A $100 \mathrm{~L}$ cylinder containing $\mathrm{H}_2$ exerted a pressure of $4 \mathrm{~atm}$ at $300…
A $100 \mathrm{~L}$ cylinder containing $\mathrm{H}_2$ exerted a pressure of $4 \mathrm{~atm}$ at $300 \mathrm{~K}$. It was accidentally opened and some $\mathrm{H}_2$ was escaped. When it was closed, it exerted a pressure of $3 \mathrm{~atm}$ at $300 \mathrm{~K}$. The number of moles of $\mathrm{H}_2$ remaining in the cylinder is equal to
(Assume $\mathrm{H}_2$ as an ideal gas; $\mathrm{R}=$ gas constant)
$\frac{1}{2 \mathrm{R}}$
$\mathrm{R}$
$\frac{1}{\mathrm{R}}$
$2 \mathrm{R}$
Solution
$\mathrm{n}_1=\frac{\mathrm{P}_1 \mathrm{~V}}{\mathrm{RT}}=\frac{4 \mathrm{~V}}{\mathrm{RT}}$ and $\mathrm{n}_2=\frac{\mathrm{P}_2 \mathrm{~V}}{\mathrm{RT}}=\frac{3 \mathrm{~V}}{\mathrm{RT}}$ $\Rightarrow$ Number of moles remaining $=$ $\frac{4 \mathrm{~V}}{\mathrm{RT}}-\frac{3 \mathrm{~V}}{\mathrm{RT}}=\frac{1}{\mathrm{R}}$