with temperature, Eotvos equation, Guggenheim-Katayama equation, Debye-Huckel-Onsager theory of conductivity of ions in dilute solutions, Liquid drop model of Nucleus, Nuclear Shell Model, Ionic character percentage of a diatomic molecule, and various incomplete dictionary kinds of collection for Course of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions.
CBSE 12 & IIT-JEE Chem Survival Guide-Empirical Formulae by Prof. Subhashish
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IIT-JEE, NCERT / CBSE, I.Sc., PU, Board exam, EAMCET, BITS Math Books with lots of Questions and Solutions, Examples ( Free pdf download of Math Books, Chapter wise / Topic wise Solutions )
17 ] CBSE & IIT-JEE Math Survival Guide – Trigonometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Trigonometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Trigonometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Trigonometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Trigonometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE & IIT-JEE Math Survival Guide-Trigonometry by Prof. Subhashish
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16 ] CBSE & IIT-JEE Math Survival Guide – 3D Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding 3D Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – 3D Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers 3D Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of 3D Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE & IIT-JEE Math Survival Guide-3D Geometry by Prof. Subhashish
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15 ] CBSE & IIT-JEE Math Survival Guide – Hyperbola Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Hyperbola Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Hyperbola Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Hyperbola Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Hyperbola Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE & IIT-JEE Math Survival Guide-Hyperbola by Prof. Subhashish
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14 ] CBSE & IIT-JEE Math Survival Guide – Ellipse Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Ellipse Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Ellipse Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Ellipse Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Ellipse Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE & IIT-JEE Math Survival Guide-Ellipse by Prof. Subhashish
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13 ] CBSE & IIT-JEE Math Survival Guide – Parabola Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Parabola Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Parabola Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Parabola Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Parabola Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CBSE & IIT-JEE Math Survival Guide-Parabola by Prof. Subhashish
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12 ] CBSE & IIT-JEE Math Survival Guide – Pair of Straight Lines Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Pair of Straight Lines Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Pair of Straight Lines Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Pair of Straight Lines Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Pair of Straight Lines Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE & IIT-JEE Math Survival Guide-Pair of Straight Lines by Prof. Subhashish
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11 ] CBSE 11 & IIT-JEE Math Survival Guide – Circles Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Circles Coordinate Geometry” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Circles Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Circles Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Circles Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE 11 & IIT-JEE Math Survival Guide-Circles by Prof. Subhashish
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10 ] CBSE 11 & IIT-JEE Math Survival Guide – Straight Lines Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Lines Coordinate Geometry” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Lines Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Straight Lines Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Straight Lines Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE 11 & IIT-JEE Math Survival Guide-Straight Lines by Prof. Subhashish
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9 ] CBSE 11 & IIT-JEE Math Survival Guide – Complex Numbers or Imaginary Numbers by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Complex Numbers or Imaginary Numbers” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Complex Numbers or Imaginary Numbers by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Complex Numbers or Imaginary Numbers with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Complex Numbers or Imaginary Numbers, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CBSE 11 & IIT-JEE Math Survival Guide-Complex Number by Prof. Subhashish
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8 ] CBSE 12 & IIT-JEE Math Survival Guide – Quadratic Equations by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Quadratic Equations” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Quadratic Equation by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Quadratic Equations with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Quadratic Equations, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE 11 & IIT-JEE Math Survival Guide-Quadratic Equation by Prof. Subhashish
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7 ] CBSE 12 & IIT-JEE Math Survival Guide – Continuity and Differentiability by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Continuity & Differentiability” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Continuity and Differentiability by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Continuity and Differentiability with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Continuity and Differentiability, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CBSE 12 & IIT-JEE Math Survival Guide-Continuity & Differentiability by Prof. Subhashish
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6 ] CBSE 12 & IIT-JEE Math Survival Guide – Relations and Functions by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Relations & Functions” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Relations and Functions by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Relations and Functions with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Relations and Functions, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CBSE 12 & IIT-JEE Math Survival Guide-Relations & Functions by Prof. Subhashish
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5 ] CBSE 12 & IIT-JEE Math Survival Guide – Graphs and Functions by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Graphs & Functions” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Graphs and Functions by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Graphs and Functions with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Graphs and Functions, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE 12 & IIT-JEE Math Survival Guide-Functions & Graphs by Prof. Subhashish
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4 ] CBSE 12 & IIT-JEE Math Survival Guide – Indefinite Integrals by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Indefinite Integrals & Calculus” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Indefinite Integrals by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE IGCSE IB AP-Mathematics and other exams.
This e-Book covers Indefinite Integrals with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Indefinite Integrals, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
CBSE 12 & IIT-JEE Math Survival Guide-Indefinite Integrals by Prof. Subhashish
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3 ] CBSE 12 & IIT-JEE Math Survival Guide – Area & Volume by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Area and Volume ” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 and IIT-JEE Math Survival Guide – Area and Volume by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE IGCSE IB AP-Mathematics and other exams.
This e-Book covers various kinds of graphs, such as graph of Ln x, ( ln x )/x, x Ln x, floor x [ x ] , Shifting of graphs, roots of Quadratic, cubic, and other higher powers of x ( polynomials ), asymptotes, ( How to find Asymptotes ) etc. Volume by revolution and hundreds of Area problems of IIT-JEE, CET, etc with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CBSE 12 & IIT-JEE Math Survival Guide-Area & Volume by Prof. Subhashish
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2 ] CBSE 12 & IIT-JEE Math Survival Guide – Definite Integrals by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Definite Integrals ” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide-Definite Integrals by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE IGCSE IB AP-Mathematics and other exams.
CBSE 12 & IIT-JEE Math Survival Guide-Definite Integrals by Prof. Subhashish
This e-Book covers Definite Integrals with [ x ] greatest integer functions, { x } fraction function, Max and Min functions. Gamma function, Beta function, Integration after converting to Complex number, Leibnitz forms of Differentiating Integrals, L Hospital’s rule applied to limits with Integrals, Inequalities of Integrals, Rules / Tricks / Properties of Definite Integrals, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions.Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal’s Solutions.
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1 ] CBSE 12 Math Survival Guide – Differential Equations by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Differential Equations ” for IIT-JEE, I.Sc. , CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide – Differential Equations by Prof. Subhashish Chattopadhyay SKMClasses Bangalore Useful for I.Sc. PU-II CET CEE IGCSE IB AP-Mathematics and other exams.
CBSE 12 & IIT-JEE Math Survival Guide-Differential Equations by Prof. Subhashish
This e-Book covers all kinds of Differential equations, and methods to solve them. There is a priority checklist for the approach to be taken for solving the problems. Covers ISc, CBSE, COMED-K IIT-JEE problems, Linear, Homogeneous, Variable separable by substitution, Exact, Reducible to exact, Bernoulli, Integrating Factors or Multiplying Factors, even Clairaut’s Differential Equations ( IIT-JEE 1999, Bihar CEE 1999 ). Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
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Various States have different names for the Engineering Entrance Exams.
CET – Common Engineering Entrance Test or Common Entrance Test is for Karnataka, Maharastra, Gujrat, Himachal Pradesh, J&K
GUJCET Exam – Gujarat Entrance Common Entrance Test – Engineering
HPCET – Himachal Pradesh Common Entrance Test
CEE – Commissionerate of Entrance Examinations Kerala. Some people say Common Entrance Exam. The exam in Kerala actually is known as KEAM – Kerala
Engineering Agriculture Medical Degree.
ASSAM CEE – Assam Combined Entrance Exam
EAMCET – Engineering and Medical Common Entrance Test
MP PET – Madhya Pradesh Pre Engineering Test. Randomly I liked lots of Physics Questions of MP-PET, as these were of very high quality / interesting.
RPET or R-PET – Rajasthan Pre Engineering Test
WBJEE or WB-JEE – West Bengal Joint Entrance Exam. The questions of these are very good / high quality.
UPSEE – Utter Pradesh State Entrance Exam
BCECEB – Bihar Combined Entrance Competitive Examination Board. The exam name is BCECE. Some call it as Bihar Combined Engineering Entrance Exam BCEEE or
BCECE (Bihar Combined Entrance Competitive Examination)
OJEE – Orissa Joint Entrance Exam
Tamilnadu does not have any state ( common ) entrance test. The admissions in colleges / universities are through standard 12 marks.
TNEA is a State Engineering Entrance Examination, which is conducted by Anna University. Tamil Nadu Engineering Admission.
COMEDK PGET – Consortium of Medical, Engineering and Dental Colleges of Karnataka for PG Post Graduate
NATA – National Aptitude Test in Architecture. National Institute of Advanced Studies in Architecture (NIASA) conducts this.
ISAT by IISAT – Indian Institute of Space Science and Technology (IISAT) Admission Test (ISAT) is a National Level Entrance Examination.
NAT – National Aptitude Test by Society for Research & Development in Education (SRDE), New Delhi
ENAT – EPSI National Admission Test. by Manipal Institute of Technology. Manipal Online Entrance Test Manipal-OET
VITEEE – VIT Engineering Entrance Exam, Vellore Institute of Technology. Conducted by VIT university
BITSAT – Birla Institute of Technology and Science Admission Test.
Punjab PET – Punjab Engineering Admission, Pre Engineering Test
ASSAM CEE – Assam Combined Entrance Exam
Tripura JEE – Tripura Joint Entrance Exam
NEE – NERIST Entrance Examination. Conducted by the North Eastern Regional Institute of Science & Technology (NERIST), Nirjuli, Itanagar, Arunachal Pradesh
1 ] CET CEE EAMCET JEE Math Survival Guide – Hyperbola Coordinate Geometry by Prof. Subhashish Chattopadhyay
Description – “Spoon Feeding Hyperbola Coordinate Geometry” for IIT-JEE, I.Sc., CBSE, Karnataka PU, State Boards etc. CBSE Standard 12 Math Survival Guide-Hyperbola Coordinate Geometry by Prof. Subhashish Chattopadhyay SKMClasses Bangalore. Useful for I.Sc. PU-II CET CEE COMED-K IGCSE IB AP-Mathematics and other exams.
This e-Book covers Hyperbola Coordinate Geometry with lots of Video explanations. The classroom teaching videos can be seen by clicking on the given links. The videos can be downloaded also. Hundreds of tricky problems solved. Rules / Tricks / Properties of Hyperbola Coordinate Geometry, with CBSE, COMED-K, IIT-JEE ( Main and Advanced ) Problems and Solutions. Includes NCERT / CBSE Text Book Solutions, Chapter wise Solutions, AIEEE ( Now known as IIT-JEE main ) Solutions, Roorkey Entrance Exam Solutions, CET, CEE, PET, EAMCET Solutions. R D Sharma Solutions, R S Aggarwal ’s Solutions.
CET CEE PET EAMCET JEE Math Survival Guide-Hyperbola by Prof. Subhashish
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Some books which are must read. I tell all my friends and students to read these
You should read the books by Daniel Kahneman,
https://vk.com/doc23267904_175119602
The Black Swan – by Nassim Taleb
http://shifter-magazine.com/wp-content/uploads/2015/02/Taleb_The-Black-Swan.pdf
also
see http://stavochka.com/files/Nate_Silver_The_Signal_and_the_Noise.pdf
Nudge by Thaler and Sunstein
https://ethicslab.georgetown.edu/studio/wordpress/wp-content/uploads/2015/02/Richard_H._Thaler_Cass_R._Sunstein_Nudge_Impro_BookFi.org_.pdf
book which explains pricing is ” The undercover Economist “
or
http://ebook.stepor.com/book/the-undercover-economist-76396-pdf.html
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Many more free pdf e-Books are available at ( such as H C Verma Concepts of Physics Solutions, Arihant Books, free download eBooks for IIT JEE guides, AIEEE IIT JEE advanced Chapter wise solutions, preparation materials )
1 ] A Guide Book to Mechanism in Organic Chemistry by Peter Sykes
A_GUIDE_BOOK_TO_MECHANISM_IN_ORGANIC_CHEMISTRY
2 ] Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005
Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005
3 ] Linear Algebra For Dummies
4 ] Calculus Workbook For Dummies
5 ] Differential Equations For Dummies
Differential_Equations_For_Dummies
6 ] Linear Algebra by Jim Hefferon
7 ] Mathematics – Puzzles from around the world
Mathematics—Puzzles-from-around-the-world
8 ] Graph Theory by Reinhard Diestel
9 ] Electronics for Dummies
10 ] Electronics Projects for Dummies
Electronics Projects For Dummies
11 ] Physics For Dummies
12 ] Physics Workbook For Dummies
13 ] Inorganic Chemistry James E. House
Inorganic Chemistry James E. House
14 ] Inorganic Chemistry by Cox
15 ] Inorganic Chemistry 5th Edition Miessler
Inorganic Chemistry 5th Edition Miessler
16 ] Fundamentals of Organic Chemistry Solomon
Fundamentals of Organic Chemistry Solomon
17 ] Illustrated Guide to Home Chemistry Experiments
Illustrated Guide to Home Chemistry Experiments
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e-Book-e-Book-e-Book-e-Book-e-Book-e-Book-e-Book-e-Book-e-Book-e-Book–e-Book
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Solution to Chapter 6 :
Thermodynamics ( Thermochemistry )
Must see https://zookeepersblog.wordpress.com/some-points-which-i-wish-all-my-new-prospective-students-know/
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The next chapter Solution is at https://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-7-chemical-equilibrium/
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The previous chapter Solution is at https://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-5-states-of-matter/
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The Laws of Thermochemistry
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The next chapter Solution is at https://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-7-chemical-equilibrium/
!
The previous chapter Solution is at https://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-5-states-of-matter/
!
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Heat of Neutralization :
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It is the only physical theory of universal content concerning which I am convinced that, within the framework of theapplicability of its basic concepts, it will never be overthrown.
Albert Einstein
Chemical energy stored by molecules can be released as heat during chemical reactions when a fuel like methane, cooking gas or coal burns in air. The chemical energy may also be used to do mechanical work when a fuel burns in an engine or to provide electrical energy through a galvanic cell like dry cell. Thus, various forms of energy are interrelated and under certain conditions, these may be transformed from one form into another. The study of these energy transformations forms the subject matter of thermodynamics. The laws of thermodynamics deal with energy changes of macroscopic systems involving a large number of molecules rather than microscopic systems containing a few molecules. Thermodynamics is not concerned about how and at what rate these energy transformations are carried out, but is based on initial and final states of a system undergoing the change. Laws of thermodynamics apply only when a system is in equilibrium or moves from one equilibrium state to another equilibrium state. Macroscopic properties like pressure and temperature do not change with time for a system in equilibrium state. In this unit, we would like to answer some of the important questions through thermodynamics, like:
How do we determine the energy changes involved in a chemical reaction/process? Will it occur or not?
What drives a chemical reaction/process?
To what extent do the chemical reactions proceed?
6.1 THERMODYNAMIC TERMS
We are interested in chemical reactions and the energy changes accompanying them. For this we need to know certain thermodynamic terms. These are discussed below.
6.1.1 The System and the Surroundings
A system in thermodynamics refers to that part of universe in which observations are made and remaining universe constitutes the surroundings. The surroundings include everything other than the system. System and the surroundings together constitute the universe .
The universe = The system + The surroundings
However, the entire universe other than the system is not affected by the changes taking place in the system. Therefore, for all practical purposes, the surroundings are that portion of the remaining universe which can interact with the system. Usually, the region of space in the neighbourhood of the system constitutes its surroundings.
For example, if we are studying the reaction between two substances A and B kept in a beaker, the beaker containing the reaction mixture is the system and the room where the beaker is kept is the surroundings (Fig. 6.1).
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Note that the system may be defined by physical boundaries, like beaker or test tube, or the system may simply be defined by a set of Cartesian coordinates specifying a particular volume in space. It is necessary to think of the system as separated from the surroundings by some sort of wall which may be real or imaginary. The wall that separates the system from the surroundings is called boundary. This is designed to allow us to control and keep track of all movements of matter and energy in or out of the system.
6.1.2 Types of the System
We, further classify the systems according to the movements of matter and energy in or out of the system.
1. Open System
In an open system, there is exchange of energy and matter between system and surroundings [Fig. 6.2 (a)]. The presence of reactants in an open beaker is an example of an open system*. Here the boundary is an imaginary surface enclosing the beaker and reactants.
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2. Closed System
In a closed system, there is no exchange of matter, but exchange of energy is possible between system and the surroundings [Fig. 6.2 (b)]. The presence of reactants in a closed vessel made of conducting material e.g., copper or steel is an example of a closed system.
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3. Isolated System
In an isolated system, there is no exchange of energy or matter between the system and the surroundings [Fig. 6.2 (c)]. The presence of reactants in a thermos flask or any other closed insulated vessel is an example of an isolated system.
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* We could have chosen only the reactants as system then walls of the beaker will act as boundary
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6.1.3 The State of the System
The system must be described in order to make any useful calculations by specifying quantitatively each of the properties such as its pressure (p), volume (V), and temperature (T ) as well as the composition of the system. We need to describe the system by specifying it before and after the change. You would recall from your Physics course that the state of a system in mechanics is completely specified at a given instant of time, by the position and velocity of each mass point of the system. In thermodynamics, a different and much simpler concept of the state of a system is introduced. It does not need detailed knowledge of motion of each particle because, we deal with average measurable properties of the system. We specify the state of the system by state functions or state variables.
The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties. We can describe the state of a gas by quoting its pressure (p), volume (V), temperature (T ), amount (n) etc. Variables like p, V, T are called state variables or state functions because their values depend only on the state of the system and not on how it is reached. In order to completely define the state of a system it is not necessary to define all the properties of the system; as only a certain number of properties can be varied independently. This number depends on the nature of the system. Once these minimum number of macroscopic properties are fixed, others automatically have definite values. The state of the surroundings can never be completely specified; fortunately it is not necessary to do so.
6.1.4 The Internal Energy as a State Function
When we talk about our chemical system losing or gaining energy, we need to introduce a quantity which represents the total energy of the system. It may be chemical, electrical, mechanical or any other type of energy you may think of, the sum of all these is the energy of the system. In thermodynamics, we call it the internal energy, U of the system, which may change, when
• heat passes into or out of the system,
• work is done on or by the system,
• matter enters or leaves the system.
These systems are classified accordingly as you have already studied in section 6.1.2.
(a) Work
Let us first examine a change in internal energy by doing work. We take a system containing some quantity of water in a thermos flask or in an insulated beaker. This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as adiabatic. The manner in which the state of such a system may be changed will be called adiabatic process. Adiabatic process is a process in which there is no transfer of heat between the system and surroundings. Here, the wall separating the system and the surroundings is called the adiabatic wall (Fig 6.3).
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Let us bring the change in the internal energy of the system by doing some work on it. Let us call the initial state of the system as state A and its temperature as TA. Let the internal energy of the system in state A be called UA. We can change the state of the system in two different ways.
One way: We do some mechanical work, say 1 kJ, by rotating a set of small paddles and thereby churning water. Let the new state be called B state and its temperature, as TB. It is found that TB > TA and the change in temperature, ΔT = TB-TA. Let the internal energy of the system in state B be UB and the change in internal energy, ΔU =UB– UA.
Second way: We now do an equal amount (i.e., 1kJ) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same as in the earlier case, say, TB – TA.
In fact, the experiments in the above manner were done by J. P. Joule between 184050 and he was able to show that a given amount of work done on the system, no matter how it was done (irrespective of path) produced the same change of state, as measured by the change in the temperature of the system.
So, it seems appropriate to define a quantity, the internal energy U, whose value is characteristic of the state of a system, whereby the adiabatic work, wad required to bring about a change of state is equal to the difference between the value of U in one state and that in another state, ΔU i.e.,
ΔU=U2−U1 =wad
Therefore, internal energy, U, of the system is a state function.
The positive sign expresses that wad is positive when work is done on the system. Similarly, if the work is done by the system,wad will be negative.
Can you name some other familiar state functions? Some of other familiar state functions are V, p, and T. For example, if we bring a change in temperature of the system from 25°C to 35°C, the change in temperature is 35°C-25°C = +10°C, whether we go straight up to 35°C or we cool the system for a few degrees, then take the system to the final temperature. Thus, T is a state function and the change in temperature is independent of the route taken. Volume of water in a pond, for example, is a state function, because change in volume of its water is independent of the route by which water is filled in the pond, either by rain or by tubewell or by both,
(b) Heat
We can also change the internal energy of a system by transfer of heat from the surroundings to the system or vice-versa without expenditure of work. This exchange of energy, which is a result of temperature difference is called heat, q. Let us consider bringing about the same change in temperature (the same initial and final states as before in section 6.1.4 (a) by transfer of heat through thermally conducting walls instead of adiabatic walls (Fig. 6.4).
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We take water at temperature, TA in a container having thermally conducting walls, say made up of copper and enclose it in a huge heat reservoir at temperature, TB. The heat absorbed by the system (water), q can be measured in terms of temperature difference , TB – TA. In this case change in internal energy, ΔU= q, when no work is done at constant volume.
The q is positive, when heat is transferred from the surroundings to the system and q is negative when heat is transferred from system to the surroundings.
(c) The general case
Let us consider the general case in which a change of state is brought about both by doing work and by transfer of heat. We write change in internal energy for this case as:
ΔU = q + w ————————————————(6.1)
For a given change in state, q and w can vary depending on how the change is carried out. However, q +w = ΔU will depend only on initial and final state. It will be independent of the way the change is carried out. If there is no transfer of energy as heat or as work (isolated system) i.e., if w = 0 and q = 0, then Δ U = 0.
The equation 6.1 i.e., ΔU = q + w is mathematical statement of the first law of thermodynamics, which states that
The energy of an isolated system is constant.
It is commonly stated as the law of conservation of energy i.e., energy can neither be created nor be destroyed.
Note: There is considerable difference between the character of the thermodynamic property energy and that of a mechanical property such as volume. We can specify an unambiguous (absolute) value for volume of a system in a particular state, but not the absolute value of the internal energy. However, we can measure only the changes in the internal energy, ΔU of the system.
