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

Answer: 5

$25\%$ will dissociate out of $100$
$\frac{3n}{4}$ molecules will remain same
$S$
$\frac{n}{4}$ mole become $\to \frac{n}{2}$
$\therefore$ Total molecules used
$\to \frac{3n}{4}+\frac{n}{2}=\frac{5n}{4}$
$P_{2}2V_1=\frac{5n}{4}\cdot R\cdot 2000-(ii)$
Eq. (ii/i) $\frac{2p_2{v}_1}{p_1{v}_1}=\frac{5nR\times 2000}{4nR\times 250}$
$\frac{P_2}{P_1}=5$