Question

At $300K$, the density of a certain gaseous molecule at $2$ bar is double to that of dinitrogen $(N_2)$ at $4$ bar. The molar mass of gaseous molecule is :

• A. $28gmo{l}^{-1}$
• B. $56gmo{l}^{-1}$
• C. $112gmo{l}^{-1}$
• D. $224gmo{l}^{-1}$

Answer 1

Answer: (C)

For unknown gas :
$PM=\rho RT$
$2\text{ bar }\times M={\rho }_{\text{unknown }}RT\dots \dots ..(1)$
For nitrogen gas :
$4\text{ bar }\times 28g/mol={\rho }_{\text{nitrogen }}RT\dots \dots ..(2)$
But,
${\rho }_{\text{unknown }}=2{\rho }_{\text{nitrogen }}$
Substitute this in equation (1)
$2\text{ bar }\times M=2{\rho }_{\text{nitrogen }}RT\dots \dots .(3)$
Divide equation (3) with equation (2)
$\frac{2\mathrm{bar}\times M}{4\mathrm{bar}\times 28g/mol}=\frac{2{\rho }_{\text{nitrogen }}RT}{{\rho }_{\text{nitrogen }}RT}$
$\frac{M}{2\times 28g/mol}=2$
$M=4\times 28g/mol=112g/mol$
The molar mass of the gaseous molecule is $112g/mol$