NCERT CBSE Standard 11 Chemistry Chapter 5 States Of Matter Liquid Van Der Waal Forces Osmotic Pressure

Solutions to Chapter 5 :

States Of Matter

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31a Frozen tree in my backyard

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31a Charles law

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Untitled

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Gyan Question :

36a ratio of densities

Ans : ( b )

36b ratio of densities

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Gyan Question :

32a Equal masses of methane and oxygen

Ans :  ( a )

32b Equal masses of methane and oxygen

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31b Grahams law of diffusion

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31b Aurora in Lapland

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Gyan Question :

32a Ethane and hydrogen

Ans : ( d )

32b Ethane and hydrogen

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31c Kinetic theory of gases

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31c Dog sledge

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Gyan Question :

37a Gaseous mixture of He and Oxygen

Ans : ( a )

37b Gaseous mixture of He and Oxygen

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31a Critical temperature pressure inversion temperature

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31d Will attack you in Finland

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31d Vander waals Equation of state 31d Vander waals Equation of statee

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Gyan Question :

38a the density of a gas

Ans : ( a )

38b the density of a gas

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Tigon Liger 4 with mane

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Gyan Question

33a which all correctly represts variation of density

Ans :  ( a )

33b which all correctly represts variation of density

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Gyan Question

39a Density of a gas at STP

Ans : ( b )

39b Density of a gas at STP

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31e Atlantis on carrier

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31f Reduction of Van Der waals Gas eqn to virial equation

31g Reduction of Van Der waals Gas eqn to virial equation

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Gyan Question

40a Mixture of ammonia and N2H4

Ans : ( c )

40b Mixture of ammonia and N2H4

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32a Colourful river

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Gyan Question :

34a The density of neon will be highest at

Ans : ( b )

34b The density of neon will be highest at

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31a Colourful trees

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Gyan Question :

35a The volume of a gas

Ans : ( d )

35b The volume of a gas

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Are these chicken flowers

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Van Der Waal forces with cubic equations

with n moles it is given as

12a Van der waals equation for n mole of gas

So Van der waal’s equation with 1 mole is

12b Van der waals equation for 1 mole of gas

Isotherms changes as

12c Van der waals equation for 1 mole of gas

So the Vander Waal’s equation can be multiplied and modified as

12d Van der waals equation for 1 mole of gas

The explanation of the constants

12e Van der waals equation for 1 mole of gas 12f Van der waals equation for 1 mole of gas 12h Van der waals equation for 1 mole of gas 12j Van der waals equation for 1 mole of gas 12l Van der waals equation for 1 mole of gas 12m Van der waals equation for 1 mole of gas

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12n Van der waals equation for 1 mole of gas

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12p Van der waals equation for 1 mole of gas

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12r Van der waals equation for 1 mole of gas

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12t Van der waals equation for 1 mole of gas

Critical constants of gases

12v Van der waals equation for 1 mole of gas

Derivation of Cp-Cv

12w Cp-Cv Van der waals equation for 1 mole of gas

PET Kerala Question

12x PET Kerala a by b ration Vander waal forces 13a At high pressure Van der waal equation changes to

13b At high pressure Van der waal equation changes to

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Liger Tiger Tigon 3

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Gyan Question :

36a For a fixed mass of a gas

Ans : ( d )

36b For a fixed mass of a gas

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Gyan Question :

32a at 100 deg centrigrade density of water

Ans : ( c )

32b at 100 deg centrigrade density of water

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My garden blue pink magenta yellow white flowers

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Gyan Question

37a Dimensionally correct expression

Ans : ( d )

37b Dimensionally correct expression

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steep down stairs

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Gyan Question

31a density of nitrogen will be largest

Ans : ( b )

31b density of nitrogen will be largest

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Gyan Question

33a which of the following vol temp

Ans : ( c )

33b which of the following vol temp

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Tiger fighting Liger

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Gyan Question

35a bottle of dry ammonia and dry  hydrogen

Ans : ( b )

35b bottle of dry ammonia and dry  hydrogen

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The next chapter Solution is at http://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-6-thermodynamics-thermochemistry/
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The previous chapter Solution is at https://zookeepersblog.wordpress.com/ncert-cbse-standard-11-chemistry-chapter-4-chemical-bonding-and-molecular-structure/
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Gyan Question :

32a volume is increased by

Ans : ( b )

32b volume is increased by

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The snowflake falls, yet lays not long Its feath’ry grasp on Mother Earth Ere Sun returns it to the vapors Whence it came, Or to waters tumbling down the rocky slope.

Rod O’ Connor

INTRODUCTION

In previous units we have learnt about the properties related to single particle of matter, such as atomic size, ionization enthalpy, electronic charge density, molecular shape and polarity, etc. Most of the observable characteristics of chemical systems with which we are familiar represent bulk properties of matter, i.e., the properties associated with a collection of a large number of atoms, ions or molecules. For example, an individual molecule of a liquid does not boil but the bulk boils. Collection of water molecules have wetting properties; individual molecules do not wet. Water can exist as ice, which is a solid; it can exist as liquid; or it can exist in the gaseous state as water vapour or steam. Physical properties of ice, water and steam are very different. In all the three states of water chemical composition of water remains the same i.e., H2O. Characteristics of the three states of water depend on the energies of molecules and on the manner in which water molecules aggregate. Same is true for other substances also.

Chemical properties of a substance do not change with the change of its physical state; but rate of chemical reactions do depend upon the physical state. Many times in calculations while dealing with data of experiments we require knowledge of the state of matter. Therefore, it becomes necessary for a chemist to know the physical laws which govern the behaviour of matter in different states. In this unit, we will learn more about these three physical states of matter particularly liquid and gaseous states. To begin with, it is necessary to understand the nature of intermolecular forces, molecular interactions and effect of thermal energy on the motion of particles because a balance between these determines the state of a substance.

5.1 INTERMOLECULAR FORCES

Intermolecular forces are the forces of attraction and repulsion between interacting particles (atoms and molecules). This termdoes not include the electrostatic forces that exist between the two oppositely charged ions and the forces that hold atoms of a molecule together i.e., covalent bonds. Attractive intermolecular forces are known as van der Waals forces, in honour of Dutch scientist Johannes vander Waals (1837-1923), who explained the deviation of real gases from the ideal behaviour through these forces. We will learn about this later in this unit. vander Waals forces vary considerably in magnitude and include dispersion forces or London forces, dipole-dipole forces, and dipole-induced dipole forces. A particularly strong type of dipole-dipole interaction is hydrogen bonding. Only a few elements can participate in hydrogen bond formation, therefore it is treated as a separate category. We have already learnt about this interaction in Unit 4.

At this point, it is important to note that attractive forces between an ion and a dipole are known as ion-dipole forces and these are not van der Waals forces. We will now learn about different types of vander Waals forces.

5.1.1 Dispersion Forces or London Forces

Atoms and nonpolar molecules are electrically symmetrical and have no dipole moment because their electronic charge cloud is symmetrically distributed. But a dipole may develop momentarily even in such atoms and molecules. This can be understood as follows.Suppose we have two atoms ‘A’ and ‘B’ in the close vicinity of each other (Fig. 5.1a). It may so happen that momentarily electronic charge distribution in one of the atoms, say ‘A’, becomes unsymmetrical i.e., the charge cloud is more on one side than the other (Fig. 5.1 b and c). This results in the development of instantaneous dipole on the atom ‘A’ for a very short time. This instantaneous or transient dipole distorts the electron density of the other atom ‘B’, which is close to it and as a consequence a dipole is induced in the atom ‘B’.

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31a Symmetrical distribution

32a Disperson forces

24a 400 women disguised themselves to fight

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The temporary dipoles of atom ‘A’ and ‘B’ attract each other. Similarly temporary dipoles are induced in molecules also. This force of attraction was first proposed by the German physicist Fritz London, and for this reason force of attraction between two temporary dipoles is known as London force. Another name for this force is dispersion force. These forces are always attractive and interaction energy is inversely proportional to the sixth power of the distance between two interacting particles (i.e., 1/r6 where r is the distance between two particles). These forces are important only at short distances (~500 pm) and their magnitude depends on the polarisability of the particle.

5.1.2 Dipole – Dipole Forces

Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of the dipoles possess “partial charges” and these charges are shown by Greek letter delta (δ). Partial charges are always less than the unit electronic charge (1.610–-19 C). The polar molecules interact with neighbouring molecules. Fig 5.2 (a) shows electron cloud distribution in the dipole of hydrogen chloride and Fig. 5.2 (b) shows dipole-dipole interaction between two HCl molecules. This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved. The attractive force decreases with the increase of distance between the dipoles. As in the above case here also, the interaction energy is inversely proportional to distance between polar molecules. Dipole-dipole interaction energy between stationary polar molecules (as in solids) is proportional to 1/r3 and that between rotating polar molecules is proportional to 1/r 6, where r is the distance between polar molecules. Besides dipole-dipole interaction, polar molecules can interact by London forces also. Thus cumulative effect is that the total of intermolecular forces in polar molecules increase.

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31a Fig 5.2 Distribution of electron cloud

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5.1.3 Dipole-Induced Dipole Forces

This type of attractive forces operate between the polar molecules having permanent dipole and the molecules lacking permanent dipole. Permanent dipole of the polar molecule induces dipole on the electrically neutral molecule by deforming its electronic cloud
(Fig. 5.3). Thus an induced dipole is developed in the other molecule. In this case also interaction energy is proportional to 1/r6 where r is the distance between two molecules. Induced dipole moment depends upon the dipole moment present in the permanent dipole and the polarisability of the electrically neutral molecule. We have already learnt in Unit 4 that molecules of larger size can be easily polarized. High polarisability increases the strength of attractive interactions.In this case also cumulative effect of dispersion forces and dipole-induced dipole interactions exists.

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31b Fig 5.3 Dipole

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5.1.4 Hydrogen bond

As already mentioned in section (5.1); this is special case of dipole-dipole interaction. We have already learnt about this in Unit 4. This is found in the molecules in which highly polar N-H, O-H or H-F bonds are present. Although hydrogen bonding is regarded as being limited to N, O and F; but species such as Cl- may also participate in hydrogen bonding. Energy of hydrogen bond varies between 10 to 100 kJ mol-1. This is quite a significant amount of energy; therefore, hydrogen bonds are powerful force in determining the structure and properties of many compounds, for example proteins and nucleic acids. Strength of the hydrogen bond is determined by thecoulombic interaction between the lone-pair electrons of the electronegative atom of one molecule and the hydrogen atom of othermolecule. Following diagram shows the formation of hydrogen bond.

δ+ δ− δ+ δ−
H− F…H− F

Intermolecular forces discussed so far are all attractive. Molecules also exert repulsive forces on one another. When two molecules are brought into close contact with each other, the repulsion between the electron clouds and that between the nuclei of two molecules comes into play. Magnitude of the repulsion rises very rapidly as the distance separating the molecules decreases. This is the reason that liquids and solids are hard to compress. In these states molecules are already in close contact; therefore they resist further compression; as that would result in the increase of repulsive interactions.

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51b osmotic pressure 51c osmotic pressure 51d osmotic pressure 51e osmotic pressure 51f osmotic pressure 51g osmotic pressure 51h osmotic pressure 51i osmotic pressure 51j osmotic pressure 51k osmotic pressure 51l osmotic pressure and vant hoff factor 52a IIT Gandhinagar 52b Vapour pressure problem 53a Insect circuit 53b Density of KOH solution 53c Density of KOH solution

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5.2 THERMAL ENERGY

Thermal energy is the energy of a body arising from motion of its atoms or molecules. It is directly proportional to the temperature of the substance. It is the measure of average kinetic energy of the particles of the matter and is thus responsible for movement of particles. This movement of particles is called thermal motion.

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Gyan Question :

37a grams of helium diffuse

Ans : ( d )

37b grams of helium diffuse

37c grams of helium diffuse

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5.3 INTERMOLECULAR FORCES vs THERMAL INTERACTIONS

We have already learnt that intermolecular forces tend to keep the molecules together but thermal energy of the molecules tends to keep them apart. Three states of matter are the result of balance between intermolecular forces and the thermal energy of the molecules.

