# States of Matter

## Intermolecular Forces

The forces of attraction existing among the molecules of a substance (gaseous, liquid or solid) are called intermolecular forces. Attractive intermolecular forces are known as van der Waals forces. Greater the intermolecular forces, higher is the melting and boiling point. Attractive intermolecular forces are known as van der Waals' forces. Different types of intermolecular forces are given below.## London Forces or Dispersion Forces

This force of attraction was proposed by the German physicist F. London, and for this reason, force of attraction between two temporary dipoles is known as London forces and is also called dispersion forces.We know that in non-polar molecules, the dipole moment is zero because of symmetrical distribution of their electronic charge cloud.

But it may be possible at any point of time, the electron cloud of the molecule may be distorted so that an instantaneous dipole or momentary dipole is produced in which one part of the molecule is slightly more negative than the other part. This momentary dipole induces dipoles in the neighbouring molecules. Thus, the force of attraction exists between them and are exactly same as between permanent dipoles. This force of attraction is known as London forces or Dispersion forces. These forces are always attractive and the interaction energy is inversely proportional to the sixth power of the distance between two interacting particles (i.e. 1/r

^{6}where r is the distance between two particles).

These forces are important only at short distances (~500 pm) and their magnitude depends on the polarizability of the particle. The strength of these forces increases with the increase in molecular mass, molecular size, number of electrons and surface area of the molecule.

## Dipole - Induced Dipole Forces

This type of attractive forces operate between the polar molecules and nonpolar molecules. Permanent dipole of the polar molecule induces dipole on the electrically neutral molecule (i.e. nonpolar molecules) by deforming its electronic cloud. Thus an induced dipole is developed in the other molecule. In this case also interaction energy is proportional to 1/r^{6}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.

### Dipole - Induced Dipole interaction are present in which of the following pairs

a. Cl_{2}and CCl

_{4}

b. HCl and He atoms

c. SiF

_{4}and He atoms

d. H

_{2}O and alcohole

## Dipole - Dipole Forces

Dipole-dipole forces act between molecules possessing the permanent dipole (i.e. polar molecules). The polar molecules interact with neighbouring 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. The interaction energy is also inversely proportional to distance between polar molecules. Dipole-dipole interaction energy between stationary polar molecules (as in solids) is proportional to 1/r^{3}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.

## 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.## Intermolecular Forces vs Thermal Interactions

Intermolecular forces are the forces of interaction between the molecules of that substance which try to bring the molecule closer but Thermal energy possessed by the molecules due to temperature which result into the movement of the molecule and hence tries to keep them apart. So both are inversely related to each-other.In gases, the intermolecular forces of attractions are weakest while thermal energy is highest. In solid, intermolecular forces of attraction are strongest while thermal energy is minimum.

Predominance of Intermolecular Forces-

Gas -----> Liquid -----> Solid

Predominance of Thermal Energy-

Solid -----> Liquid -----> Gas

## Boyle's Law (Pressure - Volume Relationship)

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-V ∝ 1/P at constant T and n -----(equation-1)

V = K.1/P -----(equation-2)

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

From (equation-2)-

VP = K -----(equation-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 V

_{1}at pressure P

_{1}expand to volume V

_{2}at pressure P

_{2}, then according to Boyle's law-

P

_{1}V

_{1}= P

_{2}V

_{2}= Constant -----(equation-4)

P

_{1}/P

_{2}= V

_{2}/V

_{1}-----(equation-5)

## Charles' Law

At constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature.V ∝ T -----(equation-1)

or, V = K.T -----(equation-2)

or, V/T = K -----(equation-3)

or, V

_{1}/T

_{1}= V

_{2}/T

_{2}-----(equation-4)

we know that, PV = nRT

so, V/T = nR/P -----(equation-5)

from equation-3 and equation-5, we have-

K = nR/P

or, K ∝ 1/P

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

Answer: Given, V_{1}= 2L, T

_{1}= 273+23.4 = 296.4K

V

_{2}= ?, T

_{2}= 273+26.1 = 299.1K

According to charles law,

V

_{1}/T

_{1}= V

_{2}/T

_{2}-----(equation-4)

V

_{2}= (V

_{1}x T

_{2})/T

_{1}

or, V

_{2}= (2L x 299.1k)/296.4k

or, V

_{2}= 2.018L

## Gay-Lussac's Law

The pressure exerted by a gas is proportional to the temperature of the gas when the mass is fixed and the volume is constant.P ∝ T

or, P = K.T

or, P/T = k

Where-

P is the pressure exerted by the gas

T is the absolute temperature of the gas

k is a constant.

## Avogadro's Hypothesis

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.

or, V = K.n -----(equation-1)

we know that-

n = m/M where, n = mass of the gas and M = molar mass

so, V = K.(m/M) -----(equation-2)

or, M = K.(m/V) -----(equation-3)

or, M = K. d -----(equation-4)

Here 'd' is the density of the gas. We can say that from equation-4, the density of a gas is directly proportional to its molar mass.

