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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