When molecular interactions are very weak, molecules do not cling together to make liquid or solid unless thermal energy is reduced by lowering the temperature. Gases do not liquify on compression only, although molecules come very close to each other and intermolecular forces operate to the maximum.However, when thermal energy of molecules is reduced by lowering the temperature; the gases can be very easily liquified. Predominance of thermal energy and the molecular interaction energy of a substance in three states is depicted as follows:

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31c Predominance of thermal energy

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We have already learnt the cause for the existence of the three states of matter. Now we will learn more about gaseous and liquid states and the laws which govern the behaviour of matter in these states. We shall deal with the solid state in class XII.

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Gyan Question :

38a The volume X of H2 gas effuses

Ans : ( b )

38b The volume X of H2 gas effuses

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5.4 The Gaseoous State

This is the simplest state of matter. Throughout our life we remain immersed in the ocean of air which is a mixture of gases. We spend our life in the lowermost layer of the atmosphere called troposphere, which is held to the surface of the earth by gravitational force. The thin layer of atmosphere is vital to our life. It shields us from harmful radiations and contains substances like dioxygen, dinitrogen, carbon dioxide, water vapour, etc.

Let us now focus our attention on the behaviour of substances which exist in the gaseous state under normal conditions of temperature and pressure. A look at the periodic table shows that only eleven elements exist as gases under normal conditions (Fig 5.4).

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31d Fog 5.4 Eleven elements that exist as gases

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Gyan Question

51a Pilot was sucked out of plane

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35a the degree of dissociation in the reaction

Ans : ( a )

35b the degree of dissociation in the reaction

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The gaseous state is characterized by the following physical properties.

• Gases are highly compressible.
• Gases exert pressure equally in all directions.
• Gases have much lower density than the solids and liquids.
• The volume and the shape of gases are not fixed. These assume volume and shape of the container.
• Gases mix evenly and completely in all proportions without any mechanical aid.

Simplicity of gases is due to the fact that the forces of interaction between their molecules are negligible. Their behaviour is governed by same general laws, which were discovered as a result of their experimental studies. These laws are relationships between measurable properties of gases. Some of these properties like pressure, volume, temperature and mass are very important because relationships between these variables describe state of the gas. Interdependence of these variables leads to the formulation of gas laws.In the next section we will learn about gas laws.

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Gyan Question

39a According to grahams law

Ans : ( c )

39b According to grahams law

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5.5 THE GAS LAWS

The gas laws which we will study now are the result of research carried on for several centuries on the physical properties of gases.The first reliable measurement on properties of gases was made by Anglo-Irish scientist Robert Boyle in 1662. The law which he formulated is known as Boyle’s Law. Later on attempts to fly in air with the help of hot air balloons motivated Jaccques Charles and Joseph Lewis Gay Lussac to discover additional gas laws. Contribution from Avogadro and others provided lot of information about gaseous state.

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Gyan :

Compression factor of an ideal gas is 1

Question

31a The compression factor of an ideal gas

Ans : ( c ) it is 1 so remains constant with change in temperature

The value of compression factor 31b compression factor is 1

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5.5.1 Boyle’s Law ( Pressure – Volume Relationship)

On the basis of his experiments, Robert Boyle reached to the conclusion that at constant temperature, the pressure of a fixed
amount (i.e., number of moles n) of gas varies inversely with its volume. This is known as Boyle’s law. Mathematically, it can be written as

p ∝ 1/V   ( at constant T and n)  —————————(5.1)
⇒ p = k1 (1/V )——————————–(5.2)

where k1 is the proportionality constant. The value of constant k1 depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed.

On rearranging equation (5.2) we obtain
pV = k1 ———————————(5.3)

It means that at constant temperature, product of pressure and volume of a fixed amount of gas is constant. If a fixed amount of gas at constant temperature T occupying volume V1 at pressure p1 undergoes expansion, so that volume becomes V2 and pressure becomes p2, then according to Boyle’s law :
p1V1=p2V2= constant————————————– (5.4)

⇒p1/p2 = V2/V1 —————————————(5.5)

Figure 5.5 shows two conventional ways of graphically presenting Boyle’s law. Fig. 5.5 (a) is the graph of equation (5.3) at different temperatures. The value of k1 for each curve is different because for a given mass of gas, it varies only with temperature. Each curve corresponds to a different constant temperature and is known as an isotherm (constant temperature plot). Higher curves correspond to higher temperature. It should be noted that volume of the gas doubles if pressure is halved. Table 5.1 gives effect of pressure on volume of 0.09 mol of CO2 at 300 K.

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31e Fig 5.5 Graph of Pressure

31f Table 5.1

31g Fig 5.5 graph of pressure

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Gyan Question

40a degree of dissociation alpha

Ans : ( a )

40b degree of dissociation alpha

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Experiments of Boyle, in a quantitative manner prove that gases are highly compressible because when a given mass of a gas is compressed, the same number of molecules occupy a smaller space. This means that gases become denser at high pressure. A relationship can be obtained between density and pressure of a gas by using Boyle’s law :

By definition, density ‘d’ is related to the mass ‘m’ and the volume ‘V’ by the relation d = m/V. If we put value of V in this equation from Boyle’s law equation, we obtain the relationship.

d = (m/k1) p = k’p

This shows that at a constant temperature, pressure is directly proportional to the density of a fixed mass of the gas.

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Gyan Question

31a 4 isto 1 mixture of He and methane

Ans : ( d )

31b 4 isto 1 mixture of He and methane

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Problem 5.1

A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds 0.2 bar. If at 1 bar pressure the gas occupies 2.27 L volume, upto what volume can the balloon be expanded ?

Solution

According to Boyle’s Law p1V1 =p2V2
if p1 is 1 bar, V1 will be 2.27L
if p2 = 0.2 bar, then V2=p1V1/P2
⇒V2 =1 bar×2.27L/0.2bar=11.35L

Since balloon bursts at 0.2 bar pressure,the volume of balloon should be less than 11.35 L.

5.5.2 Charles’ Law  (Temperature – Volume Relationship)

Charles and Gay Lussac performed several experiments on gases independently to improve upon hot air balloon technology. Their investigations showed that for a fixed mass of a gas at constant pressure, volume of a gas increases on increasing temperature and decreases on cooling. They found that for each degree rise in temperature, volume of a gas increases by 1/273.15 of the original
volume of the gas at 0 °C. Thus if volumes of the gas at 0 °C and at t °C are Voand Vt respectively, then

Vt = Vo + (t/273.15) Vo

⇒Vt=Vo(1+(t/273.15))

⇒Vt=Vo(273.15+(t/273.15)) —————————– (5.6)

At this stage, we define a new scale of temperature such that t °C on new scale is given by T = 273.15 + t and 0 °C will be given by T0 = 273.15. This new temperature scale is called the Kelvin temperature scale or Absolute temperature scale.

Thus 0°C on the celsius scale is equal to 273.15 K at the absolute scale. Note that degree sign is not used while writing the temperature in absolute temperature scale, i.e., Kelvin scale. Kelvin scale of temperature is also called Thermodynamic scale of temperature and is used in all scientific works.

Thus we add 273 (more precisely 273.15) to the celsius temperature to obtain temperature at Kelvin scale.

If we write Tt = 273.15 + t and T0 = 273.15

in the equation (5.6) we obtain the relationship

Vt= Vo(Tt/To)

⇒Vt/Vo=Tt/To ———————- (5.7)

Thus we can write a general equation as follows.

V2/V1 = T2/T1 ——————————-(5.8)

⇒V1/T1 = V2/T2

⇒V/T = constant= k2————————- (5.9)

Thus V = k2 T ——————————– (5.10)

The value of constant k2 is determined by the pressure of the gas, its amount and the units in which volume V is expressed.

Equation (5.10) is the mathematical expression for Charles’ law, which states that pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature. Charles found that for all gases, at any given pressure, graph of volume vs temperature (in celsius) is a straight line and on extending to zero volume, each line intercepts the temperature axis at -273.15 °C. Slopes of lines obtained at different pressure are different but at zero volume all the lines meet the temperature axis at -273.15 °C (Fig. 5.6).

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31h Fig 5.6 Volume vs Temp

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Gyan Question

32a methane and helium are allowed to diffuse

Ans : ( d )

32b methane and helium are allowed to diffuse

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Each line of the volume vs temperature graph is called isobar.

Observations of Charles can be interpreted if we put the value of t in equation (5.6) as -273.15 °C. We can see that the volume of the gas at -273.15 °C will be zero. This means that gas will not exist. In fact all the gases get liquified before this temperature is reached. The lowest hypothetical or imaginary temperature at which gases are supposed to occupy zero volume is called Absolute zero. All gases obey Charles’ law at very low pressures and high  temperatures.

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Gyan Question

33a when an ideal gas undergoes unrestrained expansion

Ans : ( b )

The molecules of an ideal gas is assumed not to exert any force of attraction in between molecules.

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Problem 5.2

On a ship sailing in pacific ocean where temperature is 23.4 °C , a balloon is filled with 2 L air. What will be the volume of the balloon when the ship reaches Indian ocean, where temperature is 26.1°C ?

Solution

V1 = 2L
T1 = (23.4 + 273)K = 296.4 K

T2 = 26.1 + 273 = 299.1 K

From Charles law
V1/T1=V2/T2

⇒V2=(V1T2)/T1
⇒V2=2L × 299.1K / 296.4K
=2L × 1.009
=2.018L

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Gyan Question

36a rate of diffusion of methane

Ans : ( a )

36b rate of diffusion of methane

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5.5.3 Gay Lussac’s Law (Pressure-Temperature Relationship)

Pressure in well inflated tyres of automobiles is almost constant, but on a hot summer day this increases considerably and tyre may
burst if pressure is not adjusted properly. During winters, on a cold morning one may find the pressure in the tyres of a vehicle
decreased considerably. The mathematical relationship between pressure and temperature was given by Joseph Gay Lussac
and is known as Gay Lussac’s law. It states that at constant volume, pressure of a fixed amount of a gas varies directly with the temperature. Mathematically,

p ∝ T
⇒p/T = constant = k3

This relationship can be derived from Boyle’s law and Charles’ Law. Pressure vs temperature (Kelvin) graph at constant molar volume is shown in Fig. 5.7. Each line of this graph is called isochore.

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31i Fig 5.7 Pressure vs temp

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Gyan Question

34a According to Kinetic theory of gases

Ans : ( d )

The mean kinetic energy of molecules is proportional to Kelvin temperature

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5.5.4 Avogadro Law (Volume – Amount Relationship)

In 1811 Italian scientist Amedeo Avogadro tried to combine conclusions of Dalton’s atomic theory and Gay Lussac’s law of
combining volumes (Unit 1) which is now known as Avogadro law. It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. This means that as long as the temperature and pressure remain constant, the volume depends upon number of molecules of the gas or in other words amount of the gas. Mathematically we can write

V ∝ n where n is the number of moles of the gas.

⇒V = k4 n ——————————– (5.11)

The number of molecules in one mole of a gas has been determined to be 6.022 x 1023 and is known as Avogadro constant. You will find that this is the same number which we came across while discussing definition of a ‘mole’ (Unit 1).

Since volume of a gas is directly proportional to the number of moles; one mole of each gas at standard temperature and pressure (STP)* will have same volume. Standard temperature and pressure means 273.15 K (0°C) temperature and 1 bar (i.e., exactly 105 pascal) pressure. These values approximate freezing temperature of water and atmospheric pressure at sea level. At STP molar volume of an ideal gas or a combination of ideal gases is 22.71098 L mol-1.

Molar volume of some gases is given in (Table 5.2).

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31j Table 5.2

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Number of moles of gas can be calculated as follows
n=m/M ——————————————– (5.12)
Where m=mass of the gas under investigation and M=molar mass
Thus,
V=k4(m/M) ———————————(5.13)

Equation (5.13) can be rearranged as follows:
M=k4m/V=k4d —————– (5.14)

The previous standard is still often used, and applies to all chemistry data more than decade old. In this definition STP
denotes the same temperature of 0°C (273.15 K), but a slightly higher pressure of 1 atm (101.325 kPa). One mole of any gas of a combination of gases occupies 22.413996 L of volume at STP.Standard ambient temperature and pressure (SATP), conditions are also used in some scientific works. SATP conditions means 298.15 K and 1 bar (i.e., exactly 105 Pa). At SATP (1 bar and 298.15 K), the molar volume of an ideal gas is 24.789 L mol-1 .

