Question

A compressed cylinder of gas contains $1.50\times {10}^{3}g$ of $N_2$ gas at a pressure of $2.0\times {10}^{7}Pa$ and a temperature of ${17.1}^{\circ }C$. What volume of gas has been released into the atmosphere if the final pressure in the cylinder is $1.80\times {10}^{5}Pa$? Assume ideal behaviour and that the gas temperature is unchanged.

• A. 1264 L
• B. 126 L
• C. 12600 L
• D. 45 L

Answer 1

The correct option is A 1264 L

Given, $n_{N_2}=\frac{1\cdot 5\times {10}^3}{28}=53.57mol$.

since, temperature and volume of cylinder is same

$\text{So,}\frac{P_1}{P_2}=\frac{n_1}{n_2}\Rightarrow \frac{2\times {10}^7}{1.8\times {10}^5}=\frac{53.57}{n_2}\Rightarrow n_2=0.48213$

$\begin{array}{c}\text{Thus, escaped moles}=(n_1-n_2)=53.087\text{.mol}\\ \text{Hence, required volume escaped}\begin{array}{cc}=\frac{nRT}{P}& =\frac{53.087\times 8.3\times 290.1}{101325}{m}^3\\ & =1.2615m^3\\ & \approx .1264L\end{array}\end{array}$

$\text{so option (A) is correct.}$