$350{\mathrm{cm}}^3$ of ${\mathrm{CH}}_4$ and $175{\mathrm{cm}}^3$ of an unknown gas ' $\mathrm{A}$ ' diffused in the same time under similar conditions. The molecular mass of gas $\mathrm{A}$ is

We know from that the rate of diffusion of any gas is directly proportional to $\frac{1}{\sqrt{\text{ molecular mass }}}$

$\therefore \frac{\text{ Volume }}{\text{ Time }}\propto \frac{1}{\sqrt{\mathrm{M}}}$

Rewriting this expression, we have: $\mathrm{V}\propto \frac{1}{\sqrt{\mathrm{M}}}$

Substituting the values provided as per the question, we have:

$\frac{{\mathrm{CH}}_4\text{ Volume diffused }}{\text{ Unknown gas volume diffused }}=\sqrt{\frac{\text{ Unknown gas weight }}{{\mathrm{CH}}_4\text{ gas weight }}}$

$\Rightarrow \frac{350}{175}=\sqrt{\frac{\text{ Unknown gas weight }}{16}}$

Therefore, the molecular mass of the given gas would be $64\mathrm{g} {\mathrm{mol}}^{-1}$.