Problem 6.1
Express the change in internal energy of a system when
(i) No heat is absorbed by the system from the surroundings, but work 
is done on the system. What type of wall does the system have ?
(ii) No work is done on the system, but q amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
(iii) w amount of work is done by the system and q amount of heat is supplied to the system. What type of system would it be?
Solution
(i) Δ U = wad, wall is adiabatic
(ii) Δ U = – q, thermally conducting walls
(iii) Δ U = q – w, closed system.
6.2 APPLICATIONS
Many chemical reactions involve the generation of gases capable of doing mechanical work or the generation of heat. It is important for us to quantify these changes and relate them to the changes in the internal energy. Let us see how!
6.2.1 Work
First of all, let us concentrate on the nature of work a system can do. We will consider only mechanical work i.e., pressure-volume work.
For understanding pressure-volume work, let us consider a cylinder which contains one mole of an ideal gas fitted with a frictionless piston. Total volume of the gas is Vi and pressure of the gas inside is p. If external pressure is pex which is greater than p, piston is moved inward till the pressure inside becomes equal to pex. Let this change be achieved in a single step and the final volume be Vf . During this compression, suppose piston moves a distance, l and is cross-sectional area of the piston is A [Fig. 6.5(a)].
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then, volume change = l x A = ΔV = (Vf – Vi )
We also know, pressure = force/area
Therefore, force on the piston = pex . A
If w is the work done on the system by movement of the piston then
w = force × distance = pex . A .l = pex . (-ΔV) = – pex ΔV = – pex (Vf – Vi ) ————————————-(6.2)
The negative sign of this expression is required to obtain conventional sign for w, which will be positive. It indicates that in case of compression work is done on the system. Here (Vf – Vi ) will be negative and negative multiplied by negative will be positive. Hence the sign obtained for the work will be positive.
If the pressure is not constant at every stage of compression, but changes in number of finite steps, work done on the gas will be summed over all the steps and will be equal to −ΣpΔV [Fig. 6.5 (b)]
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If the pressure is not constant but changes during the process such that it is always infinitesimally greater than the pressure of the gas, then, at each stage of compression, the volume decreases by an infinitesimal amount, dV. In such a case we can calculate the work done on the gas by the relation
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Here, pex at each stage is equal to (pin + dp) in case of compression [Fig. 6.5(c)]. In an expansion process under similar conditions, the external pressure is always less than the pressure of the system i.e., pex = (pin-dp). In general case we can write, pex = (pin + dp). Such processes are called reversible processes.
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A process or change is said to be reversible, if a change is brought out in such a way that the process could, at any moment, be reversed by an infinitesimal change. A reversible process proceeds infinitely slowly by a series of equilibrium states such that system and the surroundings are always in near equilibrium with each other. Processes other than reversible processes are known as irreversible processes.
In chemistry, we face problems that can be solved if we relate the work term to the internal pressure of the system. We can relate work to internal pressure of the system under reversible conditions by writing equation 6.3 as follows:
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Now, the pressure of the gas (pin which we can write as p now) can be expressed in terms of its volume through gas equation. For n mol of an ideal gas i.e., pV =nRT
⇒ p = nRT/V
Therefore, at constant temperature (isothermal process),
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Free expansion: Expansion of a gas in vacuum (pex = 0) is called free expansion. No work is done during free expansion of an ideal gas whether the process is reversible or irreversible (equation 6.2 and 6.3).
Now, we can write equation 6.1 in number of ways depending on the type of processes.
Let us substitute w = – pexΔV (eq. 6.2) in equation 6.1, and we get
ΔU = q − pexΔV
If a process is carried out at constant volume (ΔV = 0), then
ΔU = qV
the subscript V in qV denotes that heat is supplied at constant volume.
Isothermal and free expansion of an ideal gas
For isothermal (T = constant) expansion of an ideal gas into vacuum ; w = 0 since pex = 0. Also, Joule determined experimentally that q = 0; therefore, ΔU = 0
Equation 6.1, ΔU =q+w can be expressed for isothermal irreversible and reversible changes as follows:
1. For isothermal irreversible change q = -w = pex (Vf – Vi )
2. For isothermal reversible change q = – w = nRT ln Vf /Vi = 2.303 nRT log Vf /Vi
3. For adiabatic change, q = 0, ΔU = wad
Problem 6.2
Two litres of an ideal gas at a pressure of 10 atm expands isothermally into a vacuum until its total volume is 10 litres. How much heat is absorbed and how much work is done in the expansion ?
Solution
We have q = – w = pex (10 – 2) = 0(8) = 0
No work is done; no heat is absorbed.
Problem 6.3
Consider the same expansion, but this time against a constant external pressure of 1 atm.
Solution
We have q = – w = pex (8) = 8 litre-atm
Problem 6.4
Consider the same expansion, to a final volume of 10 litres conducted reversibly.
Solution
We have q = – w = 2.303 x 10 log(10/2) = 16.1 litre-atm
6.2.2 Enthalpy H
(a) A useful new state function
We know that the heat absorbed at constant volume is equal to change in the internal energy i.e., ΔU = qV. But most of chemical reactions are carried out not at constant volume, but in flasks or test tubes under constant atmospheric pressure. We need to define another state function which may be suitable under these conditions.
We may write equation (6.1) as ΔU = qp − pΔV at constant pressure, where qp is heat absorbed by the system and -pΔV represent expansion work done by the system.
Let us represent the initial state by subscript 1 and final state by 2
We can rewrite the above equation as
U2-U1 = qp – p (V2 – V1)
On rearranging, we get
qp = (U2 + pV2) – (U1 + pV1) ———————————————(6.6)
Now we can define another thermodynamic function, the enthalpy H [Greek word enthalpien, to warm or heat content] as :
H = U + pV —————————————–(6.7)
so, equation (6.6) becomes
qp= H2 – H1 = ΔH
Although q is a path dependent function, H is a state function because it depends on U, p and V, all of which are state functions. Therefore, ΔH is independent of path. Hence, qp is also independent of path.
For finite changes at constant pressure, we can write equation 6.7 as
ΔH = ΔU + ΔpV
Since p is constant, we can write
ΔH = ΔU + pΔV ——————————————-(6.8)
It is important to note that when heat is absorbed by the system at constant pressure, we are actually measuring changes in the enthalpy.
Remember ΔH = qp, heat absorbed by the system at constant pressure.
ΔH is negative for exothermic reactions which evolve heat during the reaction and ΔH is positive for endothermic reactions which absorb heat from the surroundings.
At constant volume (ΔV = 0), ΔU = qV, therefore equation 6.8 becomes
ΔH = ΔU = qV
The difference between ΔH and ΔU is not usually significant for systems consisting of only solids and / or liquids. Solids and liquids do not suffer any significant volume changes upon heating. The difference, however, becomes significant when gases are involved. Let us consider a reaction involving gases. If VA is the total volume of the gaseous reactants, VB is the total volume of the gaseous products, nA is the number of moles of gaseous reactants and nB is the number of moles of gaseous products, all at constant pressure and temperature, then using the ideal gas law, we write,
pVA = nART
and pVB = nBRT
Thus, pVB – pVA = nBRT – nART = (nB-nA)RT
or p (VB – VA) = (nB – nA) RT
or p ΔV = ΔngRT ——————————(6.9)
Here, Δng refers to the number of moles of gaseous products minus the number of moles of gaseous reactants.
Substituting the value of pΔV from equation 6.9 in equation 6.8, we get
ΔH = ΔU + ΔngRT —————————-(6.10)
The equation 6.10 is useful for calculating ΔH from ΔU and vice versa.
Problem 6.5
If water vapour is assumed to be a perfect gas, molar enthalpy change for vapourisation of 1 mol of water at 1bar and 100°C is 41kJ mol-1. Calculate the internal energy change, when
(i) 1 mol of water is vaporised at 1 bar pressure and 100°C.
(ii) 1 mol of water is converted into ice.
Solution
(i) The change H2O(l) → H2O(g)
ΔH = =ΔU + ΔngRT
or ΔU = ΔH – ΔngRT, substituting the values, we get
ΔU = 41.00 kJmol-1 x 8.3 Jmol-1 K-1 x 373 K = 41.00 kJ mol-1−3.096 kJ mol-1 = 37.904 kJ mol-1
(ii) The change H2O(l) → H2O(s)
There is negligible change in volume, So, we can put pΔV = Δng RT ≈ 0 in this case,
ΔH ≅ ΔU
so, ΔU =41.00kJ mol-1
(b) Extensive and Intensive Properties
In thermodynamics, a distinction is made between extensive properties and intensive properties. An extensive property is a property whose value depends on the quantity or size of matter present in the system. For example, mass, volume, internal energy, enthalpy, heat capacity, etc. are extensive properties.
Those properties which do not depend on the quantity or size of matter present are known as intensive properties. For example temperature, density, pressure etc. are intensive properties. A molar property, χm, is the value of an extensive property χ of the system for 1 mol of the substance. If n is the amount of matter, χm = χ/n is independent of the amount of matter. Other examples are molar volume, Vm and molar heat capacity, Cm. Let us understand the distinction between extensive and intensive properties by considering a gas enclosed in a container of volume V and at temperature T [Fig. 6.6(a)]. Let us make a partition such that volume is halved, each part [Fig. 6.6 (b)] now has one half of the original volume, V/2, but the temperature will still remain the same i.e., T. It is clear that volume is an extensive property and temperature is an intensive property.
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(c) Heat Capacity
In this sub-section, let us see how to measure heat transferred to a system. This heat appears as a rise in temperature of the system in case of heat absorbed by the system.
The increase of temperature is proportional to the heat transferred
q=coeff×ΔT
The magnitude of the coefficient depends on the size, composition and nature of the system. We can also write it as q = C ΔT
The coefficient, C is called the heat capacity.
Thus, we can measure the heat supplied by monitoring the temperature rise, provided we know the heat capacity.
When C is large, a given amount of heat results in only a small temperature rise. Water has a large heat capacity i.e., a lot of energy is needed to raise its temperature.
C is directly proportional to amount of substance. The molar heat capacity of a substance, Cm = C/n , is the heat capacity for one mole of the substance and is the quantity of heat needed to raise the temperature of one mole by one degree celsius (or one kelvin). Specific heat, also called specific heat capacity is the quantity of heat required to raise the temperature of one unit mass of a substance by one degree celsius (or one kelvin). For finding out the heat, q, required to raise the temperatures of a sample, we multiply the specific heat of the substance, c, by the mass m, and temperatures change, ΔT as
q = C× m ×ΔT =CΔT —————————————————(6.11)
(d) The relationship between Cp and CV for an ideal gas
At constant volume, the heat capacity, C is denoted by CV and at constant pressure, this is denoted by Cp . Let us find the relationship between the two.
We can write equation for heat, q
at constant volume as qV = CVΔT =ΔU
at constant pressure as qp = CpΔT =ΔH
The difference between Cp and CV can be derived for an ideal gas as:
For a mole of an ideal gas, ΔH = ΔU + Δ(pV ) = ΔU + Δ(RT ) = ΔU + RΔT
∴ ΔH= ΔU+RΔT ——————————————-(6.12)
On putting the values of ΔH and ΔU, we have
CpΔT = CVΔT + R ΔT —————————————————–(6.13)
6.3 MEASUREMENT OF ΔU AND ΔH: CALORIMETRY
We can measure energy changes associated with chemical or physical processes by an experimental technique called calorimetry. In calorimetry, the process is carried out in a vessel called calorimeter, which is immersed in a known volume of a liquid. Knowing the heat capacity of the liquid in which calorimeter is immersed and the heat capacity of calorimeter, it is possible to determine the heat evolved in the process by measuring temperature changes. Measurements are made under two different conditions:
i) at constant volume, qV
ii) at constant pressure, qp
(a) ΔU measurements
For chemical reactions, heat absorbed at constant volume, is measured in a bomb calorimeter (Fig. 6.7). Here, a steel vessel (the bomb) is immersed in a water bath. The whole device is called calorimeter. The steel vessel is immersed in water bath to ensure that no heat is lost to the surroundings. A combustible substance is burnt in pure dioxygen supplied in the steel bomb. Heat evolved during the reaction is transferred to the water around the bomb and its temperature is monitored. Since the bomb calorimeter is sealed, its volume does not change i.e., the energy changes associated with reactions are measured at constant volume. Under these conditions, no work is done as the reaction is carried out at constant volume in the bomb calorimeter. Even for reactions involving gases, there is no work done as ΔV = 0. Temperature change of the calorimeter produced by the completed reaction is then converted to qV, by using the known heat capacity of the calorimeter with the help of equation 6.11.
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(b) ΔH measurements
Measurement of heat change at constant pressure (generally under atmospheric pressure) can be done in a calorimeter shown in Fig. 6.8. We know that ΔH = qp (at constant p) and, therefore, heat absorbed or evolved, qp at constant pressure is also called the heat of reaction or enthalpy of reaction, ΔrH.
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In an exothermic reaction, heat is evolved, and system loses heat to the surroundings. Therefore, qp will be negative and ΔrH will also be negative. Similarly in an endothermic reaction, heat is absorbed, qp is positive and ΔrH will be positive.
Problem 6.6
1g of graphite is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atmospheric pressure according to the equation
C (graphite) + O2 (g) → CO2 (g)
During the reaction, temperature rises from 298 K to 299 K. If the heat capacity of the bomb calorimeter is 20.7kJ/K, what is the enthalpy change for the above reaction at 298 K and 1 atm?
Solution
Suppose q is the quantity of heat from the reaction mixture and CV is the heat capacity of the calorimeter, then the quantity of heat absorbed by the calorimeter.
q = CV x ΔT
Quantity of heat from the reaction will have the same magnitude but opposite sign because the heat lost by the system (reaction mixture) is equal to the heat gained by the calorimeter.
q = – CV x ΔT = 20.7 kJ/K x (299 – 298)K = – 20.7 kJ
(Here, negative sign indicates the exothermic nature of the reaction) Thus, ΔU for the combustion of the 1g of graphite = – 20.7 kJK-1
For combustion of 1 mol of graphite, = (12.0 gmol-1 x (20.7kJ))/1g
= – 2.48 102 kJ mol-1 , Since Δ ng = 0, Δ H = Δ U = – 2.48 102 kJ mol-1
6.4 ENTHALPY CHANGE, ΔrH OF A REACTION – REACTION ENTHALPY
In a chemical reaction, reactants are converted into products and is represented by,
Reactants → Products
The enthalpy change accompanying a reaction is called the reaction enthalpy. The enthalpy change of a chemical reaction, is given by the symbol ΔrH
ΔrH = (sum of enthalpies of products) – (sum of enthalpies of reactants)
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Enthalpy change is a very useful quantity. Knowledge of this quantity is required when one needs to plan the heating or cooling required to maintain an industrial chemical reaction at constant temperature. It is also required to calculate temperature dependence of equilibrium constant.
(a) Standard enthalpy of reactions
Enthalpy of a reaction depends on the conditions under which a reaction is carried out. It is, therefore, necessary that we must
specify some standard conditions. The standard enthalpy of reaction is the enthalpy change for a reaction when all the participating substances are in their standard states.
The standard state of a substance at a specified temperature is its pure form at 1 bar. For example, the standard state of liquid ethanol at 298 K is pure liquid ethanol at 1 bar; standard state of solid iron at 500 K is pure iron at 1 bar. Usually data are taken at 298 K.
Standard conditions are denoted by adding the superscriptVto the symbol ΔH, e.g., ΔHΘ
(b) Enthalpy changes during phase transformations
Phase transformations also involve energy changes. Ice, for example, requires heat for melting. Normally this melting takes place at constant pressure (atmospheric pressure) and during phase change, temperature remains constant (at 273 K).
H2O(s) → H2 O( l); ΔfusHΘ = 6.00 kJ mol−1
Here ΔfusHΘ is enthalpy of fusion in standard state. If water freezes, then process is reversed and equal amount of heat is given off to the surroundings.
The enthalpy change that accompanies melting of one mole of a solid substance in standard state is called standard enthalpy of fusion or molar enthalpy of fusion, ΔfusHΘ .
Melting of a solid is endothermic, so all enthalpies of fusion are positive. Water requires heat for evaporation. At constant temperature of its boiling point Tb and at constant pressure:
H2O(l) → H2O(g); ΔvapHΘ = + 40.79kJ mol-1
ΔvapHΘ is the standard enthalpy of vaporization.
Amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure (1bar) is called its standard enthalpy of vaporization or molar enthalpy of vaporization, ΔvapHΘ .
Sublimation is direct conversion of a solid into its vapour. Solid CO2 or ‘dry ice’ sublimes at 195K with ΔsubHΘ=25.2 kJ mol-1 ; naphthalene sublimes slowly and for this ΔsubHΘ = 73.0 kJ mol-1 .
Standard enthalpy of sublimation, ΔsubHΘ is the change in enthalpy when one mole of a solid substance sublimes at a constant temperature and under standard pressure (1bar).
The magnitude of the enthalpy change depends on the strength of the intermolecular interactions in the substance undergoing the phase transfomations. For example, the strong hydrogen bonds between water molecules hold them tightly in liquid phase. For an organic liquid, such as acetone, the intermolecular dipole-dipole interactions are significantly weaker. Thus, it requires less heat to vaporise 1 mol of acetone than it does to vaporize 1 mol of water. Table 6.1 gives values of standard enthalpy changes of fusion and vaporisation for some substances.
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Problem 6.7
A swimmer coming out from a pool is covered with a film of water weighing about 18g. How much heat must be supplied to evaporate this water at 298 K ? Calculate the internal energy of vaporisation at 100°C.
ΔvapHΘ for water at 373K = 40.66 kJ mol-1
Solution
We can represent the process of evaporation as evaporisation
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(c) Standard enthalpy of formation
The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation (also known as reference states) is called Standard Molar Enthalpy of Formation. Its symbol is ΔfHΘ, where the subscript ‘ f ’ indicates that one mole of the compound in question has been formed in its standard state from its elements in their most stable states of aggregation. The reference state of an element is its most stable state of aggregation at 25°C and 1 bar pressure. For example, the reference state of dihydrogen
is H2 gas and those of dioxygen, carbon and sulphur are O2 gas, C graphite and S is rhombic respectively. Some reactions with standard molar enthalpies of formation are given below.
H2 (g) + ½O2 (g) → H2 O(1);
ΔfHΘ = -285.8 kJ mol−1
C (graphite, s) + 2H2 (g)→CH4 (g);
ΔfHΘ = − 74.81kJmol−1
2C graphite,s + 3H2(g) + ½O2(g) → C2H5OH(1);
ΔfHΘ = − 277.7kJmol−1
It is important to understand that a standard molar enthalpy of formation, ΔfHΘ, is just a special case of ΔrHΘ, where one mole of a compound is formed from its constituent elements, as in the above three equations, where 1 mol of each, water, methane and ethanol is formed. In contrast, the enthalpy change for an exothermic reaction:
CaO(s)+CO2 (g)→CaCO3 (s);
ΔrHΘ = -178.3kJ mol−1
is not an enthalpy of formation of calcium carbonate, since calcium carbonate has been formed from other compounds, and not from
its constituent elements. Also, for the reaction given below, enthalpy change is not standard enthalpy of formation,
ΔfHΘ for HBr(g).
H2(g) + Br2( l) → 2HBr(g);
ΔrHΘ = -72.8 kJmol−1
Here two moles, instead of one mole of the product is formed from the elements, i.e.,
ΔrHΘ = 2ΔfHΘ.
Therefore, by dividing all coefficients in the balanced equation by 2, expression for enthalpy of formation of HBr (g) is written as
½H2(g) + ½Br2(1) → HBr(g );
ΔfHΘ = -36.4 kJ mol−1
Standard enthalpies of formation of some common substances are given in Table 6.2.
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By convention, standard enthalpy for formation, ΔfHΘ, of an element in reference state, i.e., its most stable state of aggregation is taken as zero.
Suppose, you are a chemical engineer and want to know how much heat is required to decompose calcium carbonate to lime and carbon dioxide, with all the substances in their standard state.
CaCO3(s) → CaO(s) + CO2 (g); ΔrHΘ = ?
Here, we can make use of standard enthalpy of formation and calculate the enthalpy change for the reaction. The following general equation can be used for the enthalpy change calculation.
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where a and b represent the coefficients of the products and reactants in the balanced equation. Let us apply the above equation for decomposition of calcium carbonate. Here, coefficients ‘a’ and ‘b’ are 1 each.
Therefore,
ΔrHΘ = ΔfHΘ[CaO(s)] + ΔfHΘ[CO2(g)] – ΔfHΘ[CaCO3(s)] = 1( -635.1 kJ mol-1) – 1( -393.5 kJ mol-1 ) -1( -1206.9 kJ mol-1 ) = 178.3 kJ mol-1
Thus, the decomposition of CaCO3 (s) is an endothermic process and you have to heat it for getting the desired products.
(d) Thermochemical equations
A balanced chemical equation together with the value of its ΔrH is called a thermochemical equation. We specify the physical state (alongwith allotropic state) of the substance in an equation. For example:
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O( l):
ΔrHΘ = -1367 kJ mol-1
The abov e equation describes the combustion of liquid ethanol at constant temperature and pressure. The negative sign of enthalpy change indicates that this is an exothermic reaction.
It would be necessary to remember the following conventions regarding thermochemical equations.
1. The coefficients in a balanced thermochemical equation refer to the number of moles (never molecules) of reactants and products involved in the reaction.
2. The numerical value of ΔrHΘ refers to the number of moles of substances specified by an equation. Standard enthalpy change ΔrHΘ will have units as kJ mol-1.