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Gyan Question

35a At constant volume

Ans : ( a )

35b At constant volume

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Here ‘d’ is the density of the gas. We can conclude from equation (5.14) that the density of a gas is directly proportional to its molar
mass.

A gas that follows Boyle’s law, Charles’ law and Avogadro law strictly is called an ideal gas. Such a gas is hypothetical. It is assumed that intermolecular forces are not present between the molecules of an ideal gas. Real gases follow these laws only under certain specific conditions when forces of interaction are practically negligible. In all other situations these deviate from ideal behaviour. You will learn about the deviations later in this unit.

5.6 Ideal Gas Equation

The three laws which we have learnt till now can be combined together in a single equation which is known as ideal gas equation.

At constant T and n; V ∝1/p Boyle’s Law
At constant p and n; V ∝T Charles’ Law
At constant p and T; V ∝n Avagadro Law

Thus,
V ∝ nT/P ———————————- (5.15)
⇒V =R(nT/p) ——————————– (5.16)

where R is proportionality constant. On rearranging the equation (5.16) we obtain R is called gas constant.

pV=nRT ————————————————-(5.17)
⇒R = pV/nT ———————————————- (5.18)

It is same for all gases. Therefore it is also called Universal Gas Constant. Equation (5.17) is called ideal gas equation.

Equation (5.18) shows that the value of R depends upon units in which p, V and T are measured. If three variables in this equation are known, fourth can be calculated. From this equation we can see that at constant temperature and pressure n moles of any gas will have the same volume because V = nRT/p and n,R,T and p are constant. This equation will be applicable to any gas, under those conditions when behaviour of the gas approaches ideal behaviour. Volume of one mole of an ideal gas under STP conditions (273.15 K and 1 bar pressure) is 22.710981 L mol-1. Value of R for one mole of an ideal gas can be calculated under these conditions as follows :

R =(105 Pa) (22.71 ×10–3m3)/(1mol) (273.15K)
=8.314 Pa m3 k-1 mol-1
=8.314 10-2 bar L K-1 mol-1
=8.314 JK-1mol-1

At STP conditions used earlier (00 C and 1 atm pressure), value of R is 8.20578 10-2L atm K-1 mol-1.

Ideal gas equation is a relation between four variables and it describes the state of any gas, therefore, it is also called equation
of state.

Let us now go back to the ideal gas equation. This is the relationship for the simultaneous variation of the variables. If temperature, volume and pressure of a fixed amount of gas vary from T1, V1 and p1 to T2, V2 and p2 then we can write

p1V1/T1 and p2V2/T2
⇒ p1V1/T1= p2V2/T2 ————————————(5.19)

Equation (5.19) is a very useful equation. If out of six, values of five variables are known, the value of unknown variable can be
calculated from the equation (5.19). This equation is also known as Combined gas law.

Problem 5.3

At 25°C and 760 mm of Hg pressure a gas occupies 600 mL volume. What will be its pressure at a height where temperature is 10°C and volume of the gas is 640 mL.

Solution

p1 = 760 mm Hg, V,sub>1= 600 mL
T1 = 25 + 273 = 298 K
V2 = 640 mL and T2 = 10 + 273 = 283K

According to Combined gas law

p1 V1/T1 = p2 V2/T2

⇒p2=p1 V1T2/ V1/T2

⇒p2=(760 mm Hg)×(600 ml)×(283 K)/(640 ml)×(298 K)
=676.6 mm Hg

5.6.1 Density and Molar Mass of a Gaseous Substance

Ideal gas equation can be rearranged as follows:
n/V = p/RT

Replacing n by m/M, we get

m/M V=p/RT——————————————-(5.20)
d/M = p/RT (where d is the density) —————–(5.21)

On rearranging equation (5.21) we get the relationship for calculating molar mass of a gas.
M =dRT/p ——————————(5.22)

5.6.2 Dalton’s Law of Partial Pressures

The law was formulated by John Dalton in 1801. It states that the total pressure exerted by the mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases i.e., the pressures which these gases would exert if they were enclosed separately in the same volume and under the same conditions of temperature. In a mixture of gases, the pressure exerted by the individual gas is called partial pressure. Mathematically,

pTotal = p1+p2+p3+……(at constant T, V)————————————— (5.23)

where ptotalis the total pressure exerted by the mixture of gases and p1, p2 , p3 etc. are partial pressures of gases.

Gases are generally collected over water and therefore are moist. Pressure of dry gas can be calculated by subtracting vapour pressure of water from the total pressure of the moist gas which contains water vapours also. Pressure exerted by saturated water vapour is called aqueous tension. Aqueous tension of water at different temperatures is given in Table 5.3.

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31k Table 5.3

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Partial pressure in terms of mole fraction

Suppose at the temperature T, three gases, enclosed in the volume V, exert partial pressure p1, p2 and p3 respectively. then,

p1=n1RT/V ———————-(5.25)
p2=n2RT/V ———————-(5.26)
p3=n3RT/V ———————-(5.27)

where n1n2 and n3 are number of moles of these gases. Thus, expression for total pressure will be

ptotal=p1+p2+p1
=n1(RT/V)+n2(RT/V)+n3(RT/V)
=(n1+n2+n3)RT/V ———————————-(5.28)

on dividing p1 by ptotalwe get

p1/ptotal=(n1/n1+n2+n3)RTV/RTV
= n1/(n1+n2+3) = n1/n = x1

where n=n1+n2+n3
x1 is called mole fraction of first gas.

Thus, p1=x1ptotal

Similarly for other two gases we can written as
p2=x2ptotal and p3=x3ptotal

Thus a general equation can be written as
p1=x1ptotal (5.29)

where pi and xi are partial pressure and mole fraction of ith gas respectively. If total pressure of a mixture of gases is known, the equation (5.29) can be used to find out pressure exerted by individual gases.

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Gyan Question :

51 All kinds of scams

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33a Density problem

Ans : ( c )

33b Density problem

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Problem 5.4

A neon-dioxygen mixture contains 70.6 g dioxygen and 167.5 g neon. If pressure of the mixture of gases in the cylinder is 25 bar. What is the partial pressure of dioxygen and neon in the mixture ?

Number of moles of dioxygen =70.6g/32gmol−1 = 2.21 mol

Number of moles of neon =167.5g/20gmol−1 = 8.375 mol

Mole fraction of dioxygen = 2.21/(2.21 + 8.375) = 2.21/10.585 = 0.21

Mole fraction of neon = 8.375/(2.21+ 8.375) = 0.79
Alternatively,
mole fraction of neon = 1– – 0.21 = 0.79

Partial pressure of a gas= mole fraction x total pressure
⇒ Partial pressure of oxygen = 0.21 x (25 bar) = 5.25 bar

Partial pressure of neon = 0.79 x (25 bar) = 19.75 bar

5.7 KINETIC MOLECULAR THEORY OF GASES

So far we have learnt the laws (e.g., Boyle’s law, Charles’law etc.) which are concise statements of experimental facts observed in
the laboratory by the scientists. Conducting careful experiments is an important aspect of scientific method and it tells us how the
particular system is behaving under different conditions. However, once the experimental facts are established, a scientist is curious to
know why the system is behaving in that way. For example, gas laws help us to predict that pressure increases when we compress gases but we would like to know what happens at molecular level when a gas is compressed ? A theory is constructed to answer such
questions. A theory is a model (i.e., a mental picture) that enables us to better understand our observations. The theory that attempts to elucidate the behaviour of gases is known as kinetic molecular theory.

Assumptions or postulates of the kinetic molecular theory of gases are given below. These postulates are related to atoms and
molecules which cannot be seen, hence it is said to provide a microscopic model of gases.

• Gases consist of large number of identical particles (atoms or molecules) that are so small and so far apart on the average that
the actual volume of the molecules is negligible in comparison to the empty space between them. They are considered as point masses. This assumption explains the great compressibility of gases.

• There is no force of attraction between the particles of a gas at ordinary temperature and pressure. The support for this assumption comes from the fact that gases expand and occupy all the space available to them.

• Particles of a gas are always in constant and random motion. If the particles were at rest and occupied fixed positions, then
a gas would have had a fixed shape which is not observed.

• Particles of a gas move in all possible directions in straight lines. During their random motion, they collide with each other and with the walls of the container. Pressure is exerted by the gas as a result of collision of the particles with the walls of the container.

• Collisions of gas molecules are perfectly elastic. This means that total energy of molecules before and after the collision remains same. There may be exchange of energy between colliding molecules, their individual energies may change, but the sum of their energies remains constant. If there were loss of kinetic energy, the motion of molecules will stop and gases will settle down. This is contrary to what is actually observed.

• At any particular time, different particles in the gas have different speeds and hence different kinetic energies. This assumption is reasonable because as the particles collide, we expect their speed to change. Even if initial speed of all the particles was same, the molecular collisions will disrupt this uniformity. Consequently the particles must have different speeds, which go on changing constantly. It is possible to show that though the individual speeds are changing, the distribution of speeds remains constant at a particular temperature.

• If a molecule has variable speed, then it must have a variable kinetic energy. Under these circumstances, we can talk only about average kinetic energy. In kinetic theory it is assumed that average kinetic energy of the gas molecules is directly proportional to the absolute temperature. It is seen that on heating a gas at constant volume, the pressure increases. On heating the gas, kinetic energy of the particles increases and these strike the walls of the container more frequently thus exerting more pressure.

Kinetic theory of gases allows us to derive theoretically, all the gas laws studied in the previous sections. Calculations and predictions based on kinetic theory of gases agree very well with the experimental observations and thus establish the correctness of this model.

5.8 BEHAVIOUR OF REAL GASES: DEVIATION FROM IDEAL GAS BEHAVIOUR

Our theoritical model of gases corresponds very well with the experimental observations. Difficulty arises when we try to test how far the relation pV = nRT reproduce actual pressure-volume-temperature relationship of gases. To test this point we plot pV vs p plot of gases because at constant temperature, pV will be constant (Boyle’s law) and pV vs p graph at all pressures will be a straight line parallel to x-axis. Fig. 5.8 shows such a plot constructed from actual data for several gases at 273 K.

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31l Fig 5.8 Plot

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It can be seen easily that at constant temperature pV vs p plot for real gases is not a straight line. There is a significant deviation from ideal behaviour. Two types of curves are seen.In the curves for dihydrogen and helium, as the pressure increases the value of pV also increases. The second type of plot is seen in the case of other gases like carbon monoxide and methane. In these plots first there is a negative deviation from ideal behaviour, the pV value decreases with increase in pressure and reaches to a minimum value characteristic of a gas. After that pV value starts increasing. The curve then crosses the line for ideal gas and after that shows positive deviation continuously. It is thus, found that real gases do not follow ideal gas equation perfectly under all conditions.

Deviation from ideal behaviour also becomes apparent when pressure vs volume plot is drawn. The pressure vs volume plot of experimental data (real gas) and that theoretically calculated from Boyle’s law (ideal gas) should coincide. Fig 5.9 shows these plots. It is apparent that at very high pressure the measured volume is more than the calculated volume. At low pressures, measured and calculated volumes approach each other.

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31a Fig 5.9

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It is found that real gases do not follow, Boyle’s law, Charles law and Avogadro law perfectly under all conditions. Now two questions arise.

(i) Why do gases deviate from the ideal behaviour?
(ii) What are the conditions under which gases deviate from ideality?

We get the answer of the first question if we look into postulates of kinetic theory once again. We find that two assumptions of the
kinetic theory do not hold good. These are

(a) There is no force of attraction between the molecules of a gas.
(b) Volume of the molecules of a gas is negligibly small in comparison to the space occupied by the gas.

If assumption (a) is correct, the gas will never liquify. However, we know that gases do liquify when cooled and compressed. Also, liquids formed are very difficult to compress. This means that forces of repulsion are powerful enough and prevent squashing of molecules in tiny volume. If assumption (b) is correct, the pressure vs volume graph of experimental data (real gas) and that theoritically calculated from Boyles law (ideal gas) should coincide.

Real gases show deviations from ideal gas law because molecules interact with each other. At high pressures molecules of gases
are very close to each other. Molecular interactions start operating. At high pressure, molecules do not strike the walls of the container with full impact because these are dragged back by other molecules due to molecular attractive forces. This affects the pressure exerted by the molecules on the walls of the container. Thus, the pressure exerted by the gas is lower than the pressure exerted by the ideal gas.

pideal = preal + an2/V2 ———————————- (5.30)
observed correction
pressure term

Here, a is a constant.

