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)
$\therefore M_1{V}_{rms1}^2=M_2{V}_{rms2}^2$
$\Rightarrow \frac{V_{rms1}^2}{V_{rms2}^2}=\frac{M_2}{M_1}$
$\Rightarrow \frac{V_{rms1}}{V_{rms2}}=\sqrt{\frac{M_2}{M_1}}=\sqrt{4/1}=2\left[given,\frac{M_1}{M_2}=\frac{1}{4}\right]$