**Question:**

Initially a gas of diatomic molecules is contained in a cylinder of volume $\mathrm{V}_{1}$ at a pressure $\mathrm{P}_{1}$ 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 $2 \mathrm{~V}_{1}$ is given by $P_{2}$. The ratio $P_{2} / P_{1}$ is.

**Solution:**

$\mathrm{PV}=\mathrm{nRT}$

$\mathrm{P}_{1} \mathrm{~V}_{1}=\mathrm{nR} 250$

$\mathrm{P}_{2}\left(2 \mathrm{~V}_{1}\right)=\frac{5 \mathrm{n}}{4} \mathrm{R} \times 2000$

Divide

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

$\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\frac{1}{5}$

$\frac{\mathrm{P}_{2}}{\mathrm{P}_{1}}=5$

Ans. $5.00$