Let us consider two gases A and B diffusing into one another.
Let ρ1 and ρ2 be their densities and v1 and v2 be their respective r.ms. velocities.
Pressure exerted by gas A,
\(P_1= \frac{1}{3}ρ_1V_1^2\)
and pressure exerted by gas B,
\(P_2= \frac{1}{3}ρ_2v_2^2\)
When steady state of diffusion is reached
P1 = P2
\( \frac{1}{3}ρ_1v_1^2\) = \( \frac{1}{3}ρ_2v_2^2\)
\( \frac{v_1^2}{v_2^2}=\frac{ρ_2}{ρ_1}\)
or \( \frac{v_1}{v_2}=\,\sqrt\frac{ρ_2}{ρ_1}\)
If r1 and r2 be the rates of diffusion of gases A and respectively.
\(\frac{r_1}{r_2}=\frac{v_1}{v_2}=\sqrt\frac{ρ_2}{ρ_1}\)
Thus this law states that the rate of diffusion of a gas is inversely proportional to the square root of its density.
r ∝ \(\frac{1}{\sqrtρ}\)
