Question

Two non-reactive monatomic 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

Answer 1

Answer:

The ratio of their densities is 8:9.

Explanation:

Given:

Ratio of atomic masses:

$\frac{M_1}{M_2}=\frac{2}{3}$

Ratio of partial pressures:

$\frac{P_1}{P_2}=\frac{4}{3}$

In an ideal gas equation:

$PV=nRT$

$PV=\frac{m}{M}RT$

$\frac{PM}{RT}=\frac{m}{V}=Density$

Density of the gas-1:

$D_1=\frac{P_1M_1}{RT}$...(1)

Density of gas-2:

$D_2=\frac{P_2M_2}{RT}$..(2)

Dividing (1) and (2):

$\frac{D_1}{D_2}=\frac{\frac{P_1M_1}{RT}}{\frac{P_2M_2}{RT}}=\frac{8}{9}$