Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature, pressure of A being…
Two vessels separately contain two ideal gases $A$ and $B$ at the same temperature, 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
$1: 2$
$2: 3$
$3: 4$
$2: 1$
Solution
For an ideal gas, $\mathrm{PV}=\mathrm{RT}$ and $\mathrm{M}=\rho \mathrm{V}$
$\begin{array}{ll}\therefore & \frac{P M}{\rho}=R T \\ \therefore & \frac{P_A M_A}{\rho_A}=\frac{P_B M_B}{\rho_B}\end{array}$
$\frac{M_A}{M_B}=\frac{\rho_A}{\rho_B} \times \frac{P_B}{P_A}=\frac{3}{2} \times \frac{1}{2}=\frac{3}{4}$
