Question

A cylinder contains $100\text{g}$ of an ideal gas (mol. wt. = $40\text{g/mol}$) at ${27}^{\circ }\text{C}$ and 2 atm pressure. During transportation the cylinder fell and a dent was formed. The valve present cannot sustain pressures greater than 2 atm. Hence, $10\text{g}$ of a gas got leaked out. The volume of the container before and after the formation of the dent is:

• A. 30.8 L; 27.7 L
• B. 27.7 L; 30.8 L
• C. 30.8 L; 30.8 L
• D. 27.7 L; 27.7 L

Answer 1

The correct option is A 30.8 L; 27.7 L

From the ideal gas equation:
$PV=nRT$

$V=\frac{nRT}{P}$

$\text{Number of moles}{}^{\prime }{n}^{\prime }=\frac{\text{Given mass of the substance}}{\text{Molecular mass of the substance}}$

Before the formation of dent, volume of the gas, $=\frac{nRT}{P}=\frac{100}{40}\times \frac{0.082\times 300}{2}=30.75\text{L}$

After dent, volume of gas $=\frac{nRT}{P}=\frac{90}{40}\times \frac{0.082\times 300}{2}=27.675\text{L}$