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_______
(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),
$\frac{P_{1}}{2 P_{2}}=\frac{4 \times 250}{5 \times 2000} \Rightarrow \frac{P_{1}}{P_{2}}=\frac{1}{5}$
$\therefore \frac{P_{2}}{P_{1}}=5$
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