## Ideal Gas Equation

It is also called combined gas law as it derived from the combination of Boyle's Law, Charles' Law and Avogadro's Hypothesis.We know that

Boyle's Law- V ∝ 1/P

Charles's Law- V ∝ T

Avogadro's Hypothesis- V ∝ n

On combining all these three laws we get-

V ∝ n.T/P

or, V = R.n.T/P

where, R is Gas Constant and it is same for all gases. Therefore it is also called Universal Gas Constant

or,

**PV = n.R.T**-----(equation-1)

equation-1 is known as Ideal Gas Equation.

If temperature, volume and pressure of a fixed amount of gas vary from T

_{1}, V

_{1}and p

_{1}to T

_{2}, V

_{2}and p

_{2}then we can write-

(P

_{1}.V

_{1})/T

_{1}= nR

(P

_{2}.V

_{2})/T

_{2}= nR

or, (P

_{1}.V

_{1})/T

_{1}= (P

_{2}.V

_{2})/T

_{2}-----(equation-2)

## Dalton’s Law of Partial Pressure

Dalton's Law of Partial Pressure is a gas law which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture.**p**

_{Total}= p_{1}+ p_{2}+ p_{3}+ ... (at constant T, V)where p

_{Total}is the total pressure exerted by the mixture of gases and p

_{1}, p

_{2}and p

_{3}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**.

**Partial pressure in terms of mole fraction**

Suppose at the temperature T, three gases, enclosed in the volume V, exert partial pressure p

_{1}, p

_{2}and p

_{3}respectively. then-

p

_{1}= (n

_{1}.RT)/V

similarly for other two gases-

p

_{2}= (n

_{2}.RT)/V

p

_{3}= (n

_{3}.RT)/V

where n

_{1}, n

_{2}and n

_{3}are number of moles of these gases. Thus, expression for total pressure will be-

p

_{Total}= p

_{1}+ p

_{2}+ p

_{3}

or, p

_{Total}= n

_{1}.(RT/V) + n

_{2}.(RT/V) + n

_{3}.(RT/V)

or, p

_{Total}= (n

_{1}+ n

_{2}+ n

_{3})(RT/V)

Dividing p

_{1}by p

_{Total}we get-

p

_{1}/p

_{Total}= n

_{1}/(n

_{1}+ n

_{2}+ n

_{3})= n

_{1}/n = x

_{1}

where, n

_{1}+ n

_{2}+ n

_{3}= n and x

_{1}is mole fraction of first gas.

or, p

_{1}= x

_{1}.p

_{Total}

Similarly, for other two gases-

p

_{2}= x

_{2}.p

_{Total}

p

_{3}= x

_{3}.p

_{Total}

Thus, the general equation can be written as-

**p**

_{i}= x_{i}.p_{Total}where p

_{i}and x

_{i}are partial pressure and mole fraction of i

^{th}gas respectively.

If total pressure of a mixture of gases is known, the above equation can be used to find out pressure exerted by individual gases.

## Kinetic Theory of Gases

On the basis of extensive study on the behaviour of gases, Bernouli, Boltzaman, Maxwell, Clausius and et al. gave the following main postulates of kinetic theory of gases.1. Gases consist of a large number of tiny particles (atoms and molecules). These particles are extremely small compared to the distance between the particles. The size of the individual particle is considered negligible and most of the volume occupied by the gas is empty space.

2. Gas molecules are in a state of constant random motion in all directions and the motion increases with increase of temperature.

3. Gas molecules are in constant random motion which results in colliding with each other and with the walls of the container. As the gas molecules collide with the walls of a container, the molecules impart some momentum to the walls.

4. The pressure of the gas is the force per unit area exerted when moving molecules collide with inner walls of the container.

5. The collisions between the molecules and the walls are perfectly elastic. That means when the molecules collide they do not lose kinetic energy. Molecules never slow down and will stay at the same speed.

6. Molecules of the gas don't have the potential energy i.e. all the energy of the gas molecules is kinetic.

7. The average kinetic energy of the gas molecules is directely proportional to temperature. i.e., The higher the temperature, the higher the average kinetic energy of the gas.

8. The molecules do not exert any force of attraction or repulsion on one another except during collisions.

## Deviation Of Real Gas From Ideal Gas Behavior

The deviation of real gas from ideal gas behaviour occurs due to the postulates of kinetic theory of gases. Two posulates of the kinetic theory do not hold good. These are-1. There is no force of attraction between the molecules of a gas. and

2. Volume of the molecules of a gas is negligibly small in comparison to the space occupied by the gas.

If postulate '1' 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 postulate '2' 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.

P

_{ideal}= P

_{real}+ an

^{2}/V

^{2}

Where, 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 is Ideal Gas Equation becomes-

(P + an

^{2}/V

^{2}) (V − nb) = nRT -----(equation-1)

(equation-1) 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.

