Question

A mixture of two gases is contained in a vessel. The Gas $1$ is monoatomic and gas $2$ is diatomic and the ratio of their molecular masses $\frac{M_{1}}{M_{2}}=\frac{1}{4}$ . The ratio of root mean square speeds of the molecules of two gases is

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

Answer: (A)

From kinetic theory of gases
$P=\frac{1}{3}\frac{M}{V}\times V_{rms}^{2}$
Since, $P$ and $V$ are constant (same)
$\therefore \, M_{1}V_{rms 1}^{2}=M_{2}V_{rms 2}^{2}$
$\Rightarrow \frac{V_{rms 1}^{2}}{V_{rms 2}^{2}}=\frac{M_{2}}{M_{1}}$
$\Rightarrow \frac{V_{rms 1}}{V_{rms 2}}=\sqrt{\frac{M_{2}}{M_{1}}}=\sqrt{4 / 1}=2\left[given , \frac{M_{1}}{M_{2}} = \frac{1}{4}\right]$