Question

The density of the gas is given by $\rho =4P+0.02P^2$, where $P$ is pressure in atm. The molar mass of gas is:

$(RT=50$ litre atm $mo{l}^{-1})$

• A. 100
• B. 50
• C. 200
• D. 400

Answer 1

The correct option is C 200

$\rho =\frac{PM}{RT}$ for ideal gases but actually $\frac{\rho }{P}$ varies with pressure.
Thus, molar mass is evaluated by assuming ${\left(\frac{\rho }{P}\right)}_{P\to 0}$ from the graph of $\rho /P$ vs. $P$
$\therefore \frac{\rho }{P}=4+0.02P$

As $P\to 0$

$\frac{\rho }{P}=4$

Also, $\frac{\rho }{P}=\frac{M}{RT}$

$\therefore \frac{M}{RT}=4$

$M=4\times 50=200$