Repulsive forces also become significant.Repulsive interactions are short-range interactions and are significant when molecules are almost in contact. This is the situation at high pressure. The repulsive forces cause the molecules to behave as small but impenetrable spheres. The volume occupied by the molecules also becomes significant because instead of moving in volume V, these are now restricted to volume (V-nb) where nb is approximately the total volume occupied by the molecules themselves. Here, b is a constant. Having taken into account the corrections for pressure and volume, we can rewrite equation (5.17) as

( p + an2/V2)(V – nb) = nRT ———————————– (5.31)

Equation (5.31) is known as van der Waals equation. In this equation n is number of moles of the gas. Constants a and b are called van der Waals constants and their value depends on the characteristic of a gas. Value of ‘a’ is measure of magnitude of intermolecular attractive forces within the gas and is independent of temperature and pressure.

Also, at very low temperature, intermolecular forces become significant. As the molecules travel with low average speed, these can be captured by one another due to attractive forces. Real gases show ideal behaviour when conditions of temperature and pressure are such that the intermolecular forces are practically negligible. The real gases show ideal behaviour when pressure approaches zero.

The deviation from ideal behaviour can be measured in terms of compressibility factor Z, which is the ratio of product pV and nRT. Mathematically

Z = pV/n RT————————————– (5.32)

For ideal gas Z = 1 at all temperatures and pressures because pV = n RT. The graph of Z vs p will be a straight line parallel to pressure axis (Fig. 5.10). For gases which deviate from ideality, value of Z deviates from unity. At very low pressures all gases shown have Z ≈1 and behave as ideal gas. At high pressure all the gases have Z > 1. These are more difficult to compress. At intermediate pressures, most gases have Z < 1. Thus gases show ideal behaviour when the volume occupied is large so that the volume of the molecules can be neglected in comparison to it. In other words, the behaviour of the gas becomes more ideal when pressure is very low. Upto what pressure a gas will follow the ideal gas law, depends upon nature of the gas and its temperature. The temperature at which a real gas obeys ideal gas law over an appreciable range of pressure is called Boyle temperature or Boyle point. Boyle point of a gas depends upon its nature. Above their Boyle point, real gases show positive deviations from ideality and Z values are greater than one. The forces of attraction between the molecules are very feeble. Below
Boyle temperature real gases first show decrease in Z value with increasing pressure, which reaches a minimum value. On further
increase in pressure, the value of Z increases continuously. Above explanation shows that at low pressure and high temperature gases show ideal behaviour. These conditions are different for different gases.

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31b Fig 5.10 variation

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More insight is obtained in the significance of Z if we note the following derivation
Z = pVreal/n RT ——————————(5.33)

If the gas shows ideal behaviour then Videal = n RT/p . On putting this value of nRT/p in equation (5.33) we have
Z = Vreal/Videal ————————————–(5.34)

From equation (5.34) we can see that compressibility factor is the ratio of actual molar volume of a gas to the molar volume of it, if it were an ideal gas at that temperature and pressure.

In the following sections we will see that it is not possible to distinguish between gaseous state and liquid state and that liquids
may be considered as continuation of gas phase into a region of small volumes and very high molecular attraction. We will also see how we can use isotherms of gases for predicting the conditions for liquifaction of gases.

5.9 LIQUIFACTION OF GASES

First complete data on pressure – volume – temperature relations of a substance in both gaseous and liquid state was obtained by Thomas Andrews on carbon dioxide. He plotted isotherms of carbon dioxide at various temperatures (Fig. 5.11). Later on it was found that real gases behave in the same manner as carbon dioxide. Andrews noticed that at high temperatures isotherms look like that of an ideal gas and the gas cannot be liquified even at very high pressure. As the temperature is lowered, shape of the curve changes and data shows considerable deviation from ideal behaviour. At 30.98 °C carbon dioxide remains gas upto 73 atmospheric pressure. (Point E in Fig. 5.11). At 73 atmospheric pressure, liquid carbon dioxide appears for the first time. The temperature 30.98 °C is called critical temperature (TC) of carbon dioxide. This is the highest temperature at which liquid carbon dioxide is observed. Above this temperature it is gas. Volume of one mole of the gas at critical temperature is called critical volume (VC) and pressure at this temperature is called critical pressure (pC).

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The critical temperature, pressure and volume are called critical constants. Further increase in pressure simply compresses the liquid carbon dioxide and the curve represents the compressibility of the liquid. The steep line represents the isotherm of liquid. Even a slight compression results in steep rise in pressure indicating very low compressibility of the liquid. Below 30.98 °C, the behaviour of the gas on compression is quite different.

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At 21.5 °C, carbon dioxide remains as a gas only upto point B. At point B, liquid of a particular volume appears. Further  compression does not change the pressure. Liquid and gaseous carbon dioxide coexist and further application of pressure results in the condensation of more gas until the point C is reached. At point C, all the gas has been condensed and further application of pressure merely compresses the liquid as shown by steep line. A slight compression from volume V2 to V3 results in steep rise in pressure from p2 to p3 (Fig. 5.11). Below 30.98 °C (critical temperature) each curve shows the similar trend. Only length of the horizontal line increases at lower temperatures. At critical point horizontal portion of the isotherm merges into one point. Thus we see that a point like A in the Fig. 5.11 represents gaseous state. A point like D represents liquid state and a point under the dome shaped area represents existence of liquid and gaseous carbon dioxide in equilibrium. All the gases upon compression at constant temperature (isothermal compression) show the same behaviour as shown by carbon dioxide. Also above discussion shows that gases should be cooled below their critical temperature for liquification. Critical temperature of a gas is highest temperature at which liquifaction of the gas first occurs. Liquifaction of so called permanent gases (i.e., gases which show continuous positive deviation in Z value) requires cooling as well as considerable compression. Compression brings the molecules in close vicinity and cooling slows down the movement of molecules therefore, intermolecular interactions may hold the closely and slowly moving molecules together and the gas liquifies.

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31c Fig 5.11 Isotherms

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It is possible to change a gas into liquid or a liquid into gas by a process in which always a single phase is present. For example in Fig. 5.11 we can move from point A to F vertically by increasing the temperature, then we can reach the point G by compressing the gas at the constant temperature along this isotherm (isotherm at 31.1°C). The pressure will increase. Now we can move vertically
down towards D by lowering the temperature. As soon as we cross the point H on the critical isotherm we get liquid. We end up with liquid but in this series of changes we do not pass through two-phase region. If process is carried out at the critical temperature, substance always remains in one phase.

Thus there is continuity between the gaseous and liquid state. The term fluid is used for either a liquid or a gas to recognise this continuity. Thus a liquid can be viewed as a very dense gas. Liquid and gas can be distinguished only when the fluid is below its critical temperature and its pressure and volume lie under the dome, since in that situation liquid and gas are in equilibrium and a surface separating the two phases is visible. In the absence of this surface there is no fundamental way of distinguishing between two states. At critical temperature, liquid passes into gaseous state imperceptibly and continuously; the surface separating two phases disappears (Section 5.10.1). A gas below the critical temperature can be liquified by applying pressure, and is called vapour of the substance. Carbon dioxide gas below its critical temperature is called car/subbon dioxide vapour. Critical constants for some common substances are given in Table 5.4.

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31d Table 5.4

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Problem 5.5

Gases possess characteristic critical temperature which depends upon the magnitude of intermolecular forces between the gas particles. Critical temperatures of ammonia and carbon dioxide are 405.5 K and 304.10 K respectively. Which of these gases will liquify first when you start cooling from 500 K to their critical temperature ?

Solution

Ammonia will liquify first because its critical temperature will be reached first. Liquifaction of CO2 will require more cooling.

5.10 LIQUID STATE

Intermolecular forces are stronger in liquid state than in gaseous state. Molecules in liquids are so close that there is very little empty space between them and under normal conditions liquids are denser than gases.

Molecules of liquids are held together by attractive intermolecular forces. Liquids have definite volume because molecules do not
separate from each other. However, molecules of liquids can move past one another freely, therefore, liquids can flow, can be poured and can assume the shape of the container in which these are stored. In the following sections we will look into some of the physical properties of the liquids such as vapour pressure, surface tension and viscosity.

5.10.1 Vapour Pressure

If an evacuated container is partially filled with a liquid, a portion of liquid evaporates to fill the remaining volume of the container with vapour. Initially the liquid evaporates and pressure exerted by vapours on the walls of the container (vapour pressure)  increases. After some time it becomes constant, an equilibrium is established between liquid phase and vapour phase. Vapour pressure at this stage is known as equilibrium vapour pressure or saturated vapour pressure.. Since process of vapourisation is temperature dependent; the temperature must be mentioned while reporting the vapour pressure of a liquid.

When a liquid is heated in an open vessel, the liquid vapourises from the surface. At the temperature at which vapour pressure of the liquid becomes equal to the external pressure, vapourisation can occur throughout the bulk of the liquid and vapours expand freely into the surroundings. The condition of free vapourisation throughout the liquid is called boiling. The temperature at which vapour pressure of liquid is equal to the external pressure is called boiling temperature at that pressure. Vapour pressure of some common liquids at various temperatures is given in (Fig. 5.12). At 1 atm pressure boiling temperature is called normal boiling point. If pressure is 1 bar then the boiling point is called standard boiling point of the liquid. Standard boiling point of the liquid is slightly lower than the normal boiling point because 1 bar pressure is slightly less than 1 atm pressure. The normal boiling point of water is 100 °C (373 K), its standard boiling point is 99.6 °C (372.6 K).

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31e Temp vs vapour pressure

Fig 5.12 Vapour pressure vs temperature curve of some common liquids

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At high altitudes atmospheric pressure is low. Therefore liquids at high altitudes boil at lower temperatures in comparison to that at sea level. Since water boils at low temperature on hills, the pressure cooker is used for cooking food. In hospitals surgical instruments are sterilized in autoclaves in which boiling point of water is increased by increasing the pressure above the atmospheric pressure by using a weight covering the vent.

Boiling does not occur when liquid is heated in a closed vessel. On heating continuously vapour pressure increases. At first a clear boundary is visible between liquid and vapour phase because liquid is more dense than vapour. As the temperature increases more and more molecules go to vapour phase and density of vapours rises. At the same time liquid becomes less dense. It expands because molecules move apart. When density of liquid and vapours becomes the same; the clear boundary between liquid and vapours disappears. This temperature is called critical temperature about which we have already discussed in section 5.9.

5.10.2 Surface Tension

It is well known fact that liquids assume the shape of the container. Why is it then small drops of mercury form spherical bead instead of spreading on the surface. Why do particles of soil at the bottom of river remain separated but they stick together when taken out ? Why does a liquid rise (or fall) in a thin capillary as soon as the capillary touches the surface of the liquid ? All these phenomena are caused due to the characteristic property of liquids, called surface tension. A molecule in the bulk of liquid experiences equal intermolecular forces from all sides. The molecule, therefore does not experience any net force. But for the molecule on the surface of liquid, net attractive force is towards the interior of the liquid (Fig. 5.13), due to the molecules below it. Since there are no molecules above it.

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31f Fig 5.13 Forces

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Liquids tend to minimize their surface area. The molecules on the surface experience a net downward force and have more energy than the molecules in the bulk, which do not experience any net force. Therefore, liquids tend to have minimum number of molecules at their surface. If surface of the liquid is increased by pulling a molecule from the bulk, attractive forces will have to be overcome. This will require expenditure of energy. The energy required to increase the surface area of the liquid by one unit is defined as surface energy.

Its dimensions are J m-2. Surface tension is defined as the force acting per unit length perpendicular to the line drawn on the surface of liquid. It is denoted by Greek letter γ (Gamma). It has dimensions of kg s-2 and in SI unit it is expressed as N m-1. The lowest energy state of the liquid will be when surface area is minimum. Spherical shape satisfies this condition, that is why mercury drops are spherical in shape. This is the reason that sharp glass edges are heated for making them smooth. On heating, the glass melts and the surface of the liquid tends to take the rounded shape at the edges, which makes the edges smooth. This is called fire polishing of glass.

Liquid tends to rise (or fall) in the capillary because of surface tension. Liquids wet the things because they spread across their surfaces as thin film. Moist soil grains are pulled together because surface area of thin film of water is reduced. It is surface tension which gives stretching property to the surface of a liquid. On flat surface, droplets are slightly flattened by the effect of gravity; but in the gravity free environments drops are perfectly spherical.