To illustrate the concept, let us consider the calculation of heat of reaction for the following reaction :
Fe2O3 s + 3H2 g→2Fe(s) + 3H2O(l) ,
From the Table (6.2) of standard enthalpy of formation (ΔfHΘ), we find :
ΔfHΘ(H2O, l) = -285.83 kJ mol-1;
ΔfHΘ(Fe2O3, s)= – 824.2 kJ mol-1;
Also ΔfHΘ (Fe2O3, s) = 0 and ΔfHΘ(H2 ,g ) = 0 as per convention
Then,
ΔrH1Θ= 3(-285.83 kJ mol-1) – 1(- 824.2 kJ mol-1) = (-857.5 + 824.2) kJ mol-1 = -33.3 kJ mol-1
Note that the coefficients used in these calculations are pure numbers, which are equal to the respective stoichiometric coefficients. The unit for ΔrHΘ is kJ mol-1, which means per mole of reaction. Once we balance the chemical equation in a particular way, as above, this defines the mole of reaction. If we had balanced the equation differently, for example,
(1/2)Fe2O3(s) + (3/2)H2(g)→Fe(s) + (3/2)H2O(1)
then this amount of reaction would be one mole of reaction and ΔrHΘ would be
ΔrH2Θ = (3/2)( -285.83 kJmol-1) – (1/2)(-824.2 kJmol-1) = (- 428.7 + 412.1) kJ mol-1 = -16.6 kJ mol-1 = 1/2ΔrH1Θ
It shows that enthalpy is an extensive quantity.
3. When a chemical equation is reversed, the value of ΔrHΘ is reversed in sign. For example
N2 (g) + 3H2 (g) → 2NH3 (g);
ΔrHΘ = -91.8kJ mol-1
2NH3 (g) → N2(g) + 3H2 (g);
ΔrHΘ = +91.8kJ mol-1
(e) Hess’s Law of Constant Heat Summation
We know that enthalpy is a state function, therefore the change in enthalpy is independent of the path between initial state (reactants) and final state (products). In other words, enthalpy change for a reaction is the same whether it occurs in one step or in a series of steps. This may be stated as follows in the form of Hess’s Law.
If a reaction takes place in several steps then its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.
Let us understand the importance of this law with the help of an example.
Consider the enthalpy change for the reaction
C (graphite,s) + 1/2 O2 (g) → CO (g);ΔrHΘ =?
Although CO(g) is the major product, some CO2 gas is always produced in this reaction. Therefore, we cannot measure enthalpy change for the above reaction directly. However, if we
can find some other reactions involving related species, it is possible to calculate the enthalpy change for the above reaction.
Let us consider the following reactions:
C (graphite,s) + O2 (g) → CO2 (g); ΔrHΘ = -393.5 kJmol−1 ————————————————(i)
CO (g) + 1/2 O2 (g) → CO2 (g);
ΔrHΘ = -283.0 kJmol−1 ———————————–(ii)
We can combine the above two reactions in such a way so as to obtain the desired reaction. To get one mole of CO(g) on the right,
we reverse equation (ii). In this, heat is absorbed instead of being released, so we change sign of ΔrHΘ value
CO2 (g) → CO (g) + 1/2 O2 (g);
ΔrHΘ =+283.0 kJmol−1 ———————–(iii)
Adding equation (i) and (iii), we get the desired equation,
C (graphite,s) + + 1/2 O2 (g) → CO (g);
for which ΔrHΘ = ( -393.5 + 283.0) = – 110.5 kJ mol−1
In general, if enthalpy of an overall reaction A→B along one route is ΔrH and ΔrH1, ΔrH2,ΔrH3….. representing enthalpies of reactions leading to same product, B along another route,then we have
ΔrH = ΔrH1 + ΔrH2 + ΔrH3 … —————————————————(6.16)
It can be represented as:
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6.5 ENTHALPIES FOR DIFFERENT TYPES OF REACTIONS
It is convenient to give name to enthalpies specifying the types of reactions.
(a) Standard enthalpy of combustion (symbol : ΔcHΘ )
Combustion reactions are exothermic in nature. These are important in industry, rocketry, and other walks of life. Standard enthalpy of combustion is defined as the enthalpy change per mole (or per unit amount) of a substance, when it undergoes combustion and all the reactants and products being in their standard states at the specified temperature.
Cooking gas in cylinders contains mostly butane (C4H10). During complete combustion of one mole of butane, 2658 kJ of heat is released. We can write the thermochemical reactions for this as:
C4H10 (g) + 13/2 O2 (g) → 4CO2(g) + 5H2O(1);
ΔcHΘ = -2658.0 kJ mol−1
Similarly, combustion of glucose gives out 2802.0 kJ/mol of heat, for which the overall equation is :
C6H12O6(g) + 6O2(g) → 6CO2 (g) + 6H2 O(1);
ΔcHΘ = -2802.0 kJ mol−1
Our body also generates energy from food by the same overall process as combustion, although the final products are produced after a series of complex bio-chemical reactions involving enzymes.
Problem 6.8
The combustion of one mole of benzene takes place at 298 K and 1 atm. After combustion, CO2(g) and H2O (1) are produced and 3267.0 kJ of heat is liberated. Calculate the standard enthalpy of formation, ΔfHΘ of benzene. Standard enthalpies of formation of CO2(g) and H2O(l) are -393.5 kJ mol−1 and – 285.83
kJ mol−1 respectively.
Solution
The formation reaction of benezene is given by :
6C (graphite) + 3H2 g → C6H6 (l) ;
ΔfHΘ = ? … —————————————–(i)
The enthalpy of combustion of 1 mol of benzene is :
C6H6 (l) + 15/2 O2 → 6CO2 (g) + 3H2O (l);
ΔcHΘ = -3267kJ mol−1 … ——————————–(ii)
The enthalpy of formation of 1 mol of CO2(g) :
C (graphite) + O2(g) → CO2 g ;
ΔfHΘ = -393.5kJ mol−1 … ———————————————(iii)
The enthalpy of formation of 1 mol of H2O(l) is :
H2 (g) + 1/2 O2 (g) → H2O (l);
ΔfHΘ = -285.83kJ mol−1 … ——————————————–(iv)
multiplying eqn. (iii) by 6 and eqn. (iv) by 3 we get:
6C (graphite) + 6O2 g → 6CO2 g ;
ΔfHΘ = -2361kJ mol−1
3H2 (g) + 3/2 O2 (g) → 3H2O (l);
ΔfHΘ = -857.49kJ mol−1
Summing up the above two equations :
6C (graphite) + 3H2 (g) + 15/2 O2 g → 6CO2 (g) + 3H2O(l);
ΔfHΘ = −3218.49 kJ mol-1 … ————————–(v )
Reversing equation (ii);
6CO2 (g) + 3H2O(l) → C6H6(l) + 15/2 O2;
ΔfHΘ = −3267.0 kJ mol-1 … ————————–(vi )
Adding equations (v) and (vi), we get
6C (graphite) + 3H2 (g) → C6H6(l);
ΔfHΘ = 48.51 kJ mol-1
(b) Enthalpy of atomization (symbol: ΔaHΘ )
Consider the following example of atomization of dihydrogen
H2(g) → 2H(g); ΔaHΘ = 435.0 kJ mol-1
You can see that H atoms are formed by breaking H—H bonds in dihydrogen. The enthalpy change in this process is known as
enthalpy of atomization, ΔaHΘ. It is the enthalpy change on breaking one mole of bonds completely to obtain atoms in the gas phase.
In case of diatomic molecules, like dihydrogen (given above), the enthalpy of atomization is also the bond dissociation enthalpy. The other examples of enthalpy of atomization can be
CH4(g) → C(g) + 4H(g); ΔaHΘ = 1665 kJ mol-1
Note that the products are only atoms of C and H in gaseous phase. Now see the following reaction:
Na(s) → Na(g) ; ΔaHΘ = 108.4 kJ mol-1
In this case, the enthalpy of atomization is same as the enthalpy of sublimation.
(c) Bond Enthalpy (symbol: ΔbondHΘ)
Chemical reactions involve the breaking and making of chemical bonds. Energy is required to break a bond and energy is released when a bond is formed. It is possible to relate heat of reaction to changes in energy associated with breaking and making of chemical bonds. With reference to the enthalpy changes associated with chemical bonds, two different terms are used in thermodynamics.
(i) Bond dissociation enthalpy
(ii) Mean bond enthalpy
Let us discuss these terms with reference to diatomic and polyatomic molecules.
Diatomic Molecules: Consider the following process in which the bonds in one mole of dihydrogen gas (H2) are broken:
H2(g) → 2H(g) ; ΔH-HHΘ = 435.0 kJ mol-1
The enthalpy change involved in this process is the bond dissociation enthalpy of H-H bond. The bond dissociation enthalpy is the change in enthalpy when one mole of covalent bonds of a gaseous covalent compound is broken to form products in the gas phase.
Note that it is the same as the enthalpy of atomization of dihydrogen. This is true for all diatomic molecules. For example:
Cl2(g) → 2Cl(g) ; ΔCl-ClHΘ = 242 kJ mol-1
OΘ(g) → 2O(g) ; ΔO=OHΘ = 428 kJ mol-1
In the case of polyatomic molecules, bond dissociation enthalpy is different for different bonds within the same molecule. Polyatomic Molecules: Let us now consider a polyatomic molecule like methane, CH4. The overall thermochemical equation for its atomization reaction is given below:
CH4 (g) → C(g) + 4H(g);
ΔaHΘ = 1665 kJ mol-1
In methane, all the four C — H bonds are identical in bond length and energy. However, the energies required to break the individual C — H bonds in each successive step differ :
CH4 (g)→CH3 (g)+H(g); ΔbondHΘ = +427 kJ mol−1
CH3 (g) →CH2 (g)+ H(g); ΔbondHΘ = +439kJ mol−1
CH2 (g)→ CH(g)+ H(g); ΔbondHΘ = +452kJ mol−1
CH(g)→C(g)+ H(g); ΔbondHΘ= +347kJ mol−1
Therefore,
CH4 (g) → C(g) + 4H(g); ΔaHΘ = 1665kJ mol−1
In such cases we use mean bond enthalpy of C — H bond.
For example in CH4, ΔC-HHΘ is calculated as:
ΔC-HHΘ = ¼(ΔaHΘ) = ¼ (1665kJ mol−1 )
= 416 kJ mol−1
We find that mean C—H bond enthalpy in methane is 416 kJ/mol. It has been found that mean C—H bond enthalpies differ slightly from compound to compound, as in CH3 CH2Cl,CH3NO2 , etc, but it does not differ in a great deal*. Using Hess’s law, bond enthalpies can be calculated. Bond enthalpy values of some single and multiple bonds are given in Table 6.3. The reaction enthalpies are very important quantities as these arise from the changes that accompany the breaking of old bonds and formation of the new bonds. We can predict enthalpy of a reaction in gas phase, if we know different bond enthalpies. The standard enthalpy of reaction, ΔrHΘ is related to bond enthalpies of the reactants and products in gas phase reactions as:
ΔrHΘ = Σbond enthalpiesreactants – Σbond enthalpiesproducts —————————————————————————–(6.17)**
This relationship is particularly more useful when the required values of ΔfHΘ are not available. The net enthalpy change of a reaction is the amount of energy required to break all the bonds in the reactant molecules minus the amount of energy required to break all the bonds in the product molecules. Remember that this relationship is approximate and is valid when all substances (reactants and products) in the reaction are in gaseous state.
| H | C | N | 0 | F | Si | P | S | Cl | Br | I | |
| 435.8 | 414 | 389 | 404 | 569 | 293 | 318 | 339 | 431 | 308 | 297 | H |
| 347 | 293 | 351 | 439 | 289 | 264 | 259 | 330 | 276 | 238 | C | |
| 159 | 201 | 272 |
–
|
209 |
–
|
201 | 243 |
–
|
N | ||
| 138 | 184 | 368 | 351 |
–
|
205 |
–
|
201 | O | |||
| 155 | 540 | 490 | 327 | 255 | 197 |
–
|
F | ||||
| 176 | 213 | 226 | 360 | 289 | 213 | Si | |||||
| 213 | 230 | 331 | 272 | 213 | P | ||||||
| 213 | 251 | 213 |
–
|
S | |||||||
| 243 | 218 | 209 | Cl | ||||||||
| 192 | 180 | Br | |||||||||
| 151 | I |
| N=N | 418 | C=C | 611 | O=O | 498 |
| N=N | 946 | C=C | 837 | ||
| C=N | 615 | C=O | 741 | ||
| C=N | 891 | C=O | 1070 |
| * Note that symbol used for bond dissociation enthalpy and mean bond enthalpy is the same.**If we use enthalpy of bond formation, (ΔfHbondΘ ), which is the enthalpy change when one mole of a particular type of bond is formed from gaseous atom, then ΔrHΘ = ΣΔfHbonds of productsΘ – ΣΔfHbonds of reactantsΘ |
(d ) Enthalpy of Solution (symbol : ΔsolHΘ )
Enthalpy of solution of a substance is the enthalpy change when one mole of it dissolves in a specified amount of solvent. The enthalpy of solution at infinite dilution is the enthalpy change observed on dissolving the substance in an infinite amount of solvent when the interactions between the ions (or solute
molecules) are negligible.
When an ionic compound dissolves in a solvent, the ions leave their ordered positions on the crystal lattice. These are now more free in solution. But solvation of these ions (hydration in case solvent is water) also occurs at the same time. This is shown diagrammatically, for an ionic compound, AB (s)
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The enthalpy of solution of AB(s), ΔsolHΘ, in water is, therefore, determined by the selective values of the lattice enthalpy, ΔlatticeHΘ and enthalpy of hydration of ions, ΔhydHΘ as
ΔsolHΘ = ΔlatticeHΘ + ΔhydHΘ
For most of the ionic compounds, ΔsolHΘ is positive and the dissociation process is endothermic. Therefore the solubility of most salts in water increases with rise of temperature. If the lattice enthalpy is very high, the dissolution of the compound may not take place at all. Why do many fluorides tend to be less soluble than the corresponding chlorides? Estimates of the magnitudes of enthalpy changes may be made by using tables of bond energies (enthalpies) and lattice energies (enthalpies).
Lattice Enthalpy
The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state.
Na+Cl–(s) → Na+(g) + Cl–(g) ;
ΔlatticeHΘ = +788 kJmol-1
Since it is impossible to determine lattice enthalpies directly by experiment, we use an indirect method where we construct an enthalpy diagram called a Born-Haber Cycle (Fig. 6.9).
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Fig 6.9 Enthalpy Diagram for Lattice enthalpy of NaCl
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Let us now calculate the lattice enthalpy of Na+Cl–(s) by following steps given below :
1. Na(s)→ Na(g) , sublimation of sodium metal, ΔsubHΘ = 108.4 kJ mol−1
2. Na(g)→Na+(g) + e−1(g) , the ionization of sodium atoms, ionization enthalpy
ΔiHΘ = 496 kJ mol−1
3. 1/2 Cl2 (g) → Cl(g), the dissociation of chlorine, the reaction enthalpy is half the bond dissociation enthalpy.
1/2 ΔbondHΘ = 121kJ mol−1
.
4. Cl(g) + e−1(g) → Cl–(g) electron gained by chlorine atoms. The electron gain enthalpy,
ΔegHΘ = -348.6 kJ mol−1 .
You have learnt about ionization enthalpy and electron gain enthalpy in Unit 3. In fact, these terms have been taken from thermodynamics. Earlier terms, ionization energy and electron affinity were in practice in place of the above terms (see the box for justification).
Ionization Energy and Electron Affinity
Ionization energy and electron affinity are defined at absolute zero. At any other temperature, heat capacities for the reactants and the products have to be taken into account. Enthalpies of reactions for
M(g) → M+(g) + e– (for ionization)
M(g) + e– → M–(g) (for electron gain)
at temperature, T is
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ΔsolHΘ = ΔlatticeHΘ + ΔhydHΘ
For one mole of NaCl(s),
lattice enthalpy = + 788 kJ mol-1
and ΔhydHΘ = – 784 kJ mol-1( from the literature)
ΔsolHΘ = + 788 kJ mol-1 – 784 kJ mol-1 = + 4 kJ mol-1
The dissolution of NaCl(s) is accompanied by very little heat change.
6.6 SPONTANEITY
The first law of thermodynamics tells us about the relationship between the heat absorbed and the work performed on or by a system. It puts no restrictions on the direction of heat flow. However, the flow of heat is unidirectional from higher temperature to lower temperature. In fact, all naturally occurring processes whether chemical or physical will tend to proceed spontaneously in one direction only. For example, a gas expanding to fill the available volume, burning carbon in dioxygen giving carbon dioxide.
But heat will not flow from colder body to warmer body on its own, the gas in a container will not spontaneously contract into one corner or carbon dioxide will not form carbon and dioxygen spontaneously. These and many other spontaneously occurring changes show unidirectional change. We may ask ‘what is the driving force of spontaneously occurring changes ? What determines the direction of a spontaneous change ? In this section, we shall establish some criterion for these processes whether these will take place or not.
Let us first understand what do we mean by spontaneous reaction or change ? You may think by your common observation that spontaneous reaction is one which occurs immediately when contact is made between the reactants. Take the case of combination of hydrogen and oxygen. These gases may be mixed at room temperature and left for many years without observing any perceptible change. Although the reaction is taking place between them, it is at an extremely slow rate. It is still called spontaneous reaction. So spontaneity means ‘having the potential to proceed without the assistance of external agency’. However, it does not tell about the rate of the reaction or process. Another aspect of spontaneous reaction or process, as we see is that these cannot reverse their direction on their own. We may summarise it as follows:
A spontaneous process is an irreversible process and may only be reversed by some external agency.
(a) Is decrease in enthalpy a criterion for spontaneity ?
If we examine the phenomenon like flow of water down hill or fall of a stone on to the ground, we find that there is a net decrease in potential energy in the direction of change. By analogy, we may be tempted to state that a chemical reaction is spontaneous in a given direction, because decrease in energy has taken place, as in the case of exothermic reactions. For example:
1/2 N2(g) + 3/2 H2(g) = NH3(g) ; ΔrHΘ = – 46.1 kJ mol-1
1/2 H2(g) + 1/2 Cl2(g) = HCl (g) ; ΔrHΘ = – 92.32 kJ mol-1
H2(g) + 1/2 O2(g) → H2O(l) ; ΔrHΘ = -285.8 kJ mol-1
The decrease in enthalpy in passing from reactants to products may be shown for any exothermic reaction on an enthalpy diagram as shown in Fig. 6.10(a).
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Thus, the postulate that driving force for a chemical reaction may be due to decrease in energy sounds ‘reasonable’ as the basis of evidence so far !
Now let us examine the following reactions:
1/2 N2(g) + O2(g) → NO2(g);
ΔrHΘ= +33.2 kJ mol-1
C(graphite, s) + 2 S(l) → CS2(l);
ΔrHΘ = +128.5 kJ mol-1
These reactions though endothermic, are spontaneous. The increase in enthalpy may be represented on an enthalpy diagram as shown in Fig. 6.10(b).
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it becomes obvious that while decrease in enthalpy may be a contributory factor for spontaneity, but it is not true for all cases.
( b ) Entropy and Spontaneity
Then, what drives the spontaneous process in a given direction ? Let us examine such a case in which ΔH = 0 i.e., there is no change in enthalpy, but still the process is spontaneous.
Let us consider diffusion of two gases into each other in a closed container which is The two gases, say, gas A and gas B are represented by black dots and white dots respectively and separated by a movable partition [Fig. 6.11 (a)]. When the partition is withdrawn [Fig.6.11( b)], the gases begin to diffuse into each other and after a period of time, diffusion will be complete.
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Let us examine the process. Before partition, if we were to pick up the gas molecules from left container, we would be sure that these will be molecules of gas A and similarly if we were to pick up the gas molecules from right container, we would be sure that these will be molecules of gas B. But, if we were to pick up molecules from container when partition is removed, we are not sure whether the molecules picked are of gas A or gas B. We say that the system has become less predictable or more chaotic.
We may now formulate another postulate: in an isolated system, there is always a tendency for the systems’ energy to become more disordered or chaotic and this could be a criterion for spontaneous change !
this point, we introduce another thermodynamic function, entropy denoted as S. The above mentioned disorder is the manifestation of entropy. To form a mental picture, one can think of entropy as a measure of the degree of randomness or disorder in the system. The greater the disorder in an isolated system, the higher is the entropy. As far as a chemical reaction is concerned, this entropy change can be attributed to rearrangement of atoms or ions from one pattern in the eactants to another (in the products). If the structure of the products is very much disordered than that of the reactants, there will be a resultant increase in entropy. The change in entropy accompanying a chemical reaction may be estimated qualitatively by a consideration of the structures of the species taking part in the reaction. Decrease of regularity in structure would mean increase in entropy. For a given substance, the crystalline solid state is the state of lowest entropy (most ordered), The gaseous state is state of highest entropy.
Now let us try to quantify entropy. One way to calculate the degree of disorder or chaotic distribution of energy among molecules would be through statistical method which is beyond the scope of this treatment. Other way would be to relate this process to the heat involved in a process which would make entropy a
thermodynamic concept. Entropy, like any other thermodynamic property such as internal energy U and enthalpy H is a state function and ΔS is independent of path.
Whenever heat is added to the system, it increases molecular motions causing increased randomness in the system. Thus heat (q) has randomising influence on the system. Can we then equate ΔS with q ? Wait ! Experience suggests us that the distribution of heat also depends on the temperature at which heat is added to the system. A system at higher temperature has greater randomness in it than one at lower temperature. Thus, temperature is the measure of average chaotic motion of particles in the system. Heat added to a system at lower temperature causes greater randomness than when the same quantity of heat is added to it at higher temperature. This suggests that the entropy change is inversely proportional to the temperature. ΔS is related with q and T for a reversible reaction as :
ΔS = qrev/T ————————————————————-(6.18)
The total entropy change ( ΔStotal) for the system and surroundings of a spontaneous process is given by surrtotal > 0 ——————————————————————–(6.19)
When a system is in equilibrium, the entropy is maximum, and the change in entropy, ΔS = 0.
