Question

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

Answer 1

$25\%$ will dissociate out of $100$
$\frac{3 n}{4}$ molecules will remain same
$S$
$\frac{n}{4}$ mole become $ \rightarrow \frac{n}{2}$
$\therefore $ Total molecules used
$ \rightarrow \frac{3 n}{4}+\frac{n}{2}=\frac{5 n}{4}$
$P_{2}2V_{1}=\frac{5 n}{4}\cdot R\cdot 2000-\left(\right.ii\left.\right)$
Eq. (ii/i) $\frac{2 p_{2} v_{1}}{p_{1} v_{1}}=\frac{5 n R \times 2000}{4 n R \times 250}$
$\frac{P_{2}}{P_{1}}=5$