Question

Pressure of He gas confined in a steel chamber drops from 4.0 to 1.0 atmosphere in 4.0 hours due to diffusion through a pin-hole in the steel chamber. If an equimolar mixture of He and methane gas at 20 atmosphere and the same temperature are confined in the same chamber, what will be the parital pressure of He after 1.0 hour. Assume rate of diffusion to be linear function of gas pressure and inverse function of square root of molar masses.

Answer 1

$-\frac{dP}{dt}=\frac{KP}{\sqrt{M}}\Rightarrow {\int }_{P_0}^P-\frac{dP}{P}=\frac{K}{\sqrt{M}}{\int }_0^{t}dt$
$\Rightarrow \ln \left(\frac{P_0}{P}\frac{Kt}{\sqrt{M}}\right)\Rightarrow \ln 4=\frac{4K}{\sqrt{4}}=2K$
$\ln \frac{10}{P}=\frac{K}{2}\Rightarrow P_{He}=7.07atm$
Also,
$\ln {\left(\frac{P_0}{P}\right)}_{He}$ and
$\ln {\left(\frac{P_0}{P}\right)}_{C{H}_4}=\frac{Kt}{4}$
$\Rightarrow {\left(\frac{P_0}{P}\right)}_{He}={\left(\frac{P_0}{P}\right)}_{C{H}_4}^2\Rightarrow \frac{10}{7.07}=\frac{100}{P_{C{H}_4}^2}$
$\Rightarrow P_{C{H}_4}=8.4atm$