We can say that entropy for a spontaneous process increases till it reaches maximum and at equilibrium the change in entropy is zero. Since entropy is a state property, we can calculate the change in entropy of a reversible process by ΔSsys = qsys,rev /T
We find that both for reversible and irreversible expansion for an ideal gas, under isothermal conditions, ΔU = 0, but ΔStotal i.e., ΔSsys + ΔSsurr is not zero for irreversible process. Thus, ΔU does not discriminate between reversible and irreversible process, whereas ΔS does.
Problem 6.9
Predict in which of the following, entropy increases/decreases :
(i) A liquid crystallizes into a solid.
(ii) Temperature of a crystalline solid is raised from 0 K to 115 K.
(iii) 2NaHCO3 (s) → Na2CO3 (s) + CO2 (g) + H2O (g)
(iv) H2 g → 2H g
Solution
(i) After freezing, the molecules attain an ordered state and therefore, entropy decreases.
(ii) At 0 K, the contituent particles are static and entropy is minimum. If temperature is raised to 115 K, these begin to move and oscillate about their equilibrium positions in the lattice and system becomes more disordered, therefore entropy increases.
(iii) Reactant, NaHCO3 is a solid and it has low entropy. Among products there are one solid and two gases. Therefore, the products represent a condition of higher entropy.
(iv) Here one molecule gives two atoms i.e., number of particles increases leading to more disordered state. Two moles of H atoms have higher entropy than one mole of dihydrogen molecule.
Problem 6.10
For oxidation of iron,
4Fe (s) +3O2 (g) → 2Fe2O3 (s)
entropy change is – 549.4 JK-1mol-1at 298 K. Inspite of negative entropy change of this reaction, why is the reaction spontaneous?
(ΔrHΘ for this reaction is -1648 103 J mol-1)
Solution
One decides the spontaneity of a reaction by considering ΔStotal (ΔSsys + ΔSsurr . For calculating ΔSsurr, we have to consider the heat absorbed by the surroundings which is equal to -ΔrHΘ. At temperature T, entropy change of the surroundings is
ΔSsurr = -(ΔrHΘ/T)(at constant pressure) = (-1648 x 103 Jmol-1 )/298 K = 5530 JK-1mol-1
Thus, total entropy change for this reaction
ΔrStotal = 5530JK-1mol-1 + (-549.4JK-1mol-1)=4980.6JK-1mol-1
This shows that the above reaction is spontaneous.
(c) Gibbs energy and spontaneity
We have seen that for a system, it is the total entropy change, ΔStotal which decides the spontaneity of the process. But most of the chemical reactions fall into the category of either closed systems or open systems. Therefore, for most of the chemical reactions there are changes in both enthalpy and entropy. It is clear from the discussion in previous sections that neither decrease in enthalpy nor increase in entropy alone can determine the direction of spontaneous change for these systems.
For this purpose, we define a new thermodynamic function the Gibbs energy or Gibbs function, G, as G = H – TS ——————————————————————-(6.20)
Gibbs function, G is an extensive property and a state function.
The change in Gibbs energy for the system, ΔGsys can be written as
ΔGsys = ΔHsys − T ΔGsys −SsysΔT
At constant temperature, ΔT = 0
∴ΔGsys = ΔHsys − TΔSsys
Usually the subscript ‘system’ is dropped and we simply write this equation as
ΔG = ΔH – TΔS ——————————————————————-(6.21)
Thus, Gibbs energy change = enthalpy change – temperature x entropy change, and is referred to as the Gibbs equation, one of the most important equations in chemistry. Here, we have considered both terms together for spontaneity: energy (in terms of ΔH) and entropy (ΔS, a measure of disorder) as indicated earlier. Dimensionally if we analyse, we find that ΔG has units of energy because, both ΔH and the TΔS are energy terms, since TΔS = (K) (J/K) = J.
Now let us consider how G is related to reaction spontaneity.
We know,
ΔStotal = ΔSsys + ΔSsurr
If the system is in thermal equilibrium with the surrounding, then the temperature of the surrounding is same as that of the system. Also, increase in enthalpy of the surrounding is equal to decrease in the enthalpy of the system.
Therefore, entropy change of surroundings,
ΔSsurr = ΔHsurr/T = -ΔHsurr/T
ΔStotal =− ΔSsys + (-ΔHsys/T)
Rearranging the above equation:
TΔStotal = TΔSsys – ΔHsys
For spontanious process, ΔStotal > 0 , so
TΔSsys – ΔHsys > 0
⇒ −(ΔHsys − TΔSsys ) > 0
Using equation 6.21, the above equation can be written as
−ΔG > 0
ΔG = ΔH − T ΔS < 0 ——————————————-(6.22)
ΔHsys is the enthalpy change of a reaction, TΔSsys is the energy which is not available to do useful work. So ΔG is the net energy available to do useful work and is thus a measure of the ‘free energy’. For this reason, it is also known as the free energy of the reaction.
ΔG gives a criteria for spontaneity at constant pressure and temperature.
(i) If ΔG is negative (< 0), the process is spontaneous. (ii) If ΔG is positive (> 0), the process is non spontaneous.
Note : If a reaction has a positive enthalpy change and positive entropy change, it can be spontaneous when TΔS is large enough to
outweigh ΔH. This can happen in two ways;
(a) The positive entropy change of the system can be ‘small’ in which case T must be large.
(b) The positive entropy change of the system can be ‘large’, in which case T may be small. The former is one of the reasons why reactions are often carried out at high temperature. Table 6.4 summarises the effect of temperature on spontaneity of reactions.
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6.7 GIBBS ENERGY CHANGE AND EQUILIBRIUM
We have seen how a knowledge of the sign and magnitude of the free energy change of a chemical reaction allows:
(i) Prediction of the spontaneity of the chemical reaction.
(ii) Prediction of the useful work that could be extracted from it.
So far we have considered free energy changes in irreversible reactions. Let us now examine the free energy changes in reversible reactions.
‘Reversible’ under strict thermodynamic sense is a special way of carrying out a process such that system is at all times in perfect equilibrium with its surroundings. When applied to a chemical reaction, the term ‘reversible’ indicates that a given reaction can proceed in either direction simultaneously, so that a dynamic equilibrium is set up. This means that the reactions in both the directions should proceed with a decrease in free energy,
which seems impossible. It is possible only if at equilibrium the free energy of the system is minimum. If it is not, the system would
spontaneously change to configuration of lower free energy.
So, the criterion for equilibrium
A + B = C + D ; is
ΔrG = 0
Gibbs energy for a reaction in which all reactants and products are in standard state, ΔrG0 is related to the equilibrium constant of the reaction as follows:
0 = ΔrGΘ + RT ln K
or ΔrGΘ = – RT ln K
or ΔrGΘ = – 2.303 RT log K ——————————————————–(6.23)
We also know that
ΔrGΘ = ΔrHΘ – TΔrSΘ = -RT ln K —————————————————–(6.24)
For strongly endothermic reactions, the value of ΔrHΘ may be large and positive. In such a case, value of K will be much smaller than 1 and the reaction is unlikely to form much product. In case of exothermic reactions, ΔrHΘ is large and negative, and ΔrGΘ is likely to be large and negative too. In such cases, K will be much larger than 1. We may expect strongly exothermic reactions to have a large K, and hence can go to near completion. ΔrGΘ also depends upon ΔrSΘ, if the changes in the entropy of reaction is also taken into account, the value of K or extent of chemical reaction will also be affected, depending upon whether ΔrSΘ is positive or negative.
* The term low temperature and high temperature are relative. For a particular reaction, high temperature could even mean room temperature.
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Using equation (6.24),
(i) It is possible to obtain an estimate of ΔGTheta; from the measurement of ΔHTheta; and ΔSTheta;, and then calculate K at any temperature for economic yields of the products.
(ii) If K is measured directly in the laboratory, value of ΔGTheta; at any other temperature can be calculated.
Problem 6.11
Calculate ΔrGTheta; for conversion of oxygen to ozone, 3/2 O2(g) → O3(g) at 298 K. if Kp for this conversion is 2.47 x 10–29 .
Solution
We know ΔrGTheta; = – 2.303 RT log Kp and R = 8.314 JK-1mol-1
Therefore, ΔrGTheta; = – 2.303 (8.314 JK-1mol-1) x (298 K) (log 2.47 10-29) = 163000 J mol-1 = 163 kJ mol-1.
Problem 6.12
Find out the value of equilibrium constant for the following reaction at 298 K.
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Problem 6.13
At 60°C, dinitrogen tetroxide is fifty percent dissociated. Calculate the standard free energy change at this temperature and at one atmosphere.
Solution
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SUMMARY
Thermodynamics deals with energy changes in chemical or physical processes and enables us to study these changes quantitatively and to make useful predictions. For these purposes, we divide the universe into the system and the surroundings. Chemical or physical processes lead to evolution or absorption of heat (q), part of which may be converted into work (w). These quantities are related through the first law of thermodynamics via ΔU = q + w. ΔU, change in internal energy, depends on initial and final states only and is a state function, whereas q and w depend on the path and are not the state functions. We follow sign conventions of q and w by giving the positive sign to these quantities when these are added to the system. We can measure the transfer of heat from one system to another which causes the change in temperature. The magnitude of rise in temperature depends on the heat capacity (C) of a substance. Therefore, heat absorbed or evolved is q = CΔT. Work can be measured by w = -pexΔV, in case of expansion of gases. Under reversible process, we can put pex = p for infinitesimal changes in the volume making wrev = – p dV. In this condition, we can use gas equation, pV = nRT.
At constant volume, w = 0, then ΔU = qV , heat transfer at constant volume. But in study of chemical reactions, we usually have constant pressure. We define another state function enthalpy. Enthalpy change, ΔH = ΔU + ΔngRT, can be found directly from
the heat changes at constant pressure, ΔH = qp.
There are varieties of enthalpy changes. Changes of phase such as melting, vaporization and sublimation usually occur at constant temperature and can be characterized by enthalpy changes which are always positive. Enthalpy of formation, combustion and other enthalpy changes can be calculated using Hess’s law. Enthalpy
change for chemical reactions can be determined by
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First law of thermodynamics does not guide us about the direction of chemical reactions i.e., what is the driving force of a chemica reaction. For isolated systems, ΔU = 0. We define another state function, S, entropy for this purpose. Entropy is a measure of disorder or randomness. For a spontaneous change, total entropy change is positive. Therefore, for an isolated system, ΔU = 0, ΔS > 0, so entropy change distinguishes a spontaneous change, while energy change does not. Entropy changes can be measured by the equation ΔS = qrev/T for a reversible process. qrev/T is independent of path. Chemical reactions are generally carried at constant pressure, so we define another state function Gibbs energy, G, which is related to entropy and enthalpy changes of the system by the equation:
ΔrG = ΔrH – T ΔrS
For a spontaneous change, ΔGsys < 0 and at equilibrium, ΔGsys = 0.
Standard Gibbs energy change is related to equilibrium constant by
ΔrGΘ = – RT ln K.
K can be calculated from this equation, if we know ΔrGTheta; which can be found from ΔrGΘ = ΔrHΘ − TΔrSΘ . Temperature is an important factor in the equation. Many reactions which are non-spontaneous at low temperature, are made spontaneous at high temperature for systems having positive entropy of reaction.
EXERCISES
6.1 Choose the correct answer. A thermodynamic state function is a
quantity
(i) used to determine heat changes
(ii) whose value is independent of path
(iii) used to determine pressure volume work
(iv) whose value depends on temperature only.
6.2 For the process to occur under adiabatic conditions, the correct
condition is:
(i) ΔT = 0
(ii) Δp = 0
(iii) q = 0
(iv) w = 0
6.3 The enthalpies of all elements in their standard states are:
(i) unity
(ii) zero
(iii) < 0
(iv) different for each element
6.4 ΔU0of combustion of methane is – X kJ mol-1. The value of ΔHΘ is
(i) = ΔUΘ
(ii) > ΔUΘ
(iii) < ΔUΘ
(iv) = 0
6.5 The enthalpy of combustion of methane, graphite and dihydrogen at 298 K are, -890.3 kJ mol-1 -393.5 kJ mol-1, and -285.8 kJ mol-1 respectively. Enthalpy of formation of CH4(g) will be
(i) -74.8 kJ mol-1 (ii) -52.27 kJ mol-1
(iii) +74.8 kJ mol-1 (iv) +52.26 kJ mol-1.
6.6 A reaction, A + B → C + D + q is found to have a positive entropy change. The reaction will be
(i) possible at high temperature
(ii) possible only at low temperature
(iii) not possible at any temperature
(v) possible at any temperature
6.7 In a process, 701 J of heat is absorbed by a system and 394 J of
work is done by the system. What is the change in internal energy
for the process?
6.8 The reaction of cyanamide, NH2CN (s), with dioxygen was carried out in a bomb calorimeter, and ΔU was found to be -742.7 kJ mol-1 at 298 K. Calculate enthalpy change for the reaction at 298 K.
NH2CN(g) + 3/2 O2(g) → N2(g) + CO2(g) + H2O(l)
6.9 Calculate the number of kJ of heat necessary to raise the temperature of 60.0 g of aluminium from 35°C to 55°C. Molar heat capacity of Al is 24 J mol-1 K-1.
6.10 Calculate the enthalpy change on freezing of 1.0 mol of water
at10.0°C to ice at -10.0°C. ΔfusH = 6.03 kJ mol-1 at 0°C.
Cp [H2O(l)] = 75.3 J mol-1 K-1
Cp [H2O(s)] = 36.8 J mol-1 K-1
6.11 Enthalpy of combustion of carbon to CO2 is -393.5 kJ mol-1. Calculate the heat released upon formation of 35.2 g of CO2 from carbon and dioxygen gas.
6.12 Enthalpies of formation of CO(g), CO2(g), N2O(g) and N2O4(g) are -110, – 393, 81 and 9.7 kJ mol-1 respectively. Find the value of ΔrH for the reaction:
N2O4(g) + 3CO(g) → N2O(g) + 3CO2(g)
6.13 Given N2(g) + 3H2(g) → 2NH3(g) ; ΔrHTheta; = -92.4 kJ mol-1
What is the standard enthalpy of formation of NH3 gas?
6.14 Calculate the standard enthalpy of formation of CH3OH(l) from the following data:
CH3OH (l) + 3/2 O2(g) → CO2(g) + 2H2O(l) ; ΔrHTheta; = -726 kJ mol-1
C(graphite) + O2(g) → CO2(g) ; ΔcHTheta; = -393 kJ mol-1
H2(g) + 1/2 O2(g) → H2O(l) ; ΔfHTheta; = -286 kJ mol-1.
6.15 Calculate the enthalpy change for the process CCl4(g) → C(g) + 4 Cl(g) and calculate bond enthalpy of C – Cl in CCl4(g).
ΔvapHΘ(CCl4) = 30.5 kJ mol-1.
ΔfHΘ (CCl4) = -135.5 kJ mol-1.
ΔaHΘ (C) = 715.0 kJ mol-1 , where ΔaH0 is enthalpy of atomisation ΔaHΘ (Cl2) = 242 kJ mol-1
6.16 For an isolated system, ΔU = 0, what will be ΔS ?
6.17 For the reaction at 298 K,
2A + B → C
ΔH = 400 kJ mol-1 and ΔS = 0.2 kJ K-1 mol-1
At what temperature will the reaction become spontaneous
considering ΔH and ΔS to be constant over the temperature range.
6.18 For the reaction,
2 Cl(g) → Cl2(g), what are the signs of ΔH and ΔS ?
6.19 For the reaction
2 A(g) + B(g) → 2D(g)
ΔUΘ = -10.5 kJ and ΔSΘ = -44.1 JK-1.
Calculate ΔG0 for the reaction, and predict whether the reaction
may occur spontaneously.
6.20 The equilibrium constant for a reaction is 10. What will be the value of ΔGΘ ? R = 8.314 JK-1 mol-1, T = 300 K.
6.21 Comment on the thermodynamic stability of NO(g), given
1/2 N2(g) + 1/2 O2(g) → NO(g) ; ΔrHΘ = 90 kJ mol-1
NO(g) + 1/2 O2(g) → NO2(g) : ΔrHΘ = -74 kJ mol-1
6.22 Calculate the entropy change in surroundings when 1.00 mol of H2O(l) is formed under standard conditions. ΔfHTheta; = -286 kJ mol-1.
Answer to Some Selected Problems
6.1 (ii)
6.2 (iii)
6.3 (ii)
6.4 (iii)
6.5 (i)
6.6 (iv)
6.7 q = + 701 J
w = – 394 J, since work is done by the system
ΔU = 307 J
6.8 –741.5 kJ
6.9 1.09 kJ
6.10 ΔH = –6.415 kJ mol–1
6.11 –315 kJ
6.12 ΔrH = –778 kJ
6.13 – 46.2 kJ mol–1
6.14 –239 kJ mol–1
6.15 327 kJ mol–1
6.16 ΔS > 0
6.17 2000 K
6.18 ΔH is negative (bond energy is released) and ΔS is negative (There is less randomness among the molecules than among the atoms)
6.19 0.164 kJ, the reaction is not spontaneous.
6.20 –5.744 kJ mol–1
6.21 NO(g) is unstable, but NO2(g) is formed.
6.22 qsurr = + 286 kJ mol–1 ΔSsurr = 959.73 J K–1
I. Multiple Choice Questions (Type-I)
1. Thermodynamics is not concerned about______.
(i) energy changes involved in a chemical reaction.
(ii) the extent to which a chemical reaction proceeds.
(iii) the rate at which a reaction proceeds.
(iv) the feasibility of a chemical reaction.
2. Which of the following statements is correct?
(i) The presence of reacting species in a covered beaker is an example of open system.
(ii) There is an exchange of energy as well as matter between the system and the surroundings in a closed system.
(iii) The presence of reactants in a closed vessel made up of copper is an example of a closed system.
(iv) The presence of reactants in a thermos flask or any other closed insulated vessel is an example of a closed system.
3. The state of a gas can be described by quoting the relationship between___.
(i) pressure, volume, temperature
(ii) temperature, amount, pressure
(iii) amount, volume, temperature
(iv) pressure, volume, temperature, amount
4. The volume of gas is reduced to half from its original volume. The specific heat will be ______.
(i) reduce to half
(ii) be doubled
(iii) remain constant
(iv) increase four times
5. During complete combustion of one mole of butane, 2658 kJ of heat is released. The thermochemical reaction for above change is
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6. ΔfUΘ of formation of CH4(g) at certain temperature is –393 kJ mol–1. The value of ΔfHΘ is
(i) zero
(ii) < ΔfUΘ
(iii) > ΔfUΘ
(iv) equal to ΔfUΘ
7. In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following.
(i) q = 0, ΔT ≠ 0, w = 0
(ii) q ≠ 0, ΔT = 0, w = 0
(iii) q = 0, ΔT = 0, w = 0
(iv) q = 0, ΔT < 0, w ≠ 0
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9. The entropy change can be calculated by using the expression ΔS = qrev/T. When water freezes in a glass beaker, choose the correct statement amongst the following :
(i) ΔS (system) decreases but ΔS (surroundings) remains the same.
(ii) ΔS (system) increases but ΔS (surroundings) decreases.
(iii) ΔS (system) decreases but ΔS (surroundings) increases.
(iv) ΔS (system) decreases and ΔS (surroundings) also decreases.
10. On the basis of thermochemical equations (a), (b) and (c), find out which of the algebric relationships given in options (i) to (iv) is correct.
(a) C(graphite) + O2 (g) → CO2 (g) ; ΔrH = x kJ mol–1
(b) C(graphite) + 12 O2 (g) → CO (g) ; ΔrH = y kJ mol–1
(c) CO(g) + 12 O2 (g) → CO2 (g) ; ΔrH = z kJ mol–1
(i) z = x + y
(ii) x = y – z
(iii) x = y + z
(iv) y = 2z – x
11. Consider the reactions given below. On the basis of these reactions find out which of the algebric relations given in options (i) to (iv) is correct?
(a) C(g) + 4H(g) → CH4 (g); ΔrH = x kJ mol–1
(b) C(graphite,s) + 2H2 (g) → CH4 (g); ΔrH = y kJ mol–1
(i) x = y
(ii) x = 2y
(iii) x > y
(iv) x < y
12. The enthalpies of elements in their standard states are taken as zero. The enthalpy of formation of a compound
(i) is always negative
(ii) is always positive
(iii) may be positive or negative
(iv) is never negative
13. Enthalpy of sublimation of a substance is equal to
(i) enthalpy of fusion + enthalpy of vapourisation
(ii) enthalpy of fusion
(iii) enthalpy of vapourisation
(iv) twice the enthalpy of vapourisation
14. Which of the following is not correct?
(i) ΔG is zero for a reversible reaction
(ii) ΔG is positive for a spontaneous reaction
(iii)ΔG is negative for a spontaneous reaction
(iv) ΔG is positive for a non-spontaneous reaction
II. Multiple Choice Questions (Type-II)
In the following questions two or more options may be correct.
15. Thermodynamics mainly deals with
(i) interrelation of various forms of energy and their transformation from one form to another.
(ii) energy changes in the processes which depend only on initial and final states of the microscopic systems containing a few molecules.
(iii) how and at what rate these energy transformations are carried out.
(iv) the system in equilibrium state or moving from one equilibrium state to another quilibrium state.
16. In an exothermic reaction, heat is evolved, and system loses heat to the surrounding. For such system
(i) qp will be negative
(ii) ΔrH will be negative
(iii) qp will be positive
(iv) ΔrH will be positive
17. The spontaneity means, having the potential to proceed without the assistance of external agency. The processes which occur spontaneously are
(i) flow of heat from colder to warmer body.
(ii) gas in a container contracting into one corner.
(iii) gas expanding to fill the available volume.
(iv) burning carbon in oxygen to give carbon dioxide.
18. For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression w = – nRT ln Vf/Vi
A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and at 600 K respectively. Choose the correct option.
(i) Work done at 600 K is 20 times the work done at 300 K.
