Question

Two identical containers are filled with a gas. The first is filled with methane (${CH}_4$) and the second with helium.
Which gas would effuse more rapidly out of its container and how many times faster would the process take place?
Assume all conditions are equal except the identity of the gases in the two containers.

• A. $He,4\times$ faster
• B. ${CH}_4,4\times$ faster
• C. $He,2\times$ faster
• D. ${CH}_4,2\times$ faster

Answer 1

The correct option is C $He,2\times$ faster

We know, diffusion rate ${\alpha }^{1/\sqrt{M}}$

(inversely proportional)

for $He$, $M=4$

diffusion rate $=\frac{K}{\sqrt{4}}=\frac{K}{2}$

for ${CH}_4$, $M=16$

diffusion rate $=\frac{K}{\sqrt{16}}=\frac{K}{4}$

Hence $He$ is $2$ times faster than ${CH}_4$.