Q114 / 180 · NEET 2015 (Phase 2) · Physics

Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature, the pressure of $A$ being twice that of $B$ . Under such conditions, the density of $A$ is found to be $1.5$ times the density of $B$ . The ratio of molecular weights of $A$ and $B$ is

Solution

$P_{A} = \frac{ρ_{A} R T}{M_{A}}, P_{B} = \frac{ρ_{B} R T}{M_{B}}$

$\Rightarrow \frac{P_{A}}{P_{B}} = \frac{ρ_{A}}{ρ_{B}} \frac{M_{B}}{M_{A}}$

$\Rightarrow \frac{3}{2} \frac{M_{B}}{M_{A}} = 2$
So, $\frac{M_{A}}{M_{B}} = \frac{3}{4}$

Hence, the correct answer is option: 'A'.