(ii) Work done at 300 K is twice the work done at 600 K.
(iii) Work done at 600 K is twice the work done at 300 K.
(iv) ΔU = 0 in both cases.
19. Consider the following reaction between zinc and oxygen and choose the correct options out of the options given below :
2Zn (s) + O2 (g) → 2ZnO (s); ΔH = – 693.8 kJ mol–1
(i) The enthalpy of two moles of ZnO is less than the total enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ.
(ii) The enthalpy of two moles of ZnO is more than the total enthalpy of two moles of Zn and one mole of oxygen by 693.8 kJ.
(iii) 693.8 kJ mol–1 energy is evolved in the reaction.
(iv) 693.8 kJ mol–1 energy is absorbed in the reaction.
III. Short Answer Type
20. 18.0 g of water completely vapourises at 100°C and 1 bar pressure and the enthalpy change in the process is 40.79 kJ mol–1. What will be the enthalpy change for vapourising two moles of water under the same conditions? What is the standard enthalphy of vapourisation for water?
21. One mole of acetone requires less heat to vapourise than 1 mol of water. Which of the two liquids has higher enthalpy of vapourisation?
22. Standard molar enthalpy of formation, ΔfHΘ is just a special case of enthalpy of reaction, ΔrHΘ. Is the ΔrHΘ for the following reaction same as ΔfHΘ? Give reason for your answer.
CaO(s) + CO2(g) → CaCO3(s); ΔfHΘ = –178.3 kJ mol–1
23. The value of ΔfHΘ for NH3 is –91.8 kJ mol–1. Calculate enthalpy change for the following reaction :
2NH3(g) → N2(g) + 3H2(g)
24. Enthalpy is an extensive property. In general, if enthalpy of an overall reaction A→B along one route is ΔrH and ΔrH1, ΔrH2, ΔrH3 ….. represent enthalpies of intermediate reactions leading to product B. What will be the relation between ΔrH for overall reaction and ΔrH1 , ΔrH2 ….. etc. for intermediate reactions.
25. The enthalpy of atomisation for the reaction CH4(g)→ C(g) + 4H(g) is 1665 kJ mol–1. What is the bond energy of C–H bond?
26. Use the following data to calculate ΔlatticeHΘ for NaBr. ΔsubHΘ for sodium metal = 108.4 kJ mol–1 Ionization enthalpy of sodium = 496 kJ mol–1 Electron gain enthalpy of bromine = – 325 kJ mol–1 Bond dissociation enthalpy of bromine = 192 kJ mol–1 ΔfHΘ for NaBr (s) = – 360.1 kJ mol–1
27. Given that ΔH = 0 for mixing of two gases. Explain whether the diffusion of these gases into each other in a closed container is a spontaneous process or not?
28. Heat has randomising influence on a system and temperature is the measure of average chaotic motion of particles in the system. Write the mathematical relation which relates these three parameters.
29. Increase in enthalpy of the surroundings is equal to decrease in enthalpy of the system. Will the temperature of system and surroundings be the same when they are in thermal equilibrium?
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32. The standard molar entropy of H2O (l) is 70 J K–1 mol–1. Will the standard molar entropy of H2O(s) be more, or less than 70 J K–1 mol–1?
33. Identify the state functions and path functions out of the following : enthalpy, entropy, heat, temperature, work, free energy.
34. The molar enthalpy of vapourisation of acetone is less than that of water. Why?
35. Which quantity out of ΔrG and ΔrGΘ will be zero at equilibrium?
36. Predict the change in internal energy for an isolated system at constant volume.
37. Although heat is a path function but heat absorbed by the system under certain specific conditions is independent of path. What are those conditions? Explain.
38. Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when 1 litre of ideal gas expands isothermally into vacuum until its total volume is 5 litre?
39. Heat capacity (Cp ) is an extensive property but specific heat (c) is an intensive propertyp. What will be the relation between Cp and c for 1 mol of water?
40. The difference between Cp and CV can be derived using the empirical relation H = U + pV. Calculate the difference between Cp and CV for 10 moles of an ideal gas.
41. If the combustion of 1g of graphite produces 20.7 kJ of heat, what will be molar enthalpy change? Give the significance of sign also.
42. The net enthalpy change of a reaction is the amount of energy required to break all the bonds in reactant molecules minus amount of energy required to form all the bonds in the product molecules. What will be the enthalpy change for the following reaction.
H2(g) + Br2(g) → 2HBr(g)
Given that Bond energy of H2, Br2 and HBr is 435 kJ mol–1, 192 kJ mol–1 and 368 kJ mol–1 respectively.
43. The enthalpy of vapourisation of CCl4 is 30.5 kJ mol–1. Calculate the heat required for the vapourisation of 284 g of CCl4 at constant pressure. (Molar mass of CCl4 = 154 g mol–1).
44. The enthalpy of reaction for the reaction :
2H2(g) + O2(g) → 2H2O(l) is ΔrHΘ = – 572 kJ mol–1.
What will be standard enthalpy of formation of H2O (l) ?
45. What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, pext in a single step as shown in Fig. 6.2. Explain graphically.
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46. How will you calculate work done on an ideal gas in a compression, when change in pressure is carried out in infinite steps?
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49. 1.0 mol of a monoatomic ideal gas is expanded from state (1) to state (2) as shown in Fig. 6.4. Calculate the work done for the expansion of gas from state (1) to state (2) at 298 K.
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50. An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L inone step. Calculate the amount of work done by the gas. If the same expansion were carried outreversibly, will the work done be higher or lower than the earlier case? (Given that 1 L bar = 100 J)
IV. Matching Type
In the following questions more than one correlation is possible between options of both columns.
51. Match the following :
| A | B | ||
| (i) | Adiabatic process | (a) | Heat |
| (ii) | Isolated system | (b) | At constant volume |
| (iii) | Isothermal change | (c) | First law of thermodynamics |
| (iv) | Path function | (d) | No exchange of energy and matter |
| (v) | State function | (e) | No transfer of heat |
| (vi) | ΔU = q | (f) | Constant temperature |
| (vii) | Law of conservation of energy | (g) | Internal energy |
| (viii) | Reversible process | (h) | pext = 0 |
| (ix) | Free expansion | (i) | At constant pressure |
| (x) | ΔH = q | (j) | Infinitely slow process which proceeds through a series of equilibrium states. |
| (xi) | Intensive property | (k) | Entropy |
| (xii) | Extensive property | (l) | Pressure |
| (m) | Specific heat |
52. Match the following processes with entropy change:
| Reaction | Entropy change | ||
| (i) | A liquid vapourises | (a) | ΔS = 0 |
| (ii) | Reaction is non-spontaneous at all temperatures and ΔH is positive | (b) | ΔS = positive |
| (iii) | Reversible expansion of an ideal gas | (c) | ΔS = negative |
53. Match the following parameters with description for spontaneity :
| Δ (Parameters) | Description | |||||
| ΔrHΘ | ΔrSΘ | ΔrGΘ | ||||
| (i) | + | – | + | (a) | Non-spontaneous at hightemperature. | |
| (ii) | – | – | + at high T | (b) | Spontaneous at all temperatures | |
| (iii) | – | + | – | (c) | Non-spontaneous at all temperatures | |
54. Match the following :
| (i) | Entropy of vapourisation | (a) | decreases |
| (ii) | K for spontaneous process | (b) | is always positive |
| (iii) | Crystalline solid state | (c) | lowest entropy |
| (iv) | ΔU in adiabatic expansion of ideal gas | (d) | ΔHvap/Tb |
V. Assertion and Reason Type
In the following questions a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct option out of the choices given below each question.
55. Assertion (A): Combustion of all organic compounds is an exothermic reaction.
Reason (R) : The enthalpies of all elements in their standard state are zero.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true but R is not the correct explanation of A.
(iii) A is true but R is false.
(iv) A is false but R is true.
56. Assertion (A) : Spontaneous process is an irreversible process and may be reversed by some external agency.
Reason (R) : Decrease in enthalpy is a contributory factor for spontaneity.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true but R is not the correct explanation of A.
(iii) A is true but R is false.
(iv) A is false but R is true.
57. Assertion (A) : A liquid crystallises into a solid and is accompanied by decrease in entropy.
Reason (R) : In crystals, molecules organise in an ordered manner.
(i) Both A and R are true and R is the correct explanation of A.
(ii) Both A and R are true but R is not the correct explanation of A.
(iii) A is true but R is false.
(iv) A is false but R is true.
VI. Long Answer Type
58. Derive the relationship between ΔH and ΔU for an ideal gas. Explain each term involved in the equation.
59. Extensive properties depend on the quantity of matter but intensive properties do not. Explain whether the following properties are extensive or intensive.
Mass, internal energy, pressure, heat capacity, molar heat capacity, density, mole fraction, specific heat, temperature and molarity.
60. The lattice enthalpy of an ionic compound is the enthalpy when one mole of an ionic compound present in its gaseous state, dissociates into its ions. It is impossible to determine it directly by experiment. Suggest and explain an indirect method to measure lattice enthalpy of NaCl(s).
61. ΔG is net energy available to do useful work and is thus a measure of “free energy”. Show mathematically that ΔG is a measure of free energy. Find the unit of ΔG. If a reaction has positive enthalpy change and positive entropy change, under what condition will the reaction be spontaneous?
62. Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from (pi , Vi ) to (pf , Vf ). With the help of a pV plot compare the work done in the above case with that carried out against a constant external pressure pf .
ANSWERS
I. Multiple Choice Questions (Type-I)
1. (iii) 2. (iii) 3. (iv) 4. (iii) 5. (iii) 6. (ii)
7. (iii) Justification : free expansion w = 0
adiabatic process q = 0
ΔU = q + w = 0, this means that internal energy remains constant. Therefore, ΔT = 0.
In ideal gas there is no intermolecular attraction. Hence when such a gas expands under adiabatic conditions into a vaccum no heat is absorbed or evolved since no external work is done to separate the molecules.
8. (ii) w (reversible) < w (irreversible)
Justification : Area under the curve is always more in irreversible compression as can be seen from Fig. 6.5 (a) and (b).
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9. (iii)
Justification : Freezing is exothermic process. The heat released increases the entropy of surrounding.
10. (iii)
11. (iii)
Justification : Same bonds are formed in reaction (a) and (b) but bonds between reactant molecules are broken only in reaction (b).
12. (iii) 13. (i) 14. (ii)
II. Multiple Choice Questions (Type-II)
15. (i), (iv) 16. (i), (ii) 17. (iii), (iv)
18. (iii), (iv)
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For isothermal expansion of ideal gases, ΔU = 0
since temperature is constant this means there is no change in internal energy. Therefore, ΔU = 0
19. (i), (iii)
III. Short Answer Type
20. + 81.58 kJ, ΔvapHΘ = + 40.79 kJ mol–1
21. Water
22. No, since CaCO3 has been formed from other compounds and not from its constituent elements.
23. ΔrHΘ = +91.8 kJ mol–1
24. ΔrH = ΔrH1+ ΔrH2 + ΔrH3 …..
25. 1665/4 kJ mol–1= 416.2 kJ mol–1
26. +735.5 kJ mol–1
27. It is spontaneous process. Although enthalpy change is zero but randomness or disorder (i.e., ΔS) increases. Therefore, in equation ΔG = ΔH – TΔS, the term TΔS will be negative. Hence, ΔG will be negative.
28. ΔS = qrev/T
29. Yes
30. The reaction is spontaneous ΔrGΘ= – RT ln Kp
31. ΔH (cycle) = 0
32. Less, because ice is more ordered than H2O (l).
33. State Functions : Enthalpy, Entropy, Temperature, Free energy Path Functions : Heat, Work
34. Because of strong hydrogen bonding in water, its enthalpy of vapourisation is more.
35. ΔrG will always be zero.
ΔrGΘ is zero for K = 1 because ΔGΘ = – RT lnK, ΔGΘ will be non zero for other values of K.
36. For isolated system, there is no transfer of energy as heat or as work i.e., w=0 and q=0. According to the first law of thermodynamics.
ΔU = q + w
= 0 + 0 = 0
∴ ΔU = 0
37. At constant volume By first law of thermodynamics:
q = ΔU + (–w)
(–w) = pΔV
∴ q = ΔU + pΔV
ΔV = 0, since volume is constant.
∴ qV = ΔU + 0
⇒ qV = ΔU = change in internal energy
At constant pressure
qp = ΔU + pΔV
But, ΔU + pΔV = ΔH
∴ qp = ΔH = change in enthalpy.
So, at a constant volume and at constant pressure heat change is a state function because it is equal to change in internal energy and change in enthalpy respectively which are state functions.
38. (–w) = pext (V2–V1) = 0 × (5 – 1) = 0
For isothermal expansion q = 0
By first law of thermodynamics
q = ΔU + (–w)
⇒ 0 = ΔU + 0 so ΔU = 0
39. For water, heat capacity = 18 × specific heat or Cp = 18 × c
Specific heat = c = 4.18 Jg–1K–1
Heat capacity = Cp = 18 × 4.18 JK–1 = 75.3 J K–1
40. CP – CV = nR = 10 × 4.184 J
41. Molar enthalpy change of graphite = enthalpy change for 1 g carbon × molar mass of carbon
= – 20.7 kJ g–1 × 12g mol–1
∴ ΔH = – 2.48 × 102 kJ mol–1
Negative value of ΔH ⇒ exothermic reaction.
42. ΔrHΘ= Bond energy of H2 + Bond energy of Br2 – 2 × Bond energy of HBr
= 435 + 192 – (2 × 368) kJ mol–1
⇒ ΔrHΘ
= –109 kJ mol–1
43. qp = ΔH = 30.5 kJ mol–1
∴ Heat required for vapourisation of 284 g of CCl4 = 284 g x 30.5 kJ mol–1/154 g mol–1 = 56.2 kJ
44. According to the definition of standard enthalpy of formation, the enthalpy change for the following reaction will be standard enthalpy of formation of H2O (l)
H2(g) + 1/2 O2(g) → H2O(l ).
or the standard enthalpy of formation of H2O(l) will be half of the enthalpy of the given equation i.e., ΔrHΘ is also halved.
ΔfHΘH2O(l ) = 1/2 × ΔrHΘ = − – 572 kJ mol–1/2 = – 286 kJ/mol.
45. Work done on an ideal gas can be calculated from p-V graph shown in Fig. 6.6. Work done is equal to the shaded area ABVIVII .
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46. The work done can be calculated with the help of p–V plot. A p–V plot of the work of compression which is carried out by change in pressure in infinite steps, is given in Fig. 6.7. Shaded area represents the work done on the gas.
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48. No.
Enthalpy is one of the contributory factors in deciding spontaneity but it is not the only factor. One must look for contribution of another factor i.e., entropy also, for getting the correct result.
49. It is clear from the figure that the process has been carried out in infinite steps, hence it is isothermal reversible expansion.
w = – 2.303nRT log V2/V1
But, p1V1 = p2V2 ⇒ V2/V1 = p1/p2 = 2/1 = 2
∴ w = – 2.303 nRT log p1/p2
= – 2.303 × 1 mol × 8.314 J mol–1 K–1 × 298 K–1 × log 2
= – 2.303 × 8.314 × 298 × 0.3010 J = –1717.46 J
50. w = – pex (Vf –Vi ) = –2 × 40 = – 80 L bar = – 8 kJ
The negative sign shows that work is done by the system on the surrounding. Work done will be more in the reversible expansion because internal pressure and exernal pressure are almost same at every step.
IV. Matching Type
51. (i) → (e) (ii) → (d) (iii) → (f) (iv) → (a) (v) → (g), (k), (l) (vi) → (b) (vii) → (c) (viii) → (j) (ix) → (h) (x) → (i) (xi) → (a), (l), (m) (xii) → (g), (k)
52. (i) →(b) (ii) → (c) (iii) → (a)
53. (i) → (c) (ii) → (a) (iii) → (b)
54. (i) → (b), (d) (ii) → (b) (iii) → (c) (iv) → (a)
V. Assertion and Reason Type
55. (ii) 56. (ii) 57. (i)
VI. Long Answer Type
59. Hint : Ratio of two extensive properties is always intensive
Extensive/Extensive = Intensive.
e.g., Mole fraction = Moles/Total number of moles = (Extensive)/ (Extensive)
60. • Na (s) + 1/2 Cl2 (g) → Na+(g) + Cl–(g) ; ΔlatticeHΘ
• Bonn – Haber Cycle
• Steps to measure lattice enthalpy from Bonn – Haber cycle
• Sublimation of sodium metal
(1) Na(s) → Na (g) ; ΔsubHΘ
(2) Ionisation of sodium atoms
Na(g) → Na+(g) + e–(g) ; ΔtHΘ i.e., ionisation enthalpy
(3) Dissociation of chlorine molecule
1/2 Cl2(g) → Cl(g) ; 1/2 Δbond HΘ i.e., One-half of bond dissociation enthalpy.
(4) Cl(g) + e–(g) → Cl–(g) ; ΔegHΘ i.e., electron gain enthalpy.
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61. ΔSTotal = ΔSsys + ΔSsurr
ΔSTotal = ΔSsys + (-ΔHsys/T)
T ΔSTotal = T ΔSsys – ΔHsys
For spontaneous change, ΔStotal > 0
∴ T ΔSsys – ΔHsys > 0
⇒ – (ΔHsys – T Δ Ssys ) > 0
But, ΔHsys – T ΔSsys = ΔGsys
∴ – ΔGsys > 0
⇒ ΔGsys = ΔHsys – T ΔSsys < 0
ΔHsys= Enthalpy change of a reaction.
T ΔSsys = Energy which is not available to do useful work.
ΔGsys = Energy available for doing useful work.
• Unit of ΔG is Joule
• The reaction will be spontaneous at high temperature.
62.
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LabManual
THERMOCHEMICAL MEASUREMENT
MOST of the reactions are carried out at atmospheric pressure, hence heat changes noted for these reactions are enthalpy changes. Enthalpy changes are directly related to the temperature changes by the relation:
ΔH = qp
= mCp ΔT
= VdCp ΔT … (1)
where V = Volume of the solution.
d = Density of the solution
Cp = Heat capacity
ΔT = Change in temperature
Measurement of heat changes are carried out in vessels called calorimeters. Reactions may also be carried out in beakers placed in thermos flask or in thermally insulated box or in styrofoam cup. Metallic calorimeters are not used
for measuring thermochemical changes because metals may react with substances. Stainless steel or gold plated copper calorimeters may be used. During measurement of heat changes, calorimeter, thermometer and stirrer also absorb some heat; this amount of heat should also be known. It is called calorimeter constant. In the case of a glass vessel, (e.g. beaker) calorimeter constant for that part is found, which is actually in contact with the reaction mixture. This is so because when thermal conductivity of the material of calorimeter is low, only the area of the calorimeter in contact with the liquid absorbs maximum heat. Method of mixtures is used to determine the calorimeter constant. To determine calorimeter constant, known volume of hot water at a specified temperature is added to known volume of water contained in the calorimeter at room temperature. Since energy is conserved, the heat taken by calorimeter and cold water should be equal to heat given by hot water. Thus, we can write the following equation :
ΔH1 + ΔH2 = –ΔH3 … (2)
Enthalpy change Enthalpy Enthalpy
of calorimeter, change of change of
stirrer and cold water hot water
thermometer
Let tc, th and tm be temperatures of cold water, hot water and mixture respectively. Then, in view of the definition of enthalpy change given in equation (1) we can rewrite equation (2) as
m1 Cp1 (tm–tc) + m2Cp(tm–tc) + m3Cp (tm–th) = 0 … (3)
where m1, m2 and m3 are masses of calorimeter, cold water and hot water respectively and Cp1 and Cp are heat capacities of calorimeter and water respectively. Since, thermal conductivity of glass is low, only that part of the beaker gains maximum heat which comes in contact with water therefore, we can calculate only effective m1 Cp1 (i.e. calorimeter constant, W). On rewriting equation (3) we get
W (tm– tc) + m2Cp (tm– tc) + m3Cp (tm– th) = 0
W =(m2Cp (tm– tc) + m3Cp (tm– th))/(tm– tc) … (4)
but mCp = VdCp, where V, d and Cp are volume, density and heat capacity of water respectively. By definition, heat capacity of a substance is the amount of energy required to raise the temperature of 1 g of substance by 1 K (or 1°C). The amount of energy required to raise the temperature of 1 g of water by 1 K (or 1°C) is 4.184 Joules. This means that for 1 g water for rise of 1 Kelven temperature VdCp = 4.184 JK–1. Therefore, product of density and heat capacity can be taken as 4.184 J.mL–1.K–1. Thus, equation (4) can be written as :
W = (4.184) [Vc(tm – tc) + Vh(tm – th) J K–1 / (tm – tc) … (5)
where Vc = volume of cold water
Vh = volume of hot water
Technique for measuring the enthalpy changes are given in the following experiments.
EXPERIMENT 3.1
Aim
To determine the enthalpy of dissolution of copper sulphate/potassium nitrate.
Theory
In thermochemical measurements generally aqueous solutions are mixed therefore, water in the reaction medium and the temperature changes result due to the chemical reactions taking place in solution.
According to law of conservation of energy, the sum of enthalpy changes taking place in the calorimeter (loss and gain of energy) must be zero. Thus, we can write the following equation-
| (ΔH1) Heat gained by calorimeter, thermometer and stirrer |
+ | (ΔH2) Enthalpy change of solution/water in calorimeter |
+ | (ΔH3) Enthalpy change of added solution/ water in calorimeter |
+ | (ΔH4) Enthalpy change of reaction |
= | 0 |
..(6)
In these reactions we take the product of density and heat capacity of solutions, dCp, to be 4.184 J.mL–1.K–1, nearly the same as that of pure water.*
Solution formation often accompanies heat changes. Enthalpy of solution is the amount of heat liberated or absorbed when one mole of a solute (solid/liquid) is dissolved in such a large quantity of solvent (usually water) that further dilution does not make any heat changes.
