Question

The mass of molecule $A$ is twice that of molecule $B$. The root mean square velocity of molecule $A$ is twice that of molecule $B$. If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_A}{P_B}$ will be:

• A. 8 : 1
• B. 1 : 8
• C. 4 : 1
• D. 1 : 4

Answer 1

The correct option is A 8 : 1

Given that, $M_A=2M_B$, and $(v_{\text{rms}}{)}_A=2(v_{\text{rms}}{)}_B$

$v_{\text{rms}}=\sqrt{\frac{3PV}{nM}}$
For same number of moles n and volume V,
$v_{\text{rms}}\propto \sqrt{\frac{P}{M}}$

$\frac{(v_{\text{rms}}{)}_A}{(v_{\text{rms}}{)}_B}=\sqrt{\frac{P_A}{P_B}\times \frac{M_B}{M_A}}$

Squaring both sides, we get,

$4=\frac{P_A}{P_B}\times \frac{1}{2}$
$\frac{P_A}{P_B}=8:1$