The magnitude of surface tension of a liquid depends on the attractive forces between the molecules. When the attractive forces are large, the surface tension is large. Increase in temperature increases the kinetic energy of the molecules and effectiveness of intermolecular attraction decreases, so surface tension decreases as the temperature is raised.

5.10.3 Viscosity

It is one of the characteristic properties of liquids. Viscosity is a measure of resistance to flow which arises due to the internal friction between layers of fluid as they slip past one another while liquid flows. Strong intermolecular forces between molecules hold them together and resist movement of layers past one another.

When a liquid flows over a fixed surface, the layer of molecules in the immediate contact of surface is stationary. The velocity of upper layers increases as the distance of layers from the fixed layer increases. This type of flow in which there is a regular gradation of velocity in passing from one layer to the next is called laminar flow. If we choose any layer in the flowing liquid (Fig.5.14), the layer above it accelerates its flow and the layer below this retards its flow.

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31g Fig 5.14

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If the velocity of the layer at a distance dz is changed by a value du then velocity gradient is given by the amount du/dz . A force is required to maintain the flow of layers. This force is proportional to the area of contact of layers and velocity gradient i.e.
F ∝ A (A is the area of contact)
f ∝ du/dz (where, du/dz is velocity gradient; the change in velocity with distance)

F ∝ A. du/dz

⇒F=ηAdu/dz

‘ η’ is proportionality constant and is called coefficient of viscosity. Viscosity coefficient is the force when velocity gradient
is unity and the area of contact is unit area. Thus ‘ η’ is measure of viscosity. SI unit of viscosity coefficient is 1 newton second per square metre (N s m-2) = pascal second (Pa s = 1kg m-1s-1). In cgs system the unit of coefficient of viscosity is poise (named after great scientist Jean Louise Poiseuille).

1 poise = 1 g cm-1s-1 = 10–1kg m-1s-1

Greater the viscosity, the more slowly the liquid flows. Hydrogen bonding and van der Waals forces are strong enough to cause high
viscosity. Glass is an extremely viscous liquid. It is so viscous that many of its properties resemble solids. However, property of flow of glass can be experienced by measuring the thickness of windowpanes of old buildings. These become thicker at the bottom than at the top.

Viscosity of liquids decreases as the temperature rises because at high temperature molecules have high kinetic energy and can overcome the intermolecular forces to slip past one another between the layers.

SUMMARY

Intermolecforces ular forces operate between the particles of matter. These differ from pure electrostatic forces that exist between two oppositely charged ions. Also, these do not include forces that hold atoms of a covalent molecule together through covalent bond. Competition between thermal energy and intermolecular interactions determines the state of matter. ‘Bulk’ properties of matter such as behaviour of gases, characteristics of solids and liquids and change of state depend upon energy of constituent particles and the type of interaction between them. Chemical properties of a substance do not change with change of state, but the reactivity depends upon the physical state.

Forces of interaction between gas molecules are negligible and are almost independent of their chemical nature. Interdependence of some observable properties namely pressure, volume, temperature and mass leads to different gas laws obtained from experimental studies on gases. Boyle’s law states that under isothermal condition, pressure of a fixed amount of a gas is inversely roportional to its volume. Charles’ law is a relationship between volume and absolute temperature under isobaric condition. It states that volume of a fixed amount of gas is directly proportional to its absolute temperature (V∝T) . If state of a gas is represented by p1, V1 and T1 and it changes to state at p2, V2 and T2, then relationship between these two states is given by combined gas law according to which p1V1/T1 = p2V2/T2. Any one of the variables of this gas can be found out if other five variables are known. Avogadro law states that equal volumes of all gases under same conditions of temperature and pressure contain equal number of molecules. Dalton’s law of partial pressure states that total pressure exerted by a mixture of non-reacting gases is equal to the sum of partial pressures exerted by them. Thus p = p1+p2+p3+ … . Relationship between pressure, volume, temperature and number of moles of a gas describes its state and is called equation of state of the gas. Equation of state for ideal gas is pV=nRT, where R is a gas constant and its value depends upon units chosen for pressure, volume and temperature.

At high pressure and low temperature intermolecular forces start operating strongly between the molecules of gases because they come close to each other. Under suitable temperature and pressure conditions gases can be liquified. Liquids may be considered as continuation of gas phase into a region of small volume and very strong molecular attractions. Some properties of liquids e.g., surface tension and viscosity are due to strong intermolecular attractive forces.

EXERCISES

5.1 What will be the minimum pressure required to compress 500 dm3 of air at 1 bar to 200 dm3 at 30°C?

5.2 A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What would be its pressure?

5.3 Using the equation of state pV=nRT; show that at a given temperature density of a gas is proportional to gas pressure p.

5.4 At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide?

5.5 Pressure of 1 g of an ideal gas A at 27 °C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

5.6 The drain cleaner, Drainex contains small bits of aluminum which react with caustic soda to produce dihydrogen. What volume of dihydrogen at 20 °C and one bar will be released when 0.15g of aluminum reacts?

5.7 What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of carbon dioxide contained in a 9 dm3 flask at 27 °C ?

5.8 What will be the pressure of the gaseous mixture when 0.5 L of H2 at 0.8 bar and 2.0 L of dioxygen at 0.7 bar are introduced in a 1L vessel at 27°C?

5.9 Density of a gas is found to be 5.46 g/dm3 at 27 °C at 2 bar pressure. What will be its density at STP?

5.10 34.05 mL of phosphorus vapour weighs 0.0625 g at 546 °C and 0.1 bar pressure. What is the molar mass of phosphorus?

5.11 A student forgot to add the reaction mixture to the round bottomed flask at 27 °C but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was 477 °C. What fraction of air would have been expelled out?

5.12 Calculate the temperature of 4.0 mol of a gas occupying 5 dm3 at 3.32 bar. (R = 0.083 bar dm3 K-1 mol-1).

5.13 Calculate the total number of electrons present in 1.4 g of dinitrogen gas.

5.14 How much time would it take to distribute one Avogadro number of wheat grains, if 1010 grains are distributed each second ?

5.15 Calculate the total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen confined in a vessel of 1 dm3 at 27°C. R = 0.083 bar dm3 K-1 mol-1.

5.16 Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kg m-3 and
R = 0.083 bar dm3 K-1 mol-1).

5.17 Calculate the volume occupied by 8.8 g of CO2 at 31.1°C and 1 bar pressure. R = 0.083 bar L K-1 mol-1.

5.18 2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C, at the same pressure. What is the molar mass of the gas?

5.19 A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight of dihydrogen. Calculate the partial pressure of dihydrogen.

5.20 What would be the SI unit for the quantity pV2T2/n ?

5.21 In terms of Charles’ law explain why -273 °C is the lowest possible temperature.

5.22 Critical temperature for carbon dioxide and methane are 31.1 °C and -81.9 °C respectively. Which of these has stronger intermolecular forces and why?

5.23 Explain the physical significance of van der Waals parameters.

Answer to Some Selected Problems
5.1 2.5 bar

5.2 0.8 bar

5.4 70 g/mol

5.5 MB = 4MA

5.6 202.5 mL

5.7 8.314 x 104 Pa

5.8 1.8 bar

5.9 3g/dm3

5.10 1247.7 g

5.11 3/5

5.12 50 K

5.13 4.2154 x 1023 electrons

5.14 1.90956 x 106 year

5.15 56.025 bar

5.16 3811.1 kg

5.17 5.05 L

5.18 40 g mol–1

5.19 0.8 bar

I. Multiple Choice Questions (Type-I)

1. A person living in Shimla observed that cooking food without using pressure cooker takes more time. The reason for this observation is that at high altitude:

(i) pressure increases
(ii) temperature decreases
(iii) pressure decreases
(iv) temperature increases

2. Which of the following property of water can be used to explain the spherical shape of rain droplets?

(i) viscosity
(ii) surface tension
(iii) critical phenomena
(iv) pressure

3. A plot of volume (V) versus temperature (T) for a gas at constant pressure is a straight line passing through the origin. The plots at different values of pressure are shown in Fig. 5.1. Which of the following order of pressure is correct for this gas?

:-)

31h Vol temp

:-)

(i) p1 > p2 > p3 > p4
(ii) p1 = p2 = p3 = p4
(iii) p1 < p2 < p3 < p4
(iv) p1 < p2 = p3 < p4

4. The interaction energy of London force is inversely proportional to sixth power of the distance between two interacting particles but their magnitude depends upon

(i) charge of interacting particles
(ii) mass of interacting particles
(iii) polarisability of interacting particles
(iv) strength of permanent dipoles in the particles.

5. Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of dipoles possess ‘partial charges’. The partial charge is

(i) more than unit electronic charge
(ii) equal to unit electronic charge
(iii) less than unit electronic charge
(iv) double the unit electronic charge

6. The pressure of a 1:4 mixture of dihydrogen and dioxygen enclosed in a vessel is one atmosphere. What would be the partial pressure of dioxygen?

(i) 0.8105 atm
(ii) 0.008 Nm–2
(iii) 8104 Nm–2
(iv) 0.25 atm

7. As the temperature increases, average kinetic energy of molecules increases. What would be the effect of increase of temperature on pressure provided the volume is constant?

(i) increases
(ii) decreases
(iii) remains same
(iv) becomes half

8. Gases possess characteristic critical temperature which depends upon the magnitude of intermolecular forces between the particles. Following are the critical temperatures of some gases.

Gases H2 He O2 N2
Critical temperature in Kelvin 33.2 5.3 154.3 126

From the above data what would be the order of liquefaction of these gases? Start writing the order from the gas liquefying first

(i) H2, He, O2, N2
(ii) He, O2, H2, N2
(iii) N2, O2, He, H2
(iv) O2, N2, H2, He

9. What is SI unit of viscosity coefficient (η)?

(i) Pascal
(ii) Nsm–2
(iii) km–2 s
(iv) N m–2

10. Atmospheric pressures recorded in different cities are as follows:

Cities Shimla Bangalore Delhi Mumbai
p in N/m2 1.01 x 105 1.2 x 105 1.02 x 105 1.21 x 105

Consider the above data and mark the place at which liquid will boil first.

(i) Shimla
(ii) Bangalore
(iii) Delhi
(iv) Mumbai

11. Which curve in Fig. 5.2 represents the curve of ideal gas?

:-)

31i Fig 5.2

:-)

(i) B only
(ii) C and D only
(iii) E and F only
(iv) A and B only

12. Increase in kinetic energy can overcome intermolecular forces of attraction. How will the viscosity of liquid be affected by the increase in
temperature?

(i) Increase
(ii) No effect
(iii) Decrease
(iv) No regular pattern will be followed

13. How does the surface tension of a liquid vary with increase in temperature?

(i) Remains same
(ii) Decreases
(iii) Increases
(iv) No regular pattern is followed

II. Multiple Choice Questions (Type-II)

In the following questions two or more options may be correct.

14. With regard to the gaseous state of matter which of the following statements are correct?

(i) Complete order of molecules
(ii) Complete disorder of molecules
(iii) Random motion of molecules
(iv) Fixed position of molecules

15. Which of the following figures does not represent 1 mole of dioxygen gas at STP?

(i) 16 grams of gas
(ii) 22.7 litres of gas
(iii) 6.022 x 1023 dioxygen molecules
(iv) 11.2 litres of gas

16. Under which of the following two conditions applied together, a gas deviates most from the ideal behaviour?

(i) Low pressure
(ii) High pressure
(iii) Low temperature
(iv) High temperature

17. Which of the following changes decrease the vapour pressure of water kept in a sealed vessel?

(i) Decreasing the quantity of water
(ii) Adding salt to water
(iii) Decreasing the volume of the vessel to one-half
(iv) Decreasing the temperature of water

III. Short Answer Type

18. If 1 gram of each of the following gases are taken at STP, which of the gases will occupy (a) greatest volume and (b) smallest volume?

CO, H2O, CH4, NO

19. Physical properties of ice, water and steam are very different. What is the chemical composition of water in all the three states.

20. The behaviour of matter in different states is governed by various physical laws. According to you what are the factors that determine the state of matter?