Material Required
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Procedure
A. Determination of Calorimeter constant of calorimeter (Beaker)
(i) Take 100 mL of water in a 250 mL beaker marked ‘A’.
(ii) Place this beaker on a wooden block kept in a larger beaker of capacity 500 mL (Fig. 3.1).
(iii) Pack the empty space between the large and the small beaker with cotton wool. Cover the beaker with a cardboard.
Insert thermometer and stirrer in the beaker through it.
* Density of the solutions is 4 to 6% higher than that of pure water and heat capacity is about 4 to 8% less than
pure water so the product of density and heat capacity (dCp ) is nearly the same as the product of pure water.
(iv) Record the temperature of water. Let this temperature be tc°C.
(v) In another beaker of 250 mL capacity marked ‘B’ take 100 mL of hot water (50-60°C).
(vi) Note the exact temperature of hot water. Let this temperature be th°C.
(vii) Lift the card board and pour the hot water contained in beaker B into beaker A. Stir the mixed water and note the
temperature. Let this temperature be tm°C.
(viii) Calculate the calorimeter constant of the beaker by using the expression (5) given above.
(Remember the three temperatures are in the order th > tm >tc).
B. Determination of Enthalpy of Dissolution
(i) Take 100 mL of distilled water in the beaker of which calorimeter constant has been determined and place it on
a wooden block kept in a larger beaker of capacity 500 mL (Fig. 3.1).
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(ii) Pack the empty space between the larger and the smaller beaker with cotton wool and cover with a cardboard.
(iii) Record the temperature of water already taken in the small beaker. Let this be t’1°C.
(iv) Add weighed amount, say W1 g of well powdered copper sulphate in water and stir the solution with a stirrer till
the entire amount of copper sulphate dissolves.
(v) Note down the temperature attained by the solution after the addition of copper sulphate. Let this be t’2°C. Calculate the enthalpy of dissolution of copper sulphate as follows:
Total mass of the solution = Mass of Solvent + Mass of Solute
= (100 + W1) g
(Assuming density of water to be equal to 1 gL–1 at the
experimental temperature)
Change in temperature = (t’2 – t’1) °C
Enthalpy change of the calorimeter (beaker) = W (t’2 – t’1)
where, W = Calorimeter constant
Enthalpy change of solution = [(100 + W1) (t’2 – t’1)]x4.184 J
for (t’2 – t’1) °C rise in temperature
Total enthalpy change
of the Calorimeter = [W (t’2 – t’1) + (100 + W1) (t’2 – t’1)]x4.184 J
(beaker) and solution
Heat liberated
on dissolution = [W (t’2 – t’1) + (100 + W1) (t’2 – t’1)]x4.184 J/W1
of 1 g copper
sulphate
Since 1 mol of copper sulphate weighs 249.5 g. Therefore,
ΔsolH of CuSO4.5H2O = 249.5 × ([W (t’2 – t’1) + (100 + W1) (t’2 – t’1)]x4.184 J mol–1)/W1
Result
Enthalpy change in the dissolution of copper sulphate/potassium nitrate is _______ Jmol–1.
Precautions
(a) To record the temperature of water, use a thermometer with 0.1°C graduation.
(b) In the determination of calorimeter constant record the temperature of hot water just before mixing.
(c) Avoid using very large amounts of copper sulphate/potassium nitrate.
(d) Stir the solution well to dissolve the solid and record the temperature. Avoid too much stirring, it may produce heat due to friction.
(e) Weigh copper sulphate carefully as it is hygroscopic in nature.
(f) Use cotton wool to create insulation between the two beakers.
Discussion Questions
(i) What is meant by the term, calorimeter constant?
(ii) Why is ΔSolH for some substances negative while for others it is positive?
(iii) How does ΔSolH vary with temperature?
(iv) Will the enthalpy change for dissolution of same amount of anhydrous copper sulphate and hydrated copper sulphate in the same amount of water be the same or different? Explain.
(v) How will the solubility of copper sulphate and potassium nitrate be affected on increasing the temperature? Explain.
EXPERIMENT 3.2
Aim
To determine the enthalpy of neutralisation of a strong acid (HCl) with a strong base (NaOH).
Theory
A neutralisation reaction involves the combination of H+(aq) ions furnished by an acid and OH–(aq) ions furnished by a base, evidently leading to the formation of H2O (l). Since the reaction envisages bond formation, therefore, this reaction is always exothermic. Enthalpy of neutralisation is defined as the amount of heat liberated when 1mol of H+ ions furnished by acid combine with 1 mole of OH– ions furnished by base to form water. Thus:
H+(aq) + OH–(aq) → H2O (l), Δneut H is negative
(Acid) (Base)
where Δneut H is known as enthalpy of neutralisation.
If both the acid and the base are strong then for the formation of 1 mol H2O (l), always a fixed amount of heat, viz, 57 kJ mol–1 is liberated. If any one of the acid or the base is weak or if both of these are weak, then some of the heat liberated is used for the ionisation of the acid or base or both of them (as the case may be) and the amount of heat liberated is less than 57 kJ mol–1.
Material Required
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Procedure
A. Determination of calorimeter constant
This may be determined by following the procedure, as detailed in experiment 3.1.
B. Determination of Enthalpy of Neutralisation
(i) Take 100 mL of 1.0 M HCl solution in the calorimeter (beaker) and cover it with cardboard. In another beaker of 250 mL capacity take 100 mL of 1.0 M NaOH solution.
(ii) Note down the temperature of both the solutions, which is likely to be the same. Let it be t1°C.
(iii) Pour 100 mL 1 M NaOH solution into the calorimeter containing 100 mL of 1.0 M HCl solution.
(v) Mix the solutions by stirring and note the final temperature of the mixture. Let it be t2°C.
Calculate the enthalpy of neutralisation as follows:
(i) Note the rise in temperature of the mixture, which in this case is (t2-t1) °C.
(ii) Calculate the total amount of heat produced during the neutralisation process, using the following expression
Heat evolved = (100 + 100 + W) (t2 – t1) 4.18 J (where W, is the calorimeter constant)
(iii) Finally calculate the heat evolved when 1000 mL of 1M HCl is allowed to neutralise 1000 mL of 1M NaOH. This quantity would be ten times the quantity obtained in step (ii).
(iv) Express the quantity of heat evolved in kJ mol–1.
Result
Enthalpy change in the neutralisation of hydrochloric acid solution with sodium hydroxide solution _______ kJmol–1.
Precautions
(a) Record the temperature carefully with the help of a thermometer graduated up to 0.1°C.
(b) Measure the volume of hydrochloric acid and sodium hydroxide solution to be taken for the experiment carefully.
(c) Proper insulation should be made between the two beakers.
(d) Avoid unnecessary and excessive stirring to prevent heating due to friction.
Discussion Questions
(i) Why do we calculate the heat evolved for the neutralisation of 1000 mL of a (1 M) acid by 1000 mL of a (1 M) monoacidic base?
(ii) In comparison to heat evolved in neutralisation reaction between a strong acid and a strong base. Why is lesser quantity of heat evolved when any one of the acid or the base is weak and still less when both are weak?
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EXPERIMENT 3.3
Aim
To determine the enthalpy change for the interaction between acetone and chloroform (hydrogen bond formation).
Theory
On mixing, liquid pairs show departure from ideal behaviour. Acetone and chloroform form non-ideal liquid pair system, which shows a negative deviation from Raoult’s law. This negative deviation from Raoult’s law implies that the two components are strongly held together in liquid state on mixing due to hydrogen bonding. On the other hand in the pure state, only weak Van der waal’s forces hold molecules of chloroform as well as acetone. The hydrogen bonding between the molecules of acetone and chloroform is depicted as follows:
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In this process enthalpy change takes place due to hydrogen bond formation. The enthalpy change is an extensive
thermodynamic property, therefore, the heat evolved from the system depends upon the amount of the liquid components
mixed. It is for this reason that the heat change is reported for specified amount. Therefore, enthalpy change during mixing of 1 mol chloroform with 1 mol acetone is reported.
| (ΔH1)Heat gained by calorimeter, thermometer and stirrer |
+ | (ΔH2) Enthalpy change of caloroform |
+ | (ΔH3) Enthalpy change for acetone |
+ | (ΔH4) Enthalpy change of interaction |
= | 0 |
ΔH4 = – (ΔH1+ΔH2+ΔH3)
Material Required
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Procedure
A. Determination of calorimeter constant
This may be determined in a manner detailed in previous experiments; except that here instead of a beaker, boiling tube
may be taken and 8 mL of cold and 7.5 mL of hot water can be used instead of 100 mL.
B. Determination of Enthalpy Change on Mixing Chloroform and Acetone*
(i) Transfer the volume of chloroform equivalent to 0.1 mol (≈ 8.14 mL) after measuring from a measuring cylinder into the insulated boiling tube as shown in Fig. 3.2. Let the mass of chloroform taken be m1 grams.
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(ii) Record the temperature of chloroform. Let it be t1°C.
(iii) Transfer the volume of acetone equivalent to 0.1 mol of acetone (≈ 7.34 mL) in a clean measuring cylinder. Let its mass be m2 grams.
(iv) Record the temperature of acetone. Let it be t2°C.
(v) Pour acetone from the measuring cylinder into the chloroform contained in the insulated boiling tube.
(vi) Stir gently the mixture of chloroform and acetone carefully with the help of a stirrer.
(vii) Record the temperature of the mixture of chloroform and acetone. Let it be t3°C.
*Volume of one mole of CHCl3 = Molar mass of CHCl3/Density of CHCl3
Volume of 0.1 mole = 1/10 th of the above volume
(Similarly you can calculate the volume of 0.1 mole of acetone).
Density of chloroform= 1.47 g /mL
Molar mass of chloroform = 119.5 g
1.47 g = 1 mL volume
119.5 g = 119.5/1.47 mL
1 mole = 81.4 mL
0.1 mole = 8.14 mL
Density of acetone = 0.79 g /mL
Molar mass of acetone = 58.0
0.79 g = 1 mL
58 g = 58/0.79 mL
1 mole = 73.4 mL
0.1 mole = 7.34 mL
Total volume of acetone and chloroform = 8.14 +7.34 = 15.48 mL
Calculate the enthalpy of interaction as follows :
(i) Let the room temperature be t°C, then heat gained by calorimeter (boiling tube) is W (t3 – t), where W is the calorimeter constant, i.e. boiling tube in this experiment.
(ii) Note the value of specific heat of chloroform from literature. Let it be q1.
Then heat gained by chloroform = m1 x q1 (t3 – t1).
(iii) Note the value of the specific heat for acetone from literature. Let it be q2. Thus heat gained by acetone = m2 x q2 (t3 – t2).
(iv) Total heat gained by all the three components, i.e. boiling tube, chloroform and acetone = – {W(t3 – t1) + m1q1(t3 – t1) + m2q2 (t3 – t2)}. This in fact is the enthalpy change of interaction, on mixing 0.1 mol chloroform with 0.1 mol acetone.
The negative sign simply implies that the mixing of chloroform and acetone is an exothermic process.
Note : Here, care should be taken that the total volume of acetone and chloroform is equal to the volume of water for which water equivalent of the calorimeter has been calculated.
Precautions
(a) Measure chloroform and acetone carefully.
(b) Record the temperature very carefully with a thermometer graduated up to 0.1°C.
Discussion Questions
(i) Chloroform and acetone do not form an ideal liquid pair, whereas acetone and benzene do form. Why?
(ii) Why does liquid pair of ethanol and water show positive deviation from Raoult’s law?
(iii) Give two examples of each of the liquid pairs for which ΔMixing H is negative and positive respectively.
(vi) How is the vapour pressure of the liquids related to interaction pattern between the molecules of the components of a liquid mixture?
(v) How can you correlate the heat evolved from the system with the strength of the hydrogen bond?
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Simplified Knowledge Management Classes
Must see https://zookeepersblog.wordpress.com/some-points-which-i-wish-all-my-new-prospective-students-know/
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Do you want to make money working at home ?
see http://skmclasses.weebly.com/jobs.html
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you will get most videos. I say most because I do not upload all videos that I make. I have many more videos which are not in the net.
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The following Videos are available for you ( As of Now ). These explain tricky Physics and Mathematics Numericals.
Eventually I will try to give Videos for full course here for you.
These covers PU ( Pre University courses, school / college ) courses, IIT JEE, AIEEE ( All India Engineering Entrance Examination ) , CET ( Combined Engineering Test ), AIPMT ( All India Pre Medical Test ), ISc ( Intermediate Science / Indian School Certificate Exam ), CBSE ( Central Board Secondary Exam ), Roorkey Joint Entrance Test Questions ( Discontinued since 2002 ), APhO ( Asian Physics Olympiad ), IPhO ( International Physics Olympiad ), IMO ( International Mathematics Olympiad ) , NSEP ( National Standard Exam in Physics ), RMO ( Regional Math Olympiad , India ), INMO ( Indian National Maths Olympiad ), Irodov Solutions, Prof. H C Verma ( Concepts of Physics ) Solutions etc.
( You can see the history of Indian Participation in various Olympiads at ->
https://zookeepersblog.wordpress.com/indian-participation-in-ipho-icho-ibo-and-astronomy-olympiad/ )
[ In each of these videos there is at-least 1 or more errors. Please tell me about those ]
search for videos in http://www.skmclasses.kinja.com
You should get to see all the Uploaded videos. Though we have many more study videos.
Thanks and Regards
Zookeeper ;-D Subhashish Chattopadhyay
[ I suggest you see the videos starting with 1- first then starting with 2- ….. in that sequence. ]
[ Tell your friends about this link if you liked the videos ]
In case of doubts or suggestions, Please send me email at mokshya@gmail.com
search for videos in http://www.skmclasses.kinja.com
Answers to -> Frequently Asked Questions ( FAQ ) [ commonly asked intelligent Questions 🙂 ]
1 ) How do I prepare for IIT ?
Ans : – See the videos made by me ( search for videos in http://www.skmclasses.kinja.com
Though we have many more which have not been uploaded ). While watching the videos, take notes and try to solve the problems yourself by pausing the video. Tell me if any calculation is wrong. See the videos with 1- first then 2- and so on. Write to IAPT Kothrud, Pune office to buy ( 150 Rs approx ) the book with previous papers of NSEP ( National Standard Exam in Physics – The 1st level ), INPhO ( Indian National Physics Olympiad – 2nd level ). Prepare with these and see how much you are scoring. You can guess your ALL INDIA rank easily from NSEP, and INPhO rank. Since 1998 the IIT JEE toppers have been mostly representing India in IPhO.
2 ) Which codec and Player do I use to see the videos ?
Ans : – You can use GOM Player, or VLC Player. You have to have good speakers with filters or good earphones with filters. We have checked mostly it is OK with these. ( If you are depending only on your embedded speakers of computer /screen / keyboard then there may be extra distortions. As these speakers are often not of good Quality. Also install latest KL Codecs ) In any case reduce the volume see the board, imagine sitting in the last bench and solving the problems of your own. See if your solution differs anywhere with the scribbles on the board.
3 ) Why are you giving these ( high Quality ) lecture for free ?
Ans : Well there are lot of good things free in this world. Linux, My-SQL, Open-Office ….. Go to sourceforge and get thousands of high quality software free along with source code. Yes all officially free …. Why do you think Richard Stallman, Zimmerman, ….. etc are considered Guru philosophers ? In Punjab and Gurudwaras worldwide there are so many Langars where you get better food than Restaurants. ….. why ? Why do you have Dharmasalas and subsidized rest rooms near hospitals / Famous Temples / various places ? in Iftar party anyone can eat for free …. why ?
I am teaching since 1989 I have observed most students can do much better if they have the self motivation to solve and practice. Cheap books are available in second hand bookstalls, where you get thousands of Numericals to solve ….. but most students will like to blow their time going and coming for tuition, travel time …. TV for hours and hours watching cricket / Tennis games, playing computer games …. My free lectures are not going to make much difference in spending of unnecessary money for coaching ….. I know very well , how much people enjoy …. ! spending unnecessarily !!
–
Do you know that there are NO poor / needy students in Bangalore.
–
Sometime back I had tried to teach for IIT JEE FREE. Discussed with a few NGOs and social service guys. Arranged rooms but got only 1 student. We had informed many people in many ways to inform students …. We did not get students who are ready to learn for free. So I am sure these lectures are NOT FREE. If anyone learns from these, s/he changes and that’s the gain / benefit. This change ( due to learning ) is very costly …. Most do not want to learn ………..
search for videos in http://www.skmclasses.kinja.com
You will get most videos. I say most because I do not upload all videos that I make. I have many more videos which are not in the net.
🙂
4 ) How can I get all your lectures ?
Ans : – Apart from my lectures there are approx 700 GB of PCM ( Phy, Chem, Math ) lectures. It takes approx 3 years of continuous download from scattered sources. I have ( 20,000 )Thousands of these. You can take ALL of them from me in an external 1 TB hard disk, instead of spending so much money and time again for downloading. These cover ( by Various Professors ) everything of Chemistry, Physics, Maths… Lot of this is from outside India … as foreigners have much wider heart than Indians ( as most of GNU / open source software have been developed by Non-Indians ). I observed the gaps in these videos, and thus I am solving IIT, APhO, Roorkey, IPhO Numericals. Videos made by me along with these videos gives a complete preparation.
Send me a mail at mokshya@gmail.com to contact me.
search for videos in http://www.skmclasses.kinja.com
You will get most videos. I say most because I do not upload all videos that I make. I have many more videos which are not in the net.
🙂
5 ) How do you get benefited out of this ?
Ans :- If anyone learns we all will have better people in this world. I will have better “ YOU “.
🙂
6 ) Why do you call yourself a Zookeeper ?
Ans :- This is very nicely explained at https://zookeepersblog.wordpress.com/z00keeper-why-do-i-call-myself-a-zoookeeper/
🙂
7 ) Where do you stay ?
Ans :- Presently I am in Bangalore.
🙂
8 ) If I need videos in a few topics can you make them for me ?
Ans :- We actively answers doubts at doubtpoint.
see http://skmclasses.weebly.com/doubtpoint.html
In case you appreciate our time and efforts involved in answering complicated Questions, then get Quality answers at doubtpoint.
🙂
9 ) Why did you write an article saying there are No Poor students ?
Ans :- There are lots of NGOs and others working for rural / poor children education at lower classes. While very less effort is on for std 9 till 12. Also see the answer in question number ( 3 ) above. In more than 2 decades of teaching I never met a Poor child who was seriously interested in ( higher ) studies. As I have a mind / thinking of a ” Physicist “, I go by ” Experimental Observation “.
It is not about what is being said about poor in media / TV etc, or ” what it should be ” ( ? ) …. It is about what I see happening. Also to add ( confuse ? you more )…. You must be knowing that in several states over many years now girl students have better ( by marks as well as by pass percentage ) result in std 10 / Board Exams….. well but NEVER a girl student came FIRST in IIT JEE … why ? [ The best rank by a Girl student is mostly in 2 digits, very rarely in single digit ] ????? So ????
🙂
10 ) How much do I have to study to make it to IIT ?
Ans :- My experience of Teaching for IIT JEE since 1989, tells me, Total 200 hours per subject ( PCM ) is sufficient. If you see my Maths and Physics videos, each subject is more than 200 hours. So if someone sees all the videos diligently, takes notes and remembers, …… Done.
🙂
11 ) What is EAMCET ?
Ans :- Engineering Agriculture and Medicine Common Entrance Test is conducted by JNT University Hyderabad on behalf of APSCHE. This examination is the gateway for entry into various professional courses offered in Government/Private Colleges in Andhra Pradesh.
12 ) In your videos are you covering other Exams apart from IIT ?
Ans : – Yes. See many videos made by solving problems of MPPET, Rajasthan / J&K CET, UPSEAT ( UPES Engineering Aptitude Test ), MHCET, BCECE ( Bihar Combined Entrance Competitive Examination Board ), WB JEE etc
🙂
13 ) What is SCRA ?
Ans : – Special Class Railway Apprentice (SCRA) exam is conducted by Union Public Service Commission (UPSC) board, for about 10 seats.That translates into an astonishing ratio of 1 selection per 10,000 applicants. The SCRA scheme was started in 1927 by the British, to select a handful of most intelligent Indians to assist them in their Railway Operations, after training at their Railway’s largest workshop, i.e. Jamalpur Workshop, and for one year in United Kingdom. The selected candidates were required to appear in the Mechanical Engineering Degree Examination held by Engineering Council (London).
Thanks for your time. To become my friend in google+ ( search me as mokshya@gmail.com and send friend request )
Read http://edge.org/responses/what-scientific-concept-would-improve-everybodys-cognitive-toolkit
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The following video is a must see for full CO2 cycle, plates of Earth, Geological activities, stability of weather
http://www.youtube.com/watch?v=oIuoNtRBG4w
🙂
Article in Nature says CO2 increase is good for the trees
http://thegwpf.org/science-news/6086-co2-is-greening-the-planet-savannahs-soon-to-be-covered-by-forests.html
🙂
http://climaterealists.com/index.php?id=9752
BBC documentary Crescent and Cross shows the 1000 years of fight between Christians and Muslims. Millions have been killed in the name of Religion. To decided whose GOD is better, and which GOD to follow. The fight continues.
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Summary of Women
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The Virus of Faith
http://www.youtube.com/watch?v=scarHc8RA0g
🙂
The God delusion
http://www.youtube.com/watch?v=LVr9bJ8Sctk
🙂
cassiopeia facts about evolution
–
Intermediate Fossil records shown and explained nicely Fossils, Genes, and Embryos http://www.youtube.com/watch?v=fdpMrE7BdHQ
The Rise Of Narcissism In Women
http://www.youtube.com/watch?v=wZHKCbHGlS0
🙂
13 type of women whom you should never court
http://timesofindia.indiatimes.com/life-style/relationships/man-woman/13-Women-you-should-never-court/articleshow/14637014.cms
🙂
Media teaching Misandry in India http://www.youtube.com/watch?v=-M2txSbOPIo
Summary of problems with women
http://problemwithwomentoday.blogspot.in/2009/12/problem-with-women-today-what-in-hell.html
🙂
Eyeopener men ? women only exists
http://www.youtube.com/watch?v=6ZAuqkqxk9A
🙂
Most unfortunate for men
http://www.youtube.com/watch?v=73fGqUwmOPg
🙂
Each of you is an Activist in some way or other. You are trying to propagate those thoughts, ideas that you feel concerned / excited about.
