Question

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

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

Answer 1

The correct option is A $112gmo{l}^{-1}$

For unknown gas :

$PM=\rho RT$

$2bar\times M={\rho }_{unknown}RT$.......(1)

For nitrogen gas :

$4bar\times 28g/mol={\rho }_{nitrogen}RT$......(2)

But,

${\rho }_{unknown}=2{\rho }_{nitrogen}$

Substitute this in equation (1)

$2bar\times M=2{\rho }_{nitrogen}RT$.......(3)

Divide equation (3) with equation (2)

$\frac{2bar\times M}{4bar\times 28g/mol}=\frac{2{\rho }_{nitrogen}RT}{{\rho }_{nitrogen}RT}$

$\frac{M}{2\times 28g/mol}=2$

$M=4\times 28g/mol=112g/mol$

The molar mass of the gaseous molecule is $112g/mol$

Therefore, the correct option is A.