Question

Two vessels separately contains 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 weight of $A$ and $B$ is

• A. $1:2$
• B. $2:3$
• C. $3:4$
• D. $4:5$

Answer 1

The correct option is C $3:4$

Let $P_A$ and $P_B$ be the pressure, ${\rho }_A$ and ${\rho }_B$ be the density of gases $A$ and $B$ respectively.
Given:
$P_A=2P_B$
${\rho }_A=1.5{\rho }_B$
We know that,
$PM=\rho RT$
$\Rightarrow M=\frac{\rho RT}{P}$
At a given temperature,
$M\propto \frac{\rho }{P}$
So, $\frac{M_A}{M_B}=\frac{{\rho }_A{P}_B}{{\rho }_B{P}_A}$
$\Rightarrow \frac{M_A}{M_B}=\frac{1.5{\rho }_B{P}_B}{{\rho }_B\times 2P_B}$
$\Rightarrow \frac{M_A}{M_B}=\frac{3}{4}=3:4$