# Graham’s Law of Diffusion

Graham’s Law of Diffusion (1829):

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”.

I.e.
$r \propto \sqrt{\dfrac{1}{d}}$

where r = rate of diffusion and d =density

$\dfrac{r_1}{r_2}$ = $\sqrt{ \dfrac{d_2}{d_1}}$ = $\sqrt{\dfrac{M_2}{M_1}}$

where M stands for molar mass of the gas. When two gases are compared at different pressures then we may write,

$r \propto \dfrac{P}{\sqrt{M}} \\ Or \\ r \propto \dfrac{P}{\sqrt{d}}$

where P is the pressure of the gas. Therefore,

$\dfrac{r_1}{r_2}$ = $\dfrac{P_1}{P_2} \sqrt{\dfrac{d_2}{d_1}}$ = $\dfrac{P_1}{P_2} \sqrt{\dfrac{M_2}{M_1}}$

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