Question

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2:3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4:3. The ratio of their densities is

• A. 1 : 4
• B. 1 : 2
• C. 6 : 9
• D. 8 : 9

Answer 1

Answer: (D)

8 : 9

$Sol$ : (D)
$PV=nRT=\frac{m}{M}RT$

$\Rightarrow PM=\rho RT$

$\frac{{\rho }_1}{{\rho }_2}=\frac{P_1{M}_1}{P_2{M}_2}=\left(\frac{P_1}{P_2}\right)\times \left(\frac{M_1}{M_2}\right)=\frac{4}{3}\times \frac{2}{3}=\frac{8}{9}$
Here ${\rho }_1$ and ${\rho }_2$ are the densities gases in the vessel containing the mixture.