Question

derive the grahams law of diffusion

Answer 1

Graham's law of effusion sometimes called Graham's law of diffusion was formulated by Scottish physical chemist Thomas Graham Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles

Answer 2

Answer:

Graham's law of diffusion :-

This law states that, 'At constant temperature and pressure, the rate of diffusion of various gases is inversely proportional to the square root of their density. That is :

$r \: \infty \: \sqrt{ \frac{1}{d} }$

where r = rate of diffusion and d = density

$\frac{r1}{r2} \: = \: \sqrt{ \frac{d2}{d1} } = \sqrt{ \frac{M2}{M1} }$

Where, M stands for molar mass of gas.

When two gases are compared at different pressure, then we may write :

$r \: \infty \frac{p}{ \sqrt{m} } \: or \: r \infty \frac{p}{ \sqrt{d} }$

Where p is pressure of the gas. Therefore,

$\frac{r1}{r2} = \frac{P1}{P2} \sqrt{ \frac{d2}{d1} } = \frac{P1}{P2} \sqrt{ \frac{M2}{M1} }$

and, that's the required answer!