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Did you analyze your effectiveness ?
http://www.youtube.com/watch?v=61qn7S9NCOs
Culturomics can help you
😀
see how biased women are. Experimental proof. Women are happy when they see another woman is beating a man ( see how women misbehave with men )
🙂
http://www.youtube.com/watch?v=LlFAd4YdQks
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see detailed statistics at
http://www.youtube.com/watch?v=5lHmCN3MBMI
An eye opener in Misandry
http://www.youtube.com/watch?v=YiTaDS_X6CU
My sincere advice would be to be EXTREMELY careful ( and preferably away ) of girls. As girls age; statistically certain behavior in them has been observed. Most Male can NOT manage those behaviors… Domestic violence, divorce etc are rising very fast. Almost in all cases boys / males are HUGE loosers. Be extremely choosy ( and think from several angles ) before even talking to a girl.
🙂
https://zookeepersblog.wordpress.com/save-the-male/
🙂
How women manipulate men
http://www.angryharry.com/esWomenManipulateMen.htm
Gender Biased Laws in India
https://zookeepersblog.wordpress.com/biased-laws/
🙂
Violence against Men
http://www.youtube.com/watch?v=MLS2E-rRynE
🙂
Only men are victimised
http://www.youtube.com/watch?v=4JA4EPRbWhQ
Men are BETTER than women
http://www.menarebetterthanwomen.com/
🙂
see http://www.youtube.com/watch?&v=T0xoKiH8JJM#!
🙂
Male Psychology http://www.youtube.com/watch?v=uwxgavf2xWE
Women are more violent than men
http://www.independent.co.uk/news/uk/home-news/women-are-more-violent-says-study-622388.html
🙂
In the year 2010, 168 men ended their lives everyday ( on average ). More husbands committed suicide than wives.
🙂
http://www.rediff.com/news/report/ncrb-stats-show-more-married-men-committing-suicide/20111028.htm
It is EXTREMELY unfortunate that media projects men as fools, women as superiors, Husbands as servants, and replaceable morons. In ad after ad worldwide from so many companies, similar msg to disintegrate the world is being bombarded. It is highly unacceptable misandry
🙂
http://www.youtube.com/watch?v=oq14WHkFq30
It is NOT at all funny that media shows violence against MEN. Some advertisers are trying to create a new ” Socially acceptable culture ” of slapping Men ( by modern city women ). We ( all men ) take objection to these advertisements.
We oppose this Misandry bad culture. Please share to increase awareness against Men bashing
🙂
http://www.youtube.com/watch?v=D8ecN2rh0uU
🙂
Think what are you doing … why are you doing ?
http://www.youtube.com/watch?v=qp0HIF3SfI4
Every Man must know this …
http://www.youtube.com/watch?v=cIFmQHJEG1M
🙂
Manginas, White Knights, & Other Chivalrous Dogs
http://www.youtube.com/watch?v=oXQDtBT70B8
!
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International Residential School Nithyananda Nagar, Kumbalagudu, Gollahalli Kengeri, Bangalore Solutions, India, IPhO, APhO, IMO, RMO, INMO, through, lectures, problems numericals Zookeeper, Subhashish, Chattopadhyay, Projectile, Latent, Heat Thermodynamics std 11 12 ISc Calculus BE BTech Differentiation Integration Mechanics Surface Tension Viscosity Accelerating Frame velocity wedge mass pulley Moment Inertia Roorkey Joint Entrance Exam CET AIEEE Irodov HCV Verma South Bangalore Intermediate Algebra Trigonometry Sexy Free Coaching study material preparation Olympiad Friction sin Modelling cos Potential tan cot Gravitation Electrostatics sec Field cosec Ellipse Parabola Hyperbola inverse string Tuition Kinetic Theory Gases Isothermal Adiabatic Isochoric Isobaric Processes Root Mean Square Differential Equation Soomrit Specific Cp Cv PV Diagram Bending Stress Strain Geostationary Satellite Entropy Coefficient Linear Expansion Alpha Beta Gamma Pendulum Conductivity Latent ice water 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Resistance Battery Trick Questions Infinite Ladder Quadratic Cubic Quartic Quintic Orissa NSEP ckt eqn mesh Folding Lenzs J&K Karnataka RMS instantaneous BCECE Maharastra MHCET RPET stepup stepdown transformer Bilekahalli UPSEAT shunt galvanometer susceptibility oscillating magnetometer pole strength Bihar Rajasthan Uttarpradesh Punjab Hariana TN Tamilnadu Andhra WB west Bengal Vacuum Diode Triode Rectifier Truth Table Thermionic emission, Radioactivity Half Life Langmiur, Child Law FCC BCC Cube Optics Lens Mirror Focus Focal Concave Convex Lux Phot Lumen Double slit Complex Integral coordinate Geometry compounds, Biochemistry, Plastic, Organic Chemistry Physical Analytical Inorganic Metallurgy, Biotechnology, Polymer Science, Rubber Technology Geology, Pharma, Veterinary Science,Food Technology, Cryogenics, Ceramics acid species IITJEE SKMClasses.weebly.com proton donor activation energy minimum energy IITJEE SKMClasses.weebly.com reaction breaking bonds addition polymer very long molecular chain formed repeated addition reactions many unsaturated alkene molecules monomers addition polymerisation process unsaturated alkene molecules monomers add growing polymer chain one timeIITJEE SKMClasses.weebly.com long saturated molecular chain addition polymer addition reaction reaction IITJEE SKMClasses.weebly.com reactant added IITJEE SKMClasses.weebly.com unsaturated molecule saturated molecule adsorption process IITJEE SKMClasses.weebly.com occurs gas, liquid solute surface solid rarely liquid alicyclic hydrocarbon hydrocarbon IITJEE SKMClasses.weebly.com carbon atoms joined together ring structure aliphatic hydrocarbon hydrocarbon IITJEE SKMClasses.weebly.com carbon atoms joined together straight branched chains alkali type base IITJEE SKMClasses.weebly.com dissolves water forming hydroxide ions OH (aq) ions alkanes homologous series IITJEE SKMClasses.weebly.com general formula C alkyl group alkane IITJEE SKMClasses.weebly.com hydrogen atom removed CH alkyl groups IITJEE SKMClasses.weebly.com IITJEE skmclasses.weebly.com ‘R’ amount substance quantity whose unit mole Chemists amount substance IITJEE skmclasses.weebly.com IITJEE counting atoms anhydrous substance IITJEE SKMClasses.weebly.com contains water molecules anion negatively charged ion atom economy atomic orbital region within atom hold two electrons IITJEE SKMClasses.weebly.com opposite spins atomic proton number number protons nucleus atom 100 products masses molecular sum product desired mass molecular economy atom Chemistry average bond enthalpy average enthalpy change IITJEE SKMClasses.weebly.com place IITJEE SKMClasses.weebly.com breaking homolytic fission 1 molIITJEE SKMClasses.weebly.com type bond molecules gaseous species Avogadro constant,isotope number atoms mole carbon base species IITJEE SKMClasses.weebly.com proton acceptor biodegradable material substance IITJEE SKMClasses.weebly.com broken IITJEE SKMClasses.weebly.com naturally environment living organisms Boltzmann distribution distribution energies molecules particular temperature IITJEE skmclasses.weebly.com graph bond enthalpy enthalpy change IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com breaking homolytic fission 1 mol bond molecules gaseous species carbanion organic ion IITJEE SKMClasses.weebly.com carbon atom hIITJEE skmclasses.weebly.com negative charge carbocation organic ion IITJEE SKMClasses.weebly.com carbon atom hIITJEE skmclasses.weebly.com positive charge catalyst substance IITJEE SKMClasses.weebly.com increases rate chemical reaction process cation positively charged ion cis trans isomerism special type isomerism IITJEE SKMClasses.weebly.com non hydrogen group skmclasses.weebly.com hydrogen atom C C=C double bond cis isomer ( Z isomer) IITJEE skmclasses.weebly.com H atoms on IITJEE SKMClasses.weebly.com carbon same side trans isomer E isomer H atoms carbon different bond compound substance formed IITJEE SKMClasses.weebly.com two IITJEE SKMClasses.weebly.com chemically bonded elements fixed ratio, usually chemical formula concentration amount solute mol IITJEE SKMClasses.weebly.com 1 dm 3 1000 cm solution coordinate bond shared pair electrons provided one bonding atoms called dative covalent bond covalent bond bond formed shared pair electrons cracking breaking long chained saturated hydrocarbonsIITJEE SKMClasses.weebly.com mixture shorter chained alkanesalkenes curly arrow symbol IITJEE SKMClasses.weebly.com reaction mechanisms IITJEE SKMClasses.weebly.com show movement electron Coaching ICWA Coaching CFA Coaching CFP Coaching CMAT Coaching School Tuitions CBSE School Tuitions Home Tuitions 9th STD Tuitions PUC Coaching 10th Std Tuitions College Tuitions Maths Tuitions Engineering Tuitions Accounts & Finance Tuitions MBA & BBA Coaching Microbiology & Biotech Tuitions Study Abroad GRE & SAT Coaching GMAT Coaching IELTS/TOEFL Coaching PTE Coaching proteins protonation pyridines pyrroles quinones quinolines radical reaction radicals rearrangement receptors reduction regioselectivity retro reaction rhodium ring closure ring contraction ring expansion ring opening ruthenium samarium scandium Schiff bases selenium self-assembly silicon sodium solid-phase synthesis solvent effects spectroscopy sphingolipids spiro compounds stereoselective synthesis stereoselectivity steric hindrance steroids Stille reaction substituent effects sulfates sulfonamides sulfones sulfoxides sulfur supported catalysis supramolecular tandem reaction tautomerism terpenoids thioacetals thiols tin titanium total synthesis transesterification transition metals transition states tungsten Umpolung vinylidene complexes vitamins Wacker reaction Wittig reaction ylides zeolites zinc BRST Quantization Effective field theories Field Theories Higher Dimensions Field Theories Lower Dimensions Large Extra Dimensions Lattice Quantum Field Theory Nonperturbative Effects Renormalization Group Renormalization Regularization skmclasses.weebly.com Renormalons Sigma Models Solitons Monopoles skmclasses.weebly.com Instantons Supersymmetric gauge theory Topological Field Theories 1/N Expansion Anyons Chern-Simons Theories Confinement Duality Gauge Field Theories Lattice Gauge Field Theories Scattering Amplitudes Spontaneous Symmetry Breaking Strong Coupling Expansion Topological States Matter Wilson ‘t Hooft skmclasses.weebly.comPolyakov loops Anomalies Field skmclasses.weebly.comString Theories BRST Symmetry Conformal skmclasses.weebly.com W Symmetry Discrete skmclasses.weebly.comFinite Symmetries Gauge Symmetry Global Symmetries Higher Spin Symmetry Space-Time Symmetries AdS-CFT Correspondence Black Holes String Theory Bosonic Strings Brane Dynamics Gauge Theories Conformal Field Models String Theory D-branes dS vacua string theory F-Theory Flux compactifications Gauge-gravity correspondence Holography skmclasses.weebly.comcondensed matter physics (AdS CMT) Holography skmclasses.weebly.comquark-gluon plasmas Intersecting branes models Long strings M(atrix) Theories M-Theory p-branes Penrose limit skmclasses.weebly.compp-wave background String Duality String Field Theory String theory skmclasses.weebly.comcosmic string Superstring Vacua Superstrings skmclasses.weebly.comHeterotic Strings Tachyon Condensation Topological Strings 2D Gravity Black Holes Classical Theories Gravity Higher Spin Gravity Lattice Models Gravity Models Quantum Gravity Spacetime Singularities Extended Supersymmetry Supergravity Models Superspaces Supersymmetric Effective Theories Supersymmetry skmclasses.weebly.com Duality Supersymmetry Breaking Differential skmclasses.weebly.comAlgebraic Geometry Integrable Hierarchies Non-Commutative Geometry Quantum Groups Statistical Methods Stochastic Processes Cosmology Theories beyond SM Solar skmclasses.weebly.comAtmospheric Neutrinos Thermal Field Theory Be Ansatz Boundary Quantum Field Theory Exact S-Matrix Quantum Dissipative Systems Random Systems B-Physics Beyond Standard Model Compactification skmclasses.weebly.com String Models CP violation Electromagnetic Processes skmclasses.weebly.com Properties GUT Heavy Quark Higgs Kaon LEP HERA skmclasses.weebly.com SLC Neutrino Physics Quark Masses skmclasses.weebly.comSM Parameters Rare Decays Standard Model Supersymmetric Standard Model Technicolor skmclasses.weebly.com Composite Models Chiral Lagrangians Deep Inelastic Scattering Higher Twist Effects Lattice QCD Parton Model Phase Diagram QCD Phenomenological Models QCD Quark-Gluon Plasma Resummation Sum Rules Aim Global Education Koramangala Computer Networking Training Cloud Computing Training JBOSS Training Juniper Certification Training L2 & L3 Protocol Training MCTS Training Engineering design Training CAD & CAM Training MATLAB Training PLC Training SCADA Training VLSI Design Multimedia & Design Training 2D Animation Training 3D Animation Training 4D Animation Training CorelDRAW Training VFX Training Web Technologies Training ASP.Net Training JQuery pair breaking formation covalent bond dative covalent shared pair electrons IITJEE SKMClasses.weebly.com hIITJEE skmclasses.weebly.com been provided one bonding atoms only IITJEE SKMClasses.weebly.com called coordinate bond dehydration elimination reaction IITJEE SKMClasses.weebly.com water removed saturated molecule IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com unsaturated molecule delocalised Electrons IITJEE SKMClasses.weebly.com shared IITJEE SKMClasses.weebly.com two atoms displacement reaction reaction IITJEE SKMClasses.weebly.com reactive element displaces less reactive element IITJEE SKMClasses.weebly.com aqueous solution latter’s ions displayed formula showing relative positioning atoms molecule skmclasses.weebly.com bonds IITJEE SKMClasses.weebly.com disproportionation oxidation skmclasses.weebly.com reduction element redox reaction dynamic equilibrium equilibrium IITJEE SKMClasses.weebly.com exists closed system IITJEE SKMClasses.weebly.com rate forward reaction equal IITJEE SKMClasses.weebly.com rate reverse reaction E/Z isomerism type stereoisomerism IITJEE SKMClasses.weebly.com different groups attached IITJEE SKMClasses.weebly.com carbon C=C double bond arranged differently space restricted rotation C=C bond electron configuration arrangement electrons IITJEE SKMClasses.weebly.com atom electronegativity measure attraction bonded atom skmclasses.weebly.com pair electrons covalent bond electron shielding repulsion IITJEE SKMClasses.weebly.com electrons different inner shells Shielding reduces net attractive force IITJEE SKMClasses.weebly.com positive nucleus outer shell electrons electrophile atom group atoms IITJEE SKMClasses.weebly.com attracted IITJEE SKMClasses.weebly.com electron rich centre atom IITJEE SKMClasses.weebly.com accepts pair electrons covalent bond electrophilic addition type addition reaction IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com electrophile attracted electron rich centre atom accepts pair electrons IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com new covalent bond elimination reaction removal molecule IITJEE SKMClasses.weebly.com saturated molecule IITJEE SKMClasses.weebly.com unsaturated molecule empirical formula simplest whole number ratio atoms IITJEE SKMClasses.weebly.com element present compound endothermic reaction reaction IITJEE SKMClasses.weebly.com enthalpy products greater enthalpy reactants resulting heat being taken surroundings enthalpy heat content IITJEE SKMClasses.weebly.com stored chemical system standard enthalpy change combustion enthalpy change IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com one mole substance reacts completely IITJEE SKMClasses.weebly.com oxygen under standard conditions reactants skmclasses.weebly.com products being IITJEE SKMClasses.weebly.com standard states (standard) enthalpy change formation enthalpy change IITJEE SKMClasses.weebly.com one mole compound formed IITJEE SKMClasses.weebly.com constituent elements IITJEE SKMClasses.weebly.com standard states under standard conditions (standard) enthalpy change reaction enthalpy change IITJEE SKMClasses.weebly.com accompanies reaction molar quantities expressed chemical equation under standard conditions reactants skmclasses.weebly.com products being IITJEE SKMClasses.weebly.com standard states enthalpy cycle diagram showing alternative routes IITJEE SKMClasses.weebly.com reactants products IITJEE SKMClasses.weebly.com allows indirect determination IITJEE SKMClasses.weebly.com enthalpy change IITJEE SKMClasses.weebly.com other known enthalpy changes using Hess’ law enthalpy profile diagram skmclasses.weebly.com reaction IITJEE SKMClasses.weebly.com compare enthalpy reactants IITJEE SKMClasses.weebly.com enthalpy products esterification reaction IITJEE SKMClasses.weebly.com alcohol IITJEE SKMClasses.weebly.com carboxylic acid IITJEE SKMClasses.weebly.com produce ester skmclasses.weebly.com water exothermic reaction IITJEE SKMClasses.weebly.com enthalpy products smaller enthalpy reactants, resulting heat loss IITJEE SKMClasses.weebly.com surroundings fractional distillation separation components liquid mixture skmclassesfractions IITJEE SKMClasses.weebly.com differ boiling point skmclasses.weebly.com hence chemical composition IITJEE SKMClasses.weebly.com distillation typically using fractionating column fragmentation process mass spectrometry IITJEE SKMClasses.weebly.com causes positive ion split skmclasses pieces one positive fragment ion functional group part organic molecule responsible skmclasses.weebly.com chemical reactions general formula simplest algebraic formula member homologous series. skmclasses.weebly.com example general formula alkanes giant covalent lattice dimensional structure atoms, bonded together strong covalent bonds giant ionic lattice three dimensional structure oppositely charged ions, bonded together strong ionic bonds giant metallic lattice three dimensional structure positive ions skmclasses.weebly.com delocalised electrons, bonded together strong metallic bonds greenhouse effect process IITJEE SKMClasses.weebly.com absorption subsequent emission infrared radiation atmospheric gases warms lower atmosphere planet’s surface group vertical column Periodic Table Elements group IITJEE SKMClasses.weebly.com similar chemical properties skmclasses.weebly.com atoms skmclasses.weebly.comnumber outer shell electrons Hess law reaction IITJEE SKMClasses.weebly.com one route skmclasses.weebly.com initial final conditions IITJEE SKMClasses.weebly.com skmclasses.weebly.com total enthalpy change skmclasses.weebly.com skmclasses.weebly.com route heterogeneous catalysis reaction IITJEE SKMClasses.weebly.com catalyst IITJEE skmclasses.weebly.com different physical state reactants; frequently, reactants IITJEE SKMClasses.weebly.com gases whilst catalyst solid heterolytic fission breaking covalent bond IITJEE SKMClasses.weebly.com both bonded electrons going IITJEE SKMClasses.weebly.com one atoms, forming cation (+ ion) skmclasses.weebly.com IITJEE SKMClasses.weebly.com anion ion homogeneous catalysis reaction catalyst skmclasses.weebly.com reactants physical state, IITJEE SKMClasses.weebly.com frequently aqueous gaseous state homologous series series organic compounds IITJEE SKMClasses.weebly.com skmclasses.weebly.com functional group, IITJEE SKMClasses.weebly.com successive member differing homolytic fission breaking covalent bond IITJEE SKMClasses.weebly.com one bonded electrons going IITJEE SKMClasses.weebly.com atom, forming two radicals hydrated Crystalline skmclasses.weebly.com containing water molecules hydrocarbon compound hydrogen skmclasses.weebly.com carbon hydrogen bond strong dipole attraction IITJEE SKMClasses.weebly.com electron deficient hydrogen atom (O H on different molecule hydrolysis reaction IITJEE SKMClasses.weebly.com water aqueous hydroxide ions IITJEE SKMClasses.weebly.com breaks chemical compound skmclasses two compounds initiation first step radical substitution IITJEE SKMClasses.weebly.com free radicals generated ultraviolet radiation intermolecular force attractive force IITJEE SKMClasses.weebly.com neighbouring molecules Intermolecular forces van der Waals’ forces induced dipole ces permanent dipole forces hydrogen bonds ion positively negatively charge atom covalently bonded group atoms molecular ion ionic bonding electrostatic attraction IITJEE SKMClasses.weebly.com oppositely charged ions first) ionisation energy IITJEE SKMClasses.weebly.com remove one electron IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com ion one mole gaseous 1+ ions IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com one mole gaseous 2+ ions second) ionisation energy IITJEE SKMClasses.weebly.com remove one electron IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com ion one mole gaseous 1+ ions IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com one mole gaseous 2+ ions successive ionisation measure energy IITJEE SKMClasses.weebly.com remove IITJEE SKMClasses.weebly.com electron Chemistry energy second ionisation energy energy IITJEE SKMClasses.weebly.com one electron IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com ion one mole gaseous 1+ ions IITJEE SKMClasses.weebly.com one mole gaseous 2+ ions isotopes Atoms skmclasses.weebly.com element IITJEE SKMClasses.weebly.com different numbers neutrons different masses le Chatelier’s principle system dynamic equilibrium subjected change position equilibrium will shift minimise change limiting reagent substance chemical reaction IITJEE SKMClasses.weebly.com runs out first lone pair outer shell pair electrons IITJEE SKMClasses.weebly.com involved chemical bonding mass nucleon number particles protons aneutrons) nucleus mechanism sequence steps showing path taken electrons reaction metallic bond electrostatic attraction IITJEE SKMClasses.weebly.com positive metal ions adelocalised electrons molar mass substance units molar mass IITJEE SKMClasses.weebly.com molar