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

Z = PV/nRT

when-

Z = 1 (Ideal Gas at all Temperature)

Z = >1 (Positive deviation from Ideal Gas Above their Boyle Temperature)

Z = < 1 (negative deviation from Ideal Gas below their Boyle Temperature)

## Unit of Vander Waal Constants

Unit of 'a': atm lit² mol⁻²Unit of 'b': liter mol⁻¹

## Physical Significance of Vander Waal Constants 'a' & 'b'

*Physical Significance of Vander Waal Constants 'a'*

Vander Waal constant 'a' represents the magnitude of intermolecular forces of attraction.

*Physical Significance of Vander Waal Constants 'b'*

Vander Waals constant 'b' represents the effective size of the molecules.( or average volume excluded from v by a particle).

## Boyle's Temperature (T_{B})

The temperature at which normal gases start to behave like ideal gases(due to the absence of both attractive and repulsive forces at that particular temperature).T

_{B}= a/Rb

### A real gas behaves as an ideal gas

a. at high temperature and low pressureb. at low temperature and high pressure

c. at high temperature and high pressure

d. at low temperature and low pressure

## Liquefaction of Gas

The liquefaction of a gas is a phenomena which takes place when the intermolecular forces of attraction increases to such an extent that they combine the gas molecules together forming a liquid state. Liquefaction of gas can be increased by increasing the intermolecular forces of attraction, which in turn can be increased either by increasing the pressure, which will reduce the distance between the molecules or decreasing the kinetic energy by cooling the gas making them slower. Hence, a gas can be liquefied by cooling or by application of pressure or the combined effect of both.The temperature at which a gas can be liquified is called liquifaction temperature. Above this temperature, the gas can not be liquidfied no matter how high is the pressure. Thus liquifaction temperature of a gas is the critical temperature (T

_{c}). Above this temperature, gaseous state exists, at this temperature liquifaction occurs and below this temperature liquid state exists. Critical temperature depends on the attractive forces present in the gaseous molecules.

The volume and pressure corresponding to critical temperature is called critical volume(V

_{c}) and critical pressure(P

_{c})respectively.

The value of T

_{c}, P

_{c}and V

_{c}are-

T

_{c}= 8a/27Rb

P

_{c}= a/27b

^{2}

V

_{c}= 3b

### The value of Z_{c} at T_{c}, P_{c} and V_{c} is

a. 3/8b. 4/8

c. 1

d. zero

## Surface Tension

Surface tension is a property of liquid which arises due to the different situation of the liquid molecules on the surface and in the bulk of the liquid.A molecule lying inside (bulk) the liquid is surrounded by other molecules and so is attracted equally in all directions. Thus, the resultant force of attraction acting on the molecule is zero.

However, A molecule lying at the surface of liquid is attracted by liquid molecules from the bulk of the liquid and feel inward pull. As a result of this inward pull on all molecules lying at the surface, the surface behave as if it were under tension and the surface of the liquid tends to the smallest possible area for a given volume of the liquid. This gives the lowest energy state of the liquid.

Surface tension of a liquid is defined as the force in dyne acting at right angles to the surface along one cm length of the liquid surface.

unit of surface tension is dyne per centimetre or Newton per metre.

Surface tension is a property that arises due to the intermolecular forces of attraction among the liquid molecules. Greater the intermolecular force of attraction, higher is the surface tension of the liquid.

Surface tension of liquid generally decreases with increase of temperature and becomes zero at the critical temperature. Surface tension decreases with increase in temperature is due to on increasing the temperature, the kinetic energy of the molecules increases ,and, therefore the intermolecular attraction decreases.

**Surface Energy**

The work in ergs required to be done to increase or extend the surface area by one square centimeter is called surface energy.

The unit of surface energy is ergs per square centimeter or joules per square meter.

## Viscosity

Viscosity is a property of liquid which resist to flow. Due to viscosity some liquid flow slowly and some liquid flow quickly. Viscosity is nothing but internal reistance to flow possessed by liquid.Liquids which flow slowly, have high internal resistance which is due to strong intermolecular forces says more viscous or are of high viscosity.

However, Liquids which flow rapidly have low internal resistance which is due to weak intermolecular forces says less viscous or are of low viscosity.

Greater are the intermolecular forces, higher is the viscosity of the liquid. Viscosity decreases with increasing the temperature. Kinetic energy increases on increasing temperature and so intermolecular force of attraction decreases, consequently, viscosity decreases and liquid flow quickly.

We know that liquid flow in layers in a tube. Liquid that contact in the surface of tube is almost stationary. As we move from the surface towards the centre of the tube, the velocity of the liquid layers keeps on increasing till it is maximum at the centre.

The force of friction F between two layers each having area A cm

^{2}, separated by a distance dx cm , and having a velocity difference of dv cm/sec ,is given by-

F ∝ A ( dv / dx )

F = η A ( dv/dx)

where η is coefficient of viscosity.

dv / dx is viscosity gradient

If dx = 1cm, A = 1cm

^{2}and dV = 1cm/sec

F = η

Coefficient of viscosity may be defined as the force of friction required to maintain a velocity difference of 1 cm/sec between two parallel layers, 1 cm apart and each having an area of 1 sq cm.

The unit of viscosity are dynes sec cm

^{-2}.This is also called 1 Poise.