21. Use the information and data given below to answer the questions (a) to (c):

• Stronger intermolecular forces result in higher boiling point.
• Strength of London forces increases with the number of electrons in the molecule.
• Boiling point of HF, HCl, HBr and HI are 293 K, 189 K, 206 K and 238 K respectively.

(a) Which type of intermolecular forces are present in the molecules HF, HCl, HBr and HI?
(b) Looking at the trend of boiling points of HCl, HBr and HI, explain out of dipole-dipole interaction and London interaction, which one is predominant here.
(c) Why is boiling point of hydrogen fluoride highest while that of hydrogen chloride lowest?

22. What will be the molar volume of nitrogen and argon at 273.15K and 1 atm?

23. A gas that follows Boyle’s law, Charle’s law and Avogadro’s law is called an ideal gas. Under what conditions a real gas would behave ideally?

24. Two different gases ‘A’ and ‘B’ are filled in separate containers of equal capacity under the same conditions of temperature and pressure. On increasing the pressure slightly the gas ‘A’ liquefies but gas B does not liquify even on applying high pressure until it is cooled. Explain this phenomenon.

25. Value of universal gas constant (R) is same for all gases. What is its physical significance?

26. One of the assumptions of kinetic theory of gases states that “there is no force of attraction between the molecules of a gas.” How far is this statement correct? Is it possible to liquefy an ideal gas? Explain.

27. The magnitude of surface tension of liquid depends on the attractive forces between the molecules. Arrange the following in increasing order of surface tension :
water, alcohol (C2H5OH) and hexane [CH3(CH2)4CH3)].

28. Pressure exerted by saturated water vapour is called aqueous tension. What correction term will you apply to the total pressure to obtain pressure of dry gas?

29. Name the energy which arises due to motion of atoms or molecules in a body. How is this energy affected when the temperature is increased?

30. Name two intermolecular forces that exist between HF molecules in liquid state. 31. One of the assumptions of kinetic theory of gases is that there is no force of attraction between the molecules of a gas. State and explain the evidence that shows that the assumption is not applicable for real gases.

32. Compressibility factor, Z, of a gas is given as Z = pV/nRT

(i) What is the value of Z for an ideal gas?
(ii) For real gas what will be the effect on value of Z above Boyle’s temperature?

33. The critical temperature (Tc) and critical pressure ( pc ) of CO2 are 30.98°C and 73 atm respectively. Can CO2 ( g) be liquefied at 32°C and 80 atm pressure?

34. For real gases the relation between p, V and T is given by van der Waals equation:

p + an2/V2 (V – nb) = nRT

where ‘a’ and ‘b’ are van der Waals constants, ‘nb’ is approximately equal to the total volume of the molecules of a gas.

‘a’ is the measure of magnitude of intermolecular attraction.

(i) Arrange the following gases in the increasing order of ‘b’. Give reason. O2, CO2, H2, He

(ii) Arrange the following gases in the decreasing order of magnitude of ‘a’. Give reason.
CH4, O2, H2

35. The relation between pressure exerted by an ideal gas (pideal) and observed pressure (preal) is given by the equation

pideal = preal + an2/V2

If pressure is taken in Nm–2, number of moles in mol and volume in m3, Calculate the unit of ‘a’.

What will be the unit of ‘a’ when pressure is in atmosphere and volume in dm3?

36. Name two phenomena that can be explained on the basis of surface tension.

37. Viscosity of a liquid arises due to strong intermolecular forces existing between the molecules. Stronger the intermolecular forces, greater is the viscosity. Name the intermolecular forces existing in the following liquids and arrange them in the increasing order of their viscosities. Also give reason for the assigned order in one line.

Water, hexane (CH3CH2CH2CH2CH2CH3), glycerine (CH2OH CH(OH) CH2OH)

38. Explain the effect of increasing the temperature of a liquid, on intermolecular forces operating between its particles, what will happen to the viscosity of a liquid if its temperature is increased?

39. The variation of pressure with volume of the gas at different temperatures can be graphically represented as shown in Fig. 5.3.
On the basis of this graph answer the following questions.

:-)

31j Vol Pressure

:-)

(i) How will the volume of a gas change if its pressure is increased at constant temperature?

(ii) At a constant pressure, how will the volume of a gas change if the temperature is increased from 200K to 400K?

40. Pressure versus volume graph for a real gas and an ideal gas are shown in Fig. 5.4. Answer the following questions on the basis of this graph.

:-)

31k Fig 5.4 Vol pressure

:-)

(i) Interpret the behaviour of real gas with respect to ideal gas at low pressure.

(ii) Interpret the behaviour of real gas with respect to ideal gas at high pressure.

(iii) Mark the pressure and volume by drawing a line at the point where real gas behaves as an ideal gas.

IV. Matching Type

41. Match the graphs between the following variables with their names :

Graphs Names
(i) Pressure vs temperature graph at constant molar volume. (a) Isotherms
(ii) Pressure vs volume graph at constant temperature. (b) Constant temperature curve
(iii) Volume vs temperature graph at constant pressure. (c) Isochores
(d) Isobars

42. Match the following gas laws with the equation representing them.

(i) Boyle’s law (a) V ∝ n at constant T and p
(ii) Charle’s law (b) pTotal = p1 + p2 + p3+…… at constant T, V
(iii) Dalton’s law (c) pV/T = Constant
(iv) Avogadro law (d) V ∝ T at constant n and p
(e) p ∝ V at constant n and T

43. Match the following graphs of ideal gas with their co-ordinates :

:-)

31l Graphical representation

:-)

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.

44. Assertion (A): Three states of matter are the result of balance between intermolecular forces and thermal energy of the molecules.
Reason (R): Intermolecular forces tend to keep the molecules together but thermal energy of molecules tends to keep them apart.

(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.

45. Assertion (A): At constant temperature, pV vs V plot for real gases is not a straight line.
Reason (R) : At high pressure all gases have Z > 1 but at intermediate pressure most gases have Z < 1.

(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.

46. Assertion (A): The temperature at which vapour pressure of a liquid is equal to the external pressure is called boiling temperature.
Reason (R) : At high altitude atmospheric pressure is high.

(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.

47. Assertion (A): Gases do not liquefy above their critical temperature, even on applying high pressure.
Reason (R) : Above critical temperature, the molecular speed is high and intermolecular attractions cannot hold the molecules together because they escape because of high speed.

(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.

48. Assertion (A): At critical temperature liquid passes into gaseous state imperceptibly and continuously.
Reason (R) : The density of liquid and gaseous phase is equal to critical temperature.

(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.

49. Assertion (A): Liquids tend to have maximum number of molecules at their surface.
Reason (R) : Small liquid drops have spherical shape.

(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

50. Isotherms of carbon dioxide at various temperatures are represented in Fig. 5.5. Answer the following questions based on this figure.

:-)

31m Vol pressure

:-)

(i) In which state will CO2 exist between the points a and b at temperature T1?

(ii) At what point will CO2 start liquefying when temperature is T1?

(iii) At what point will CO2 be completely liquefied when temperature is T2.

(iv) Will condensation take place when the temperature is T3.

(v) What portion of the isotherm at T1 represent liquid and gaseous CO2 at equilibrium?

51. The variation of vapour pressure of different liquids with temperature is shown in Fig. 5.6.

:-)

31a Temp vapour pressure

Fig 5.6

:-)

(i) Calculate graphically boiling points of liquids A and B.

(ii) If we take liquid C in a closed vessel and heat it continuously. At what temperature will it boil?

(iii) At high altitude, atmospheric pressure is low (say 60 mm Hg). At what temperature liquid D boils?

(iv) Pressure cooker is used for cooking food at hill station. Explain in terms of vapour pressure why is it so?

52. Why does the boundary between liquid phase and gaseous phase disappear on heating a liquid upto critical temperature in a closed vessel? In this situation what will be the state of the substance?

53. Why does sharp glass edge become smooth on heating it upto its melting point in a flame? Explain which property of liquids is responsible for this phenomenon.

54. Explain the term ‘laminar flow’. Is the velocity of molecules same in all the layers in laminar flow? Explain your answer.

55. Isotherms of carbon dioxide gas are shown in Fig. 5.7. Mark a path for changing gas into liquid such that only one phase (i.e., either a gas or a liquid) exists at any time during the change. Explain how the temperature, volume and pressure should be changed to carry out the change.

:-)

31b Pr Volume

Fig 5.7

:-)

ANSWERS

I. Multiple Choice Questions (Type-I)

1. (iii)      2. (ii)      3. (iii)      4. (iii)      5. (iii)      6. (iii)     7. (i)      8. (iv)      9. (ii)       10. (i)      11. (i)      12. (iii)     13. (ii)

II. Multiple Choice Questions (Type-II)

14. (ii), (iii)      15. (i), (iv)      16. (ii), (iii)     17. (ii), (iv)

III. Short Answer Type

18. a. CH4      b. NO
19. Remains the same i.e., H2O.
20. Pressure, temperature, mass and volume
21. (a) In HCl, HBr and HI, dipole-dipole and London forces because molecules possess permanent dipole. In HF dipole-dipole, London forces and hydrogen bonding.
(b) Electronegativity of chlorine, bromine and iodine decreases in the order :
Cl > Br > I
Therefore, dipole moment should decrease from HCl to HI. Thus, dipole-dipole interaction should decrease from HCl to HI. But boiling point increases on moving from HCl to HI. This means that London forces are predominant. This is so because London forces increase as the number of electrons in a molecule increases and in this case number of electrons is increasing from HCl towards HI.

(c) Hydrogen fluoride has highest dipole moment due to highest electronegativity of fluorine and hydrogen bonding is also present in it. Therefore, HF has highest boiling point.

22. 22.4 litre
23. Low pressure and high temperature
24. Gas ‘A’ is at or below its critical temperature and gas ‘B’ is at a temperature higher than critical temperature.
25. Unit of R depends upon those units in which p, V and T are measured, R = pV/nT . If pressure is measured in Pascal, per mole volume is measured in m3 and temperature is measured in Kelven then. Units of ‘R’ are Pam3K–1 mol–1 or J mol–1 K–1. Jule is the unit of work done so ‘R’ is work done per mole per kelvin.

26. In the absence of intermolecular forces of attraction, it will not be possible to liquefy ideal gas.
27. hexane < alcohol < water
28. PDry gas = PTotal – aqueous tension
29. Thermal energy. It is a measure of average kinetic energy of particles. It increases with increase in temperature.
30. (i) Dipole – dipole interaction
(ii) Hydrogen – bonding
31. Real gases can be liquefied on cooling and compressing proving that forces of attraction exist between the molecules.
32. (i) Z = 1 for ideal gas
(ii) For a real gas Z > 1 above Boyle’s temperature.

33. CO2 cannot be liquefied at 32°C by applying a pressure of 80 atm. This is because the temperature is greater than critical temperature of CO2.
34. (i) H2 < He < O2 < CO2 because size increases in the same order.
(ii) CH4 > O2 > H2 intermolecular attractions are the highest in CH4 and lowest in H2 because intermolecular forces increase with number of electrons in a molecule.

35. pideal = preal + an2/V2
We write the known units in the above equation.
Nm–2 = Nm–2 + a.mol2/(m3)2

If two values with same units are added then the units of result are same as added units.
∴ Nm–2 = a.mol2/m6
a = Nm–2 .m6/mol2
a = Nm4 mol–2

Similarly, when p is in atm and volume in dm3
a = atm(dm3)2/mol2 = atm dm6 mol–2

36. (i) Rise or fall of the liquid in a capillary – capillary action.
(ii) Spherical shape of small liquid drops.

37. In water and glycerine – Hydrogen bonding. Hexane – Dispersion forces/ London forces. The order of viscosities of these liquids is hexane < water < glycerine.

Hexane has weakest intermolecular forces and glycerine the strongest. (three OH groups). Therefore, hexane has minimum viscosity and glycerine has maximum viscosity.

38. The viscosity of a liquid decreases with the increase in temperature since the kinetic energy of the molecules can overcome intermolecular forces.
So the liquid can flow more easily.

39. (1) The volume of a gas will decrease if the pressure on the gas is increased keeping the temperature constant.
(2) On increasing temperature, the volume of a gas will increase if the pressure is kept constant.

