Question

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

Answer 1

Ideal gas equation

• The ideal gas equation is as follows:

$\mathrm{PV}=\mathrm{nRT}$

• $\mathrm{P}$ is the pressure.
• $\mathrm{V}$ is the volume.
• $\mathrm{n}$ is the number of moles.
• $\mathrm{R}$ is a gas constant.
• $\mathrm{T}$ is the temperature.
• The ideal gas equation can be written as follows:

$\mathrm{PM}=\mathrm{dRT}$

• $\mathrm{d}$ is the density.
• $\mathrm{M}$ is the molar mass of gas

Calculate ratio of their densities of two gases

• Atomic masses ratio of two non-reactive monoatomic ideal gases is $2:3$.
• The ratio of their partial pressure at a constant temperature is $4:3$.
• The density of the first gas is as follows:

${\mathrm{d}}_1=\frac{{\mathrm{P}}_1{\mathrm{M}}_1}{\mathrm{RT}}$

• The density of the second gas is as follows:

${\mathrm{d}}_2=\frac{{\mathrm{P}}_2{\mathrm{M}}_2}{\mathrm{RT}}$

• The ratio of the densities of the two gases is as follows:

$\begin{array}{rcl}\frac{{\mathrm{d}}_1}{{\mathrm{d}}_2}& =& \frac{{\mathrm{P}}_1{\mathrm{M}}_1}{\bcancel{\mathrm{RT}}}\times \frac{\bcancel{\mathrm{RT}}}{{\mathrm{P}}_2{\mathrm{M}}_2}\\ & =& \frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}\times \frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}\\ & =& \frac{4}{3}\times \frac{2}{3}\\ & =& \frac{8}{9}\end{array}$

• The ratio of the densities of the two gases is $8:9$.