Question

The density of an ideal gas at $298\text{K}$ and $1.0\text{atm}$ is found to be $1.25{\text{kg m}}^{-3}$. Density of the gas at $1.5\text{atm}$ and at $298\text{K}$ is:

• A. $1.25{\text{kg m}}^{-3}$
• B. $1.20{\text{kg m}}^{-3}$
• C. $1.00{\text{kg m}}^{-3}$
• D. $1.875{\text{kg m}}^{-3}$

Answer 1

The correct option is D $1.875{\text{kg m}}^{-3}$

$P=\frac{dRT}{M}$
$P\propto d$
$[\because \text{here, temperature is kept constant for the given gas]}$
Thus, $\frac{P_1}{d_1}=\frac{P_2}{d_2}$
$\therefore d_2=\frac{P_2\times d_1}{P_1}=\frac{1.5\times 1.25}{1}=1.875{\text{kg m}}^{-3}$