IV. Matching Type

41. (i) → (c) (ii) → (a) (iii) → (d)
42. (i) → (e) (ii) → (d) (iii) → (b) (iv)v (a)
43. (i) → (b) (ii) → (c) (iii) → (a)

V. Assertion and Reason Type

44. (i)     45. (ii)     46. (iii)     47. (i)     48. (i)     49. (iv)

VI. Long Answer Type

50. (i) gaseous state      (ii) at point b     (iii) at point g
(iv) No, since T3 > Tc      (v) between b and c.

51.
(i) Boiling point of A = approximately 315 K, B = approximately 345 K
(ii) Will not boil
(iii) approximately 313 K
(iv) A liquid boils when vapour pressure becomes equal to the atmospheric pressure. Water boils at low temperature on hills because atmospheric pressure is low. Therefore even at low temperature vapour pressure becomes equal to atmospheric pressure.

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34a Showing the road 34b Vander waals forces numerical

34c Vander waals forces numerical

 

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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.in
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.in
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 http://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
:-)
The following video is a must see for full CO2 cycle, plates of Earth, Geological activities, stability of weather

:-)
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.
-

Summary of Women

:-)
The Virus of Faith

:-)
The God delusion

:-)
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

:-)
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

Miracles for Sale

:-)

The Enemies of Reason

:-)
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.
-

Did you analyze your effectiveness ?

Culturomics can help you

:-D
Why some temples become ” FAMOUS ” ? How you can be manipulated ? Luck for others ?

-

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

-

see detailed statistics at

An eye opener in Misandry

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.
:-)

http://zookeepersblog.wordpress.com/save-the-male/

:-)

How women manipulate men

http://www.angryharry.com/esWomenManipulateMen.htm

Gender Biased Laws in India

http://zookeepersblog.wordpress.com/biased-laws/

:-)

Violence against Men

:-)

Only men are victimised

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

:-)

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

:-)

Are you a nice person ? Just shout Wooooooooo , Eyye Eyye and enjoy to see someone in trouble ….

-
Extension of Milgram Experiments – In a Mob also people become cruel step by step -

:-)

Think what are you doing … why are you doing ?

Every Man must know this …

:-)
Manginas, White Knights, & Other Chivalrous Dogs

!
!
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….\__))####’#’###(((__/
……##### u r #####
……..### SWEET. ###
……/….#########…\
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(.(.(____)….`.#.´..(____).).)

 

