Critical Constant and Van der Waal's Constant

The relationship between critical constants of the gases and their Van der Waal constants is as follows:

(i) V_c = 3b

(ii) P_c = a/27b²

(iii) T_c = 8a/27Rb

(iv) The critical compressibility factor Z_c is given by,

These relations have been derived from the calculations based on Van der Waal's equation.

Boyle's Law

When the volume of the gas is reduced, the molecules move with the same speed but in lesser space. As a result, the frequency of collisions with the walls of the container increases and a pressure increase is noticed. This is the statement of Boyle's law and this can be deduced from the kinetic gas equation,

and the number of molecules N remain constant. Thus,

Charle's Law

When a gas is heated the molecules move faster increasing the pressure. But to maintain the pressure constant, the force of collision is compensated with an increase in volume. So, at constant pressure the volume of the gas increases with temperature. By kinetic gas equation we have,

substituting this we have,

This is the statement of Charles' law.

Dalton's Law

When more than one type of molecule is present (at constant T) then, the total pressure exerted by the mixture should be equal to the sum of their individual pressures when present alone. The pressure exerted by each gas is

where e₁ and e₂ are the average molecular kinetic energies of the two gases containing N₁ and N₂ molecules per unit volume. Since the molecules behave independent of each other, e₁ and e₂ = e , hence

= p₁ + p₂

The total pressure is equal to the sum of the pressures, which each gas would exert if allowed to occupy the entire space. This is Dalton's law of partial pressures.

Graham's Law of Diffusion

From kinetic theory,

Since the rate of diffusion of a gas is determined by the molecular speed,

The rate of diffusion of a gas depends inversely on the square root of its density. This is Graham's law of diffusion.