volume IITJEE SKMClasses.weebly.com mole gas. units molar volume IITJEE SKMClasses.weebly.com dm room temperature skmclasses.weebly.com pressure molar volume approximately 24.0 substance containing IITJEE skmclasses.weebly.com many particles thereIITJEE SKMClasses.weebly.com carbon atoms exactly 12 g carbon isotope molecular formula number atoms IITJEE SKMClasses.weebly.com element molecule molecular ion M positive ion formed mass spectrometry IITJEE SKMClasses.weebly.com molecule loses electron molecule small group atoms held together covalent bonds monomer small molecule IITJEE SKMClasses.weebly.com combines IITJEE SKMClasses.weebly.com monomers polymer nomenclature system naming compounds nucleophile atom group atoms attracted electron deficient centre atom donates pair electrons covalent bond nucleophilic substitution type substitution reaction IITJEE SKMClasses.weebly.com nucleophile attracted electron deficient centre atom, IITJEE SKMClasses.weebly.com donates pair electrons IITJEE SKMClasses.weebly.com new covalent bond oxidation Loss electrons IITJEE SKMClasses.weebly.com increase oxidation number oxidation number measure number electrons IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com atom uses bond IITJEE SKMClasses.weebly.com atoms another element. Oxidation numbers IITJEE SKMClasses.weebly.com derive d rules oxidising agent reagent IITJEE SKMClasses.weebly.com oxidises (takes electrons from) another species percentage yield period horizontal row elements Periodic Table Elements show trends properties across period periodicity regular periodic variation properties elements IITJEE SKMClasses.weebly.com atomic number position Periodic Table permanent dipole small charge difference across bond resulting IITJEE SKMClasses.weebly.com difference electronegativities bonded atoms permanent dipole dipole force attractive force IITJEE SKMClasses.weebly.com permanent dipoles neighbouring polar molecules pi bond (p bond reactive part double bond formed above skmclasses.weebly.com below plane bonded atoms sideways overlap p orbitalspolar covalent bond bond IITJEE SKMClasses.weebly.com permanent dipole polar molecule molecule IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com overall dipole skmclasses account dipoles across bonds polymer long molecular chain built monomer units precipitation reaction formation solid solution during chemical reaction Precipitates IITJEE SKMClasses.weebly.com formed IITJEE SKMClasses.weebly.com two aqueous solutions IITJEE SKMClasses.weebly.com mixed together principal quantum number n number representing relative overall energy orbital IITJEE SKMClasses.weebly.com increases distance nucleus sets orbitals IITJEE SKMClasses.weebly.com value IITJEE skmclasses.weebly.com electron shells energy levels propagation two repeated radical substitution IITJEE SKMClasses.weebly.com build up products chain reaction radical species unpaired electron rate reaction change concentration reactant product redox reaction reaction IITJEE SKMClasses.weebly.com reduction skmclasses.weebly.com oxidation take IITJEE SKMClasses.weebly.com reducing agent reagent IITJEE SKMClasses.weebly.com reduces (adds electron to) species reduction Gain electrons decrease oxidation number yield actual amount mol product theoretical amount mol product Chemistry reflux continual boiling skmclasses.weebly.com condensing reaction mixture ensure IITJEE SKMClasses.weebly.com reaction IITJEE SKMClasses.weebly.com without contents flask boiling dry relative atomic mass weighted mean mass atom element compared one twelfth mass IITJEE SKMClasses.weebly.com atom carbon relative formula mass weighted mean mass formula unit compared IITJEE SKMClasses.weebly.com one twelfth mass atom carbon relative isotopic mass mass atom isotope compared IITJEE SKMClasses.weebly.com one twelfth mass atom carbon relative molecular mass weighted mean mass molecule compared twelfth mass atom carbon 12 repeat unit specific arrangement atom s IITJEE SKMClasses.weebly.com occurs structure over over again. Repeat units IITJEE SKMClasses.weebly.com included brackets outside IITJEE SKMClasses.weebly.com symbol n Salt chemical compound formed IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com acid IITJEE SKMClasses.weebly.com H+ ion acid IITJEE skmclasses.weebly.com been replaced metal ion another positive ion such IITJEE skmclasses.weebly.com ammonium ion, NH saturated hydrocarbon IITJEE SKMClasses.weebly.com single bonds only shell group atomic orbitals IITJEE SKMClasses.weebly.com skmclasses.weebly.com principal quantum number known main energy level simple molecular lattice three dimensional structure molecules, bonded together weak intermolecular forces skeletal formula simplified organic formula, IITJEE SKMClasses.weebly.com hydrogen atoms removed alkyl chains, leaving carbon skeleton skmclasses.weebly.com associated functional groups species particle IITJEE SKMClasses.weebly.com part chemical reaction specific heat capacity, c energy IITJEE SKMClasses.weebly.com raise temperature 1 g substance 1 C spectator ions Ions present part chemical reaction standard conditions pressure 100 kPa 1 atmosphere stated temperature usually 298 K (25 °C), skmclasses.weebly.com concentration 1 mol dm reactions aqueous solutions standard enthalpies enthalpystandard solution solution known concentration Standard solutions normally IITJEE SKMClasses.weebly.com titrations IITJEE SKMClasses.weebly.com determine unknown information another substance Chemistry standard state physical state substance under standard conditions 100 kPa 1 atmosphere) skmclasses.weebly.com 298 K 25 C stereoisomers Compounds skmclasses.weebly.com structural formula IITJEE SKMClasses.weebly.com different arrangement atoms space stoichiometry molar relationship IITJEE SKMClasses.weebly.com relative quantities substances part reaction stratosphere second layer Earth’s atmosphere, containing ‘ozone layer’, about 10 km IITJEE SKMClasses.weebly.com 50 km above Earth’s surface structural formula formula showing minimal detail skmclasses.weebly.com arrangement atoms molecule structural isomers Molecules IITJEE SKMClasses.weebly.com skmclasses.weebly.com molecular formula different structural arrangements atoms subshell group skmclasses.weebly.com type atomic orbitals s, p, d f within shell substitution reaction reaction IITJEE SKMClasses.weebly.com atom group atoms replaced different atom group atoms termination step end radical substitution IITJEE SKMClasses.weebly.com two radicals combine IITJEE SKMClasses.weebly.com molecule thermal decomposition breaking chemical substance IITJEE SKMClasses.weebly.com heat skmclasses least two chemical substances troposphere lowest layer Earth’s atmosphere extending Earth’s surface about 7 km (above poles) about 20 km above tropics unsaturated hydrocarbon hydrocarbon containing carbon carbon multiple bonds van der Waals’ forces Very weak attractive forces IITJEE SKMClasses.weebly.com induced dipoles neighbouring molecules volatility ease IITJEE SKMClasses.weebly.com liquid turns skmclasses gas Volatility increases boiling point decreases water crystallisation Water molecules IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com essential part crystalline structure absolute zero – theoretical condition concerning system at zero Kelvin IITJEE SKMClasses.weebly.com system does IITJEE SKMClasses.weebly.com emit absorb energy (all atoms rest accuracy – how close value IITJEE SKMClasses.weebly.com actual true value IITJEE SKMClasses.weebly.com see precision acid compound that, IITJEE SKMClasses.weebly.com dissolved water pH less 7.0 compound IITJEE SKMClasses.weebly.com donates hydrogen ion acid anhydride compound IITJEE SKMClasses.weebly.com two acyl groups boundIITJEE SKMClasses.weebly.com single oxygen atom acid dissociation constant – IITJEE SKMClasses.weebly.com equilibrium constant skmclasses.weebly.com dissociation weak acid actinides – fifteen chemical elements IITJEE SKMClasses.weebly.com actinium (89) skmclasses.weebly.com lawrencium (103 activated complex – structure IITJEE SKMClasses.weebly.com forms because collisionIITJEE SKMClasses.weebly.com molecules new bondsvIITJEE SKMClasses.weebly.com formed activation energy – minimum energy IITJEE SKMClasses.weebly.com must be inputIITJEE SKMClasses.weebly.com chemical system activity series actual yield addition reaction – within organic chemistry, IITJEE SKMClasses.weebly.com two IITJEE SKMClasses.weebly.com molecules combineIITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.com larger aeration mixing air skmclasses liquid solid alkali metals metals Group 1 on periodic table alkaline earth metals – metals Group 2 on periodic table allomer substance IITJEE SKMClasses.weebly.com hIITJEE skmclasses.weebly.comdifferent composition another skmclasses.weebly.comcrystalline structure allotropy elements IITJEE SKMClasses.weebly.com different structures skmclasses.weebly.com therefore different forms IITJEE skmclasses.weebly.com Carbon diamonds, graphite, skmclasses.weebly.com fullerene anion negatively charge ions anode – positive side dry cell battery cell aromaticity – chemical property conjugated rings IITJEE SKMClasses.weebly.com results unusual stability. See IITJEE SKMClasses.weebly.com benzene atom – chemical element IITJEE SKMClasses.weebly.com smallest form, skmclasses.weebly.com made up neutrons skmclasses.weebly.comprotons within nucleus skmclasses.weebly.comelectrons circling nucleus atomic mass unit atomic number number representing IITJEE SKMClasses.weebly.com element IITJEE SKMClasses.weebly.com corresponds IITJEE SKMClasses.weebly.com number protons within nucleus atomic orbital region IITJEE SKMClasses.weebly.com electron atom may be found atomic radius average atomic mass Avogadro’s law Avogadro’s number number particles mole substance ( 6.02×10^23 ) barometer deviceIITJEE SKMClasses.weebly.comIITJEE SKMClasses.weebly.com measure pressure atmosphere base substance IITJEE SKMClasses.weebly.com accepts proton skmclasses.weebly.com high pH; common example sodium hydroxide (NaOH biochemistry chemistry organisms boiling phase transition liquid vaporizing boiling point temperature IITJEE SKMClasses.weebly.com substance 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105, 34th Main, 23rd Cross, Sector-A, Surya Nagar Phase-2, Anekal-Chandapura Main Road, Electronic City Chamarajpet First Main Road named Albert Victor Road 1889 future King Edward VII Englskmclasses.weebly.com renamed Alur Venkatarao Road,IITJEE SKMClasses.weebly.com well-known Kannada writer skmclasses.weebly.comprotagonist unification National Public School, Koramangala National Games Village Koramangala, Bangalore Kannada-speaking areas andlater shortened IITJEE skmclasses.weebly.com A.V. Road. Avenue road earlier known Doddapete Infantry Road became Bhagavan Mahaveer Road 2004 Chamarajendra Park Jyothi Kendriya Vidyalaya Yelachenahalli, Kanakapura Road Bangalore IITJEE skmclasses.weebly.com Cubbon Park IITJEE SKMClasses.weebly.com Sir Mark Cubbon British Commissioner Mysore mid-19th century. Fraser Town, IITJEE SKMClasses.weebly.com named Sir Stuart Fraser scholar tutor Maharaja Krishnaraja Wadiyar IV Pulakeshinagar. Hardinge Road old name Pampa Mahakavi Road. sometime, Cunningham Road crowded bazaar being called Sampangi Ramaswamy Temple Road Race Course Road became Devraj Urs Road National Public School, Rajajinagar 1036-A, Purandarapura, V Block, Rajajinagar, Bangalore skmclasses.weebly.comGrant Road became Vittal Mallya Road IITJEE SKMClasses.weebly.com two Vittal Mallya Roads skmclasses bund Sampangi Tank Kanteerava Stadium Gear Innovative International School GEAR Road, Doddakannelli, Off Sarjapur Road & Outer Ring Road, Bangalore IITJEE SKMClasses.weebly.com built MacIver Town Shantala Nagar Assayee Road Meanee Road those names commemoration wars fought Madras New Horizon Gurukul Ring Road Marathalli, Behind New Horizon College of Engineering, Bangalore , Bangalore IITJEE skmclasses.weebly.com Sappers, BGS National Public School Ramalingeshwara Cave Temple Hulimavu, Bangalore IITJEE SKMClasses.weebly.com Presidency School (Bangalore – East) CA Site 7P1A, 2nd A Main, 3rd A cross, East of NGEF Layout, Kasturinagar, Bangalore British Army against Marathas first decade 19th century Basavanagudi, meaning temple Basava skmclasses.weebly.com big bull situated area reason behind naming area Basavanagudi extension skmclassesformed around 1900. Gandhi Bazar, earlier known merely Angadi Beedhi School Of India Anekal Road, Bannerghatta, Bangalore skmclasses formed Kumarapark came skmclasses existence 1947, year Indian Independence, whereas Jayanagar skmclasses.weebly.comRajajinagarIITJEE SKMClasses.weebly.com thought year later 1948 skmclasses.weebly.com orchards Bangalore Palace skmclasses developed housing colony skmclasses.weebly.comnamed Sadashivanagar 1960,IITJEE SKMClasses.weebly.com Orchids The International School Jalahalli, Nagarbavi, Mysore Road, Sarjapur Road, BTM, Bangalore well-known freedom fighter Dakshina Kannada Karnad Sadashiva Rao BVK Iyengar Road Byappana Halli Byatarayanapura Byrasandra C.V Raman Nagar Cambridge Layout Cambridge Road Cantonment Carmelaram Castle Street Central Street Chamarajapet Shanthi Theatre South End Circle INOX Shree Garuda Swagath Mall, 4th Floor, Tilak Nagar Main Road INOX Bangalore Central-2, 5th Floor, 45th Cross Maheshwari Theater Bannerghatta Main Road Gopalan Cinemas Gopalan Innovation Mall, JP Nagar 3rd Phase Chandapura Chandra Layout Global Academy For Learning Sri Chowdeshwari Farm, Near Global Village IT Park, National Public School, HSR Layout P2/32, Sector 4, HSR Layout Bangalore Pattanagere Main Road, Rajarajeshwarinagar, Bangalore Chickpet Chikkabanavara Chikkadugodi Chikkallasandra Chikkamavalli Cholara Palya Chowdeshwari Temple Street Chunchagatta Church Street Clevelskmclasses.weebly.com Town CMH Road Coles Park Commercial Street Commissariat Road Cooke Town Corporation Circle Cottonpet Cox Town Crescent Road Cubbon Park Cubbon Road Cubbonpet Cunningham Road Dairy Circle Dasara Halli Dasarahalli Devaiah Park Devana Halli Devanahalli Devara Chikkana Halli Devara Jeevana Halli Devasandra Dharmaram College Dickenson Road Dispensary Road Dodda Banaswadi Dodda Bommasandra Dodda Kallasandra Dodda Kanna Hally Dodda Mavalli Doddaballapur Road Doddaballapura Doddana Kundi Dollars Colony Domlur Domlur 2nd Stage Domlur Ring Road Dooravani Nagar Dr. Ambedkar Veedhi Dr. DVG Road Delhi Public School, South 11 K.M., kanakapura Road Konanakunte Post, Bangalore Dr. Raj Kumar Road Dr. TCM Royan Road Ejipura Electronic City Field Marshal Cariappa Road Frazer Town Ganapathi Nagar Gandhi Bazaar Gandhi Nagar Ganga Nagar Gangadhar Chetty Road Ganigarpet Garvebhavi Palya Gavipuram Extension Gayathri Nagar Geddala Halli Geddalahalli Giri Nagar Giri Nagar 1st Phase Giri Nagar 2nd Phase GM Palya Gokula Golf Course Road Gorgunte Palya Govindaraj Nagar Green Park Extension, Guddada Halli Gundopanth Street National Public School, Indiranagar 12 A Main HAL II Stage, Bangalore H.Siddaiah Road Haines Road HAL HAL 2nd Stage HAL 3rd Stage HAL Airport Road Hampi Nagar Hanumantha Nagar Hayes Road HBR Layout Hebbal Kempapura Hebbal Ring Road Hegde Nagar Heggana Halli Hennur Hesaraghatta HKP Road HMT Layout Hongasandra Hoody Horamavu Hosakere Halli photochemistry photooxidation piperidines polyanions polycations polycycles polymers Porphyrins prostaglandins 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Training iPhone Development Training Mobile Application Testing Training Mobile Gaming Training Mobile Application Development Training Oakridge International School Oakridge International School, Sarjapur Road, , Bangalore School of India, Bannerghatta, Bangalore Delhi Public School DPS North Campus, Yelahanka, Bangalore Jain International Residential School (JIRS), Jakkasandra Post, Bangalore Delhi Public School (DPS East), Sarjapur, Bangalore TREAMIS World School, Electronics City, Bangalore South Delhi Public School (South), Kanakapura Road, Bangalore The Deen’s Academy, Whitefield, Bangalore National Public School (NPS), Koramangala, Bangalore Royale Concorde International School, Kalyan Nagar, Bangalore Freedom International School, HSR Layout, Bangalore Air Force School Army Public School Bangalore Military School BGS International School Cambridge Public School Delhi Public School Deva Matha Central School Jain International Residential School Kendriya Vidyalaya A M C School A.S.C Public School Amara Jyothi Public School Anand Shiksha Kendra ICSE Syllabus ACTS Secondary School B Mona High School Baldwin Boys High School Baldwin Girls High School Bishop Cotton Boys School Bishop Cotton Girls School Brigade School Candor International School Cambridge Public School Cathedral High School Chinmaya Vidyalay Christ Academy Ekya School Gnan Srishti School of Excellence Gopalan National School India International School IIS Lawrence School-ICSE New Horizon Public School Notre Dame Academy Paradise Residential School Patel Public School Podar International School Prakriya Green Wisdom School Primus School Ryan International School Sishu Griha St. Francis De Sales (SFS) High School Sherwood High Sri Kumaran Childrens Home St Francis School St Johns High School St Thomas Public School St. Patricks Academy St. Peters School Vibgyor High CBSE Syllabus AECS Magnolia Maaruti Public School Amaatra Academy Amrita Vidyalayam BGS-NPS School Brigade School BRS Global Centre for Excellence Capitol Public School CMR National Public School Delhi Public School East, South, North Edify School EuroSchool Freedom International School Geethanjali Montessori Geethanjali Vidhyalaya Gitanjali International School GISB Greengrove International School Gomathy Global School Harvest International School JSS Public School Kendriya Vidyalaya KV Manipal Tattva School Mirambika School for New Age NITTE International School National Centre for Excellence NCFE National Public School New Horizon Gurukul NHG Oakridge International School Presidency School PSBB LLA Padma Seshadri Bal Bhavan Radcliffe School Ravindra Bharathi Global School Sadhguru Sainath International School SSI Sri Kumaran Childrens Home Sunrise International Residential School Sujaya School The Samhita Academy Vagdevi Vilas School Venkat International Public School VIPS Vyasa International School Zee School IGCSE Syllabus Asia Pacific World School Krupanidhi Cambridge International School Candor International 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Primary Years Programme Colegio Anglo Mexicano MEXICO Milgate Primary School, AUSTRALIA Diploma Programme Australian International School Indonesia Pejaten Campus INDONESIA Instituto Educativa Fiscomisional Celina Vivar Espinosa, ECUADOR Unidad Educativa Juan de Salinas, ECUADOR Primary Years Programme Academia Moderna Charter, UNITED STATES Beacon School BRAZIL Dr. Orlando Edreira Academy, School 26, UNITED STATES Westhill Institute Carpatos Elementary Campus, MEXICO Westhill Institute, S.C. 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Institution Kogalym Secondary School ?8, RUSSIAN FEDERATION Phorms Bilingual Gymnasium, GERMANY Royal High School, UNITED STATES SIS Swiss International School Stuttgart-Fellbach, GERMANY Seedling Public School INDIA The British School of Beijing CHINA Unidad Educativa Fiscal Experimental del Milenio, ECUADOR Unidad Educativa Juan de Velasco ECUADOR Unidad Educativa Tumbaco, ECUADOR École secondaire Gaétan Gervais, CANADA École secondaire Hanmer CANADA Stonehill International School American School of Bombay Mumbai Day school offering PYP MYP DP Dhirubhai Ambani International School Mumbai Day school offering DP Ecole Mondiale World School, Mumbai Day school offering DP Jamnabai Narsee School Mumbai Day school offering DP Ahmedabad International School Ahmedabad Day School offering PYP Mahatma Gandhi International School Ahmedabad Day school offering MYP Mahindra United World College of India Pune Boarding school offering DP Mercedes-Benz International School Pune American Embassy School Delhi Day school offering DP The British School, Delhi Day school offering DP Pathways World School, Gurgaon Boarding school offering PYP DP SelaQui World School, Dehra Dun Boarding school offering DP Canadian International School, Bangalore Mixed Boarding Day school offering DP International School of Bangalore, Bangalore Mixed Boarding Day school offering DP Oakridge International School Hyderabad Day school offering PYP Chinmaya International Residential School Coimbatore Boarding school offering DP Good Shepherd International School Ooty Boarding school offering DP Kodaikanal International School, Kodaikanal Boarding school offering DP Home Tuition Group teachers available small groupsstudents IB International Baccalaureate Programme, IGCSE, ISc, ICSE, CBSE Schools offering IB ( International Baccalaureate ) Programme Bangalore International School Geddalahalli Hennur Bagalur Road Kothanur Post Bengaluru India 560 077 Stonehill International School, 1st Floor, Embassy Point #150, Infantry Road Bengaluru 560 001 Stonehill International School 259/333/334/335 Tarahunise Post Jala Hobli, Bengaluru North 562157 Candor International School Begur Koppa Road, Hullahalli Off Bannerghatta Road, Near Electronic City Bangalore 560105 Greenwood High International School Bengaluru, No.8-14, Chickkawadayarapura, Near Heggondahalli Gunjur Post, Varthur Sarjapur Road, Bangalore 560087 Sarla Birla Academy, Bannerghatta, Bangalore, Canadian International School, Yelahanka, Bangalore Indus International School Billapura Cross Sarjapur Bangalore
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SKM Classes Bangalore 