key words

_________________________________________________________________________
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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 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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 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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 startsIITJEE SKMClasses.weebly.com boil boiling-point elevation process IITJEE SKMClasses.weebly.com boiling point elevated adding substance bond – attraction skmclasses.weebly.com repulsion IITJEE SKMClasses.weebly.com atoms skmclasses.weebly.com molecules IITJEE SKMClasses.weebly.com cornerstone Boyle’s law Brønsted-Lowrey acid chemical species IITJEE SKMClasses.weebly.com donates proton Brønsted–Lowry acid–base reaction Brønsted-Lowrey base – chemical species IITJEE SKMClasses.weebly.com accepts proton buffered solution – IITJEE SKMClasses.weebly.com aqueous solution consisting weak acid skmclasses.weebly.comits conjugate base weak base skmclasses.weebly.comits conjugate acid IITJEE SKMClasses.weebly.com resists changes pH IITJEE SKMClasses.weebly.com strong acids basesIITJEE SKMClasses.weebly.com added burette (IITJEE SKMClasses.weebly.com buret glasswareIITJEE SKMClasses.weebly.com dispense specific amounts liquid IITJEE SKMClasses.weebly.com precision necessary titration skmclasses.weebly.com resource dependent reactions example combustion catalyst chemical compoundIITJEE SKMClasses.weebly.comIITJEE SKMClasses.weebly.com change rate IITJEE SKMClasses.weebly.com speed up slow down reaction,IITJEE SKMClasses.weebly.com regenerated at end reaction cation – positively charged ion centrifuge equipmentIITJEE SKMClasses.weebly.comIITJEE SKMClasses.weebly.com separate substances based on density rotating tubes around centred axis cell potential force galvanic cell IITJEE SKMClasses.weebly.com pulls electron through reducing agentIITJEE SKMClasses.weebly.com oxidizing agent chemical Law certain rules IITJEE SKMClasses.weebly.com pertain IITJEE SKMClasses.weebly.com laws nature skmclasses.weebly.comchemistry – examples chemical reaction – change one IITJEE SKMClasses.weebly.com substances skmclassesanother multiple substances colloid mixture evenly dispersed substances such IITJEE skmclasses.weebly.comm milks combustion IITJEE SKMClasses.weebly.com exothermic reaction IITJEE SKMClasses.weebly.com oxidant skmclasses.weebly.comfuel IITJEE SKMClasses.weebly.com heat skmclasses.weebly.comoften light compound – substance IITJEE SKMClasses.weebly.com made up two IITJEE SKMClasses.weebly.com chemically bonded elements condensation phase changeIITJEE SKMClasses.weebly.com gasIITJEE SKMClasses.weebly.com liquid conductor material IITJEE SKMClasses.weebly.com allows electric flow IITJEE SKMClasses.weebly.com freely covalent bond – chemical bond IITJEE SKMClasses.weebly.com involves sharing electrons crystal solid IITJEE SKMClasses.weebly.com packed IITJEE SKMClasses.weebly.com ions, molecules atoms IITJEE SKMClasses.weebly.com orderly fashion cuvette glasswareIITJEE SKMClasses.weebly.com spectroscopic experiments. usually made plastic glass quartz skmclasses.weebly.comshould be IITJEE possible deionization removal ions, skmclasses.weebly.com water’s case mineral ions such IITJEE skmclasses.weebly.comsodium, iron skmclasses.weebly.comcalcium deliquescence substances IITJEE SKMClasses.weebly.com absorb water IITJEE SKMClasses.weebly.com atmosphereIITJEE SKMClasses.weebly.com liquid solutions deposition – settling particles within solution mixture dipole electric magnetic separation charge dipole moment – polarity polar covalent bond dissolution solvation – spread ions monosacharide double bond sharing two pairs electradodes Microcentrifuge Eppendorf tube IITJEE SKMClasses.weebly.com Coomassie Blue solution earth metal – see alkaline earth metal electrolyte solution IITJEE SKMClasses.weebly.com conducts certain amount current skmclasses.weebly.com split categorically IITJEE skmclasses.weebly.com weak skmclasses.weebly.comstrong electrolytes electrochemical cell using chemical reaction’s current electromotive force made electromagnetic radiation type wave IITJEE SKMClasses.weebly.com through vacuums IITJEE skmclasses.weebly.comwell IITJEE skmclasses.weebly.commaterial skmclasses.weebly.comclassified IITJEE 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skmclasses.weebly.comH entropy – amount energy IITJEE SKMClasses.weebly.com available skmclasses.weebly.com work closed thermodynamic system usually symbolized IITJEE skmclasses.weebly.com S enzyme – protein IITJEE SKMClasses.weebly.com speeds up catalyses reaction Empirical Formula – IITJEE SKMClasses.weebly.com called simplest formula gives simplest whole -number ratio atoms IITJEE SKMClasses.weebly.com element present compound eppendorf tube – generalized skmclasses.weebly.comtrademarked term skmclasses.weebly.com type tube; see microcentrifuge freezing – phase transitionIITJEE SKMClasses.weebly.com liquidIITJEE SKMClasses.weebly.com solid Faraday constant unit electrical charge widelyIITJEE SKMClasses.weebly.com electrochemistry skmclasses.weebly.comequalIITJEE SKMClasses.weebly.com ~ 96,500 coulombs represents 1 mol electrons, Avogadro number electrons: 6.022 × 1023 electrons. F = 96 485.339 9(24) C/mol Faraday’s law electrolysis two part law IITJEE SKMClasses.weebly.com Michael Faraday published about electrolysis mass substance altered at IITJEE SKMClasses.weebly.com electrode during electrolysis directly proportionalIITJEE SKMClasses.weebly.com quantity electricity transferred at IITJEE SKMClasses.weebly.com electrode mass IITJEE SKMClasses.weebly.com elemental material altered at IITJEE SKMClasses.weebly.com electrode directly proportionalIITJEE SKMClasses.weebly.com element’s equivalent weight frequency number cyclesIITJEE SKMClasses.weebly.com unit time. Unit: 1 hertz = 1 cycleIITJEE SKMClasses.weebly.com 1 second galvanic cell battery made up electrochemical IITJEE SKMClasses.weebly.com two different metals connected salt bridge gas particles container IITJEE SKMClasses.weebly.com no definite shape volume geochemistry – chemistry skmclasses.weebly.comchemical composition Earth Gibbs energy – value IITJEE SKMClasses.weebly.com indicates spontaneity reaction usually symbolized G Cavalier India, Kalyan Nagar halogens Group 7 Periodic Table skmclasses.weebly.comare non-metals heat energy transferredIITJEE SKMClasses.weebly.com one systemIITJEE SKMClasses.weebly.com another thermal interaction jodium – Latin name halogen element iodine Joule SI I.M.S. Learning Resources Pvt. 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IITJEE SKMClasses.weebly.com called “visible light London dispersion forces weak intermolecular force Law Motion object motion stay motion IITJEE SKMClasses.weebly.com object rest stays rest unless IITJEE SKMClasses.weebly.com unbalanced force acts molecule IITJEE SKMClasses.weebly.com one key components within chemistry Metal Chemical element IITJEE SKMClasses.weebly.com good conductor both electricity skmclasses.weebly.comheat skmclasses.weebly.comforms cations skmclasses.weebly.comionic bonds IITJEE SKMClasses.weebly.com non-metals melting phase changeIITJEE SKMClasses.weebly.com solidIITJEE SKMClasses.weebly.com liquid metalloid substance possessing both properties metals skmclasses.weebly.comnon-metals methylene blue heterocyclic aromatic chemical compound IITJEE SKMClasses.weebly.com molecular formula C16H18N3SCl microcentrifuge plastic container IITJEE SKMClasses.weebly.com IITJEE SKMClasses.weebly.comIITJEE SKMClasses.weebly.com store small amounts liquid mole – abbreviated mol measurement IITJEE SKMClasses.weebly.com amount substance single mole contains approximately 6.022×1023 units entities mole water contains 6.022×1023 H2O molecules molecule chemically I Beacons Academy, Jaya Nagar 4th Block bonded number atoms IITJEE SKMClasses.weebly.comIITJEE SKMClasses.weebly.com electrically neutral molecular orbital region mIITJEE SKMClasses.weebly.com electron found molecule opposed atom neat Alchemy India Services Pvt. 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33, Sector IV HSR Layout, Bangalore hydrolysis hydrosilylation hydrostannation hyperconjugation imides imines indium indoles induction inhibitors insertion iodine ionic liquids iridium iron isomerization The Brigade International School , Brigade Millenium JP Nagar Brigade Millenium, JP Nagar Bangalore ketones kinetic resolution lactams lactones lanthanides Lewis acids ligands lipids lithiation lithium macrocycles magnesium manganese Mannich bases medicinal chemistry metalation metallacycles metallocenes metathesis Michael addition Mitsunobu reaction molecular recognition molybdenum multicomponent reaction nanostructures natural products neighboring-group effects nickel nitriles nitrogen nucleobases nucleophiles nucleophilic addition nucleophilic National Centre For Excellence 154/1, “Victorian Enclave”, 5th Main, Malleshpalya, Bangalore aromatic substitution nucleosides nucleotides olefination oligomerization oligonucleotides oligosaccharides organometallic reagents osmium oxidation oxygen oxygenations ozonolysis palladacycles palladium peptides pericyclic reaction peroxides phase-transfer catalysis phenols pheromones phosphates phosphorus phosphorylation Adugodi Aga Abbas Ali Road Agaram Agrahara Dasara Halli Agrahara Dasarahalli Airport Exit Road Airport Main Road Airport Road Akkipet Ali Askar Road Alur Venkatarao Road Amarjyothi Layout Amruth Nagar Amrutha Halli Ananda Nagar Anandrao Circle Anche Palya Ane Palya Anekal Anjana Nagar Anubhava Nagar APMC Yard Arabic College Arakere Arcot Sreenivasachar Street Ashok Nagar Ashwath Nagar Attibele Attiguppe Austin Town Avala Halli Avenue Road B. Narayanapura Babusahib Palya Bagalagunte Bagalur Balaji Nagar Balepet Banashankari Banashankari 1st Stage Banashankari 2nd Stage Banashankari 3rd Stage Banaswadi Banaswadi Ring Road Bangalore G.P.O Bannerghatta Bannerghatta Road Bapuji Nagar Basappa Circle Basava Nagar Basavanagudi Basaveshwara Nagar Basaveshwara Nagar 2nd Stage Basaveshwara Nagar 3rd Block Basaveshwara Nagar 3rd Stage Basaveshwara Road Bazaar Street Begur BEL Road Bellandur Bellandur Outer Ring Road Bellary Road BEML Layout Benagana Halli Bendre Nagar Benson Town Bharati Nagar Bhattara Halli Bhoopasandra Bhuvaneshwari Nagar Bidadi Bileka Halli Bilekahalli Binny Mill Road Bismillah Nagar Bommana Halli Bommanahalli Kendriya Vidyalaya Malleswaram 18th Cross Malleswaram Bangalore Bommasandra Bommasandra Industrial Area Brigade Road Brindavan Nagar Brookefield Brunton Road BTM 1st Stage BTM 2nd Stage Bull Temple Road Palace Orchards/Sadashivnagar area located north city centre IITJEE SKMClasses.weebly.com property prices higher brackets possibly IITJEE SKMClasses.weebly.com up-market residential area in Bangalore M.G. Road/Brigade Road M.G. Road skmclasses.weebly.comBrigade Road main commercial areas Bangalore. Residential areas nearbyIITJEE SKMClasses.weebly.com Brunton Road Rest House Road, St. Mark’s Road skmclasses.weebly.comLavelle Road Airport Road/Indiranagar eastern suburb, Indiranagar is easily accessible IITJEE city centre skmclasses.weebly.com Airport Koramangala Located south Indiranagar, Koramangala quite favourite IITJEE SKMClasses.weebly.com IT professionals Despite 7 kmsIITJEE SKMClasses.weebly.com city centre, property values Ulsoor scenic man-made lake Ulsoor seen a spurt building activity last few years.IITJEE SKMClasses.weebly.com proximityIITJEE SKMClasses.weebly.com M.G Road jacked up property prices here Jayanagar/J.P. Nagar/Banashankari proximity areas Electronic City main reason skmclasses.weebly.comtheir growth recent past Jayanagar largest colonies Asia skmclasses.weebly.comthese areas popular areas Bangalore. Jayanagara originally namedIITJEE SKMClasses.weebly.com Sri Jayachamarajendra wodeyar last king Mysore. 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Malleswaram PSBB Learning Leadership Academy
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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. 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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 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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 School Ekya School Gitanjali International GISB Greengrove International School Gomathy Global School Gopalan International School Harvest International School India International School (IIS) Oakridge International School Primus School Shibumi Trio World School International Baccalaureate IB Candor International School Oakridge International School (IB-PYP) State Board Amaatra Academy Lawrence School-State Board Paradise Residential School Primus School St. Francis De Sales (SFS) High School Sri Kumaran Childrens Home St Francis School Vagdevi Vilas School Special Schools Sri Rakum School for the blind Mirambika School for New Age Sri Aurobindo Shibumi (J. Krishnamurthi Aurinko Academy Chetana Kini Institute Samarthanam Residential School XSeed Schools Mirambika School New Age Sri Aurobindo Mother Teresa Public School curriculum Chrysalis High List of Schools Achievers International Academy ACTS Secondary School Amaatra Academy Amar Jyothi School Amrita Vidyalayam Army Public School Asia Pacific World School Aurinko Academy B Mona High School Baldwin Boys High School Baldwin Girls High School Bangalore International School Bangalore School Bethany High Bethany Junior School BGS-NPS School Bishop Cotton Boys School Bishop Cotton Girls School Brigade School British International School BRS Global Centre for Excellence BVM Global Cambridge Public School Candor International School Capitol Public School Cathedral High School Chinmaya Vidyalaya Christ Academy Chrysalis High CMR National Public School Delhi Public School Deva Matha Central School Edify School Ekya School EuroSchool Freedom International School Gear School Geethanjali Montessori Geethanjali Vidhyalaya Gitanjali International (GISB) Global Indian International School Gnan Srishti School Gomathy Global School Gopalan School Green County Public School Greengrove International School Greenwood High Harvest International School India International School Innisfree House School JSS Public School Kendriya Vidyalaya (KV) Lawrence School ICSE Lawrence School-State Magnolia Maaruti Public School Manipal Tattva School Mirambika School for New Age Mother Teresa Public School National Centre for Excellence National Hill View Public School National Public School New Horizon Gurukul New Horizon Public School Nitte International School Notre Dame Academy Oakridge International School Oxford Public School Parachute Regiment School Paradise Residential School Patel Public School Podar International School Prakriya Green Wisdom School Presidency School Primus School PSBB LLA Radcliffe School Ravindra Bharathi Global School Ryan International School Sadhguru Sainath International School Samarthanam Residential School SFS High School Sherwood High Shibumi Silver Oaks Sishu Griha Sri Chaitanya Techno School Sri Kumaran Childrens Home Sri Rakum School for the blind St Francis School St Johns High School St Mira School St Thomas Public School St. Patrick’s Academy St. Peters School Sujaya School Sunrise International Residential School The Samhita Academy Trio World School Vagdevi Vilas School Venkat International Public School Vibgyor High Vidyaniketan School Vyasa International School Whitefield Global School Xseed Pre-School Zee School
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. MEXICO Middle Years Programme Cooper Academy, UNITED STATES European International School VIETNAM Mark Bills Middle School UNITED STATES Mount Washington School UNITED STATES UCSI International School MALAYSIA Diploma Programme Cass Technical High School, UNITED STATES Colegio Experimental Juan Montalvo, ECUADOR Colegio Miguel Moreno Ordoñez de Cuenca ECUADOR Colegio Nacional Ibarra ECUADOR Colegio Nacional Mariano Benítez ECUADOR Colegio Nacional Velasco Ibarra, ECUADOR Colegio Nacional Veracruz, ECUADOR Colegio Pedro Vicente Maldonado ECUADOR Colegio Técnico 12 de Febrero, ECUADOR Colegio Técnico Fiscomisional Ecuador Amazónico, ECUADOR Colegio de Bachillerato Limón ECUADOR King Fahd Academy Bonn GERMANY Saudi Schools Moscow RUSSIAN FEDERATION Unidad Educativa 17 de Julio ECUADOR Unidad Educativa 12 de Febrero ECUADOR Unidad Educativa Bernardo Valdivieso ECUADOR Unidad Educativa Dayuma ECUADOR Unidad Educativa Federico González Suárez ECUADOR Unidad Educativa Fiscomisional Fray Bartolomé de las Casas ECUADOR Unidad Educativa Fiscomisional Juan Pablo II ECUADOR Unidad Educativa Fiscomisional San José de Calasanz ECUADOR Unidad Educativa León Ruales ECUADOR Unidad Educativa Nacional Napo ECUADOR Unidad Educativa Temporal Camilo Gallegos Dominguez ECUADOR Unidad Educativa Temporal Manuel Córdova Galarza ECUADOR Primary Years Programme Campus International School, UNITED STATES Carl Hankey K-8 School UNITED STATES Christa McAuliffe Elementary School UNITED STATES Goethe International Charter School , UNITED STATES Hammond Eastside Elementary Magnet School, UNITED STATES Hawthorne Elementary School UNITED STATES Idlewild Elementary School, UNITED STATES J. Colin English Elementary UNITED STATES Jose de Escandon Elementary, UNITED STATES Lincoln Elementary School, UNITED STATES Qingdao Amerasia International School CHINA Roland Park K-8 Magnet School for International Studies, UNITED STATES Theodore Roosevelt Elementary School, UNITED STATES Woodrow Wilson Elementary UNITED STATES Middle Years Programme Cache La Poudre Middle School, UNITED STATES Carl Hankey K-8 School, UNITED STATES Cedar Shoals High School UNITED STATES Concord High School, UNITED STATES Harry Stone Montessori Academy, UNITED STATES International School of Monterey, UNITED STATES Johnnie R. Carr Middle School, UNITED STATES Prairie Seeds Academy, UNITED STATES Roland Park K-8 Magnet School, UNITED STATES Sterling Middle School UNITED STATES The Aga Khan Academy, Hyderabad, INDIA Diploma Programme Ausangate Bilingual School PERU Author’s School Istochnik RUSSIAN FEDERATION Colegio Fiscal Técnico El Chaco ECUADOR Colegio Juan Bautista Montini ECUADOR Colegio Nacional Ciudad de Cuenca ECUADOR Colegio Nacional Experimental Salcedo, ECUADOR Colegio Nacional Machachi, ECUADOR Colegio Nacional Mixto El Playon, ECUADOR Colegio Técnico Cascales, ECUADOR Dar al Marefa Private School, UNITED ARAB EMIRATES Escola Internacional del Camp SPAIN Gymnasium Jovan Jovanovic Zmaj SERBIA ISTEK Private Acibadem Schools TURKEY Instituto Superior Tecnológico Carlos Cisneros ECUADOR Instituto Superior Tecnológico Daniel Alvarez Burneo ECUADOR Instituto Técnico Superior Isabel de Godin ECUADOR King Abdulaziz Saudi School Rome ITALY Riga State Gymnasium Nr. 2 LATVIA Saudi School Vienna AUSTRIA State IS Seeheim Jugenheim/Schuldorf Bergstrasse GERMANY Unidad Educativa Bolívar, ECUADOR Unidad Educativa Abelardo Moncayo, ECUADOR Unidad Educativa Fiscomisional Verbo Divino, ECUADOR Unidad Educativa Mayor ECUADOR Unidad Educativa Nueva Semilla, ECUADOR Unidad Educativa Temporal Juan Bautista Vásquez, ECUADOR Primary Years Programme Ajman Academy UNITED ARAB EMIRATES British International School Kiev UKRAINE Cache La Poudre Elementary School, UNITED STATES Dr. Thomas S. O Connell Elementary School UNITED STATES Gems World Academy Abu Dhabi UNITED ARAB EMIRATES Hebron-Harman Elementary School, UNITED STATES International School of Solothurn, SWITZERLAND Lisa-Junior Primary School AUSTRIA Madison Richard Simis Elementary School, UNITED STATES Miina Härma Gümnaasium, ESTONIA Riffenburgh Elementary School UNITED STATES Roscoe Wilson Elementary School, UNITED STATES Singapore International School INDIA William H. Wharton K-8 Dual Language Academy UNITED STATES World Academy of Tirana, ALBANIA École Centrale, CANADA École Micheline-Brodeur CANADA École Saint-Édouard, CANADA École élémentaire catholique Jean-Paul II CANADA Özel Istanbul Coskun Koleji Anaokulu & Ilkokulu TURKEY Middle Years Programme Abraham Lincoln Middle School UNITED STATES Beijing Huijia Private School CHINA Cakir Middle School TURKEY Durango High School UNITED STATES Emirates IS Meadows, UNITED ARAB EMIRATES Madison International School, MEXICO Meadow Park Middle School, UNITED STATES North Central High School, UNITED STATES Phuket International Academy Day School THAILAND Ray Wiltsey Middle School UNITED STATES Rockridge Secondary School CANADA School Lane Charter School UNITED STATES Strothoff International School Rhein-Main Campus Dreieich GERMANY Tsukuba International School JAPAN École Père-Marquette, CANADA École secondaire Saint-Luc, CANADA Diploma Programme Anania Shirakatsy Armenian National Lyceum Ed’l Complex-CJSC, ARMENIA COLEGIO ALAUDA SPAIN Colegio Británico, MEXICO Colegio Nacional Camilo Gallegos Toledo ECUADOR Colegio Nacional Experimental Amazonas, ECUADOR Colegio Nacional Experimental María Angélica Idrobo, ECUADOR Colegio Nacional San José, ECUADOR Eastern Mediterranean International School, ISRAEL Emirates National School UNITED ARAB EMIRATES GEMS American Academy Abu Dhabi, UNITED ARAB EMIRATES German International School Sharjah UNITED ARAB EMIRATES Instituto Tecnológico Superior Angel Polibio Chaves, ECUADOR International School Moshi Arusha Campus TANZANIA, UNITED REPUBLIC OF International School of Bydgoszcz POLAND Ludoteca Elementary & High School, Padre Víctor Grados, ECUADOR Léman International School Chengdu CHINA Metropolitan School of Panama, PANAMA Munic. Atms. Educ. 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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