Question

An ideal gas is contained in a cylinder at pressure $p_{1}$ and temperature $T_{1}$. The initial moles of the gas is $n_{1}$. The gas leaks from the cylinder and attains a final pressure $p_{2}$ and temperature $T_{2}$. The new moles of the gas present in the cylinder is

• A. $\frac{p_{2} T_{1}}{p_{1} n_{1} T_{2}}$
• B. $\frac{n_{1} T_{2} p_{2}}{T_{1} p_{1}}$
• C. $\frac{n_{1} T_{1} p_{2}}{T_{2} p_{1}}$
• D. Data insufficient

Answer 1

Answer: (C)

According to ideal gas equation,
$p V=n R T$
where, $R=$ gas constant.
Since, moles are changing but volume is constant. Eq. (i) can be written as
$\frac{p}{n T}=\frac{R}{V}=$ constant
$\Rightarrow \frac{p_{1}}{n_{1} T_{1}}=\frac{p_{2}}{n_{2} T_{2}} $
$\Rightarrow n_{2}=\frac{n_{1} T_{1} p_{2}}{T_{2} p_{1}}$
where, $p_{1}, p_{2}$ are the initial and final pressure of gas and $T_{1}$ and $T_{2}$ are initial and final temperature of gas.