Question

A vessel is filled with a gas at a pressure of $76$cm of mercury at a certain temperature. The mass of the gas is increased by $50\%$ by introducing more gas in the vessel at the same temperature. The resultant pressure of the gas is?

• A. $76$cm of mercury
• B. $108$cm of mercury
• C. $112$cm of mercury
• D. $114$cm of mercury

Answer 1

Answer: (D)

$114$cm of mercury

Pressure exerted by a gas.
$P=\frac{1}{2}\frac{M}{V}{v}_{rms}^2$
Since the temperature T is kept constant, $v_{av}^2$ and V are also constant.
$\therefore P\propto M$ or $\frac{P_2}{P_1}=\frac{M_2}{M_1}$
According to the question,
$\therefore \frac{P_2}{76}=\frac{[M_1+\left(\frac{50}{100}\right)M_2]}{M_1}=\frac{3}{2}$
$\Rightarrow P_2=\frac{3}{2}\times 76=114$cm of mercury.