# Initially a gas of diatomic molecules is contained in a cylinder

Question:

Initially a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature $250 \mathrm{~K}$. Assuming that $25 \%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $2000 \mathrm{~K}$, when contained in a volume $2 V_{1}$ is given by $P_{2}$. The ratio $P_{2} / P_{1}$ is_______

Solution:

(5)

Using ideal gas equation, $P V=n R T$

$\Rightarrow P_{1} V_{1}=n R \times 250 \quad\left[\because T_{1}=250 \mathrm{~K}\right] \quad \ldots(\mathrm{i})$

$P_{2}\left(2 V_{1}=\frac{5 n}{4} R \times 2000 \quad\left[\because T_{2}=2000 \mathrm{~K}\right]\right.$

Dividing eq. (i) by (ii),

$\frac{P_{1}}{2 P_{2}}=\frac{4 \times 250}{5 \times 2000} \Rightarrow \frac{P_{1}}{P_{2}}=\frac{1}{5}$

$\therefore \frac{P_{2}}{P_{1}}=5$