Deduce (a) Graham's law and (b) Daltons law from Kinetic gas equation.

Explanation

a) Graham.s law : At constant temperature and pressure the rate of diffusion of a gas is inversely.
proportional to the square root of its density, ` r prop (1)/(sqrt(d))`
Deduction : Kinetic gas equation is .
` PV = 1/3 m n u^2 =1/3 Mu^2`
` u^2= (3PV )/(M ) = (3 P)/(d)`
` therefore u= sqrt((3P )/(d ))`
At constant pressure `u=k -(1)/(sqrt(d))`
k= constant or ` u= prop (1 )/( sqrt(d))`
` therefore `The rate of diffusion of gases depends upon the velocity of the gas molecules.
So ` r prop (1)/( sqrt(d))`
This is Graham.s law.
B) Dalton.s law of partial pressures : The total pressure exerted by a mixture of chemically non reacting gases at given temperature and volume, is equal to the sum of the partial pressures of the component gases. Deduction : Consider a gas present in vessel of volume=V no. of molecules ` =n_1 `
mass of each molecule` =m_1`
RMS velocity ` = u_1`
According to kinetic gas equation the pressure of the gas. ` P_1 =1/3 (m_1 n_1 u_(1)^(2))/( V)`
When this gas is replaced by another gas in the same vessel. ` P_2 =1/3 (m_2 n_2 u_(2)^(2))/( V)`
When these two gases are mixed in the same vessel,
the total pressure of the mixture is `p = 1/3 (m_1 n_1 u_(1)^(2))/(V ) +1/3 (m_2 n_2 u_(2)^(2))/( V) = P_1 +P_2`
` therefore P=P_1 +P_2`
This is Dalton.s law of partial pressures.