Q 11-12-122JEE MainJEE Main 2020 (6 Sep, Shift 1)Medium
Initially a gas of diatomic molecules is contained in a cylinder of volume $V_1$ at a pressure $P_1$ and temperature $250$ K. Assume that $25\%$ of the molecules get dissociated, causing a change in the number of moles. The pressure of the resulting gas at temperature $2000$ K, when contained in a volume $2V_1$, is $P_2$. The ratio $P_2/P_1$ is ______.
Numerical value type. Enter your answer.
Answer: 5
Start with $n$ moles. $0.25n$ moles dissociate into $0.5n$ moles of atoms, so the total becomes $0.75n + 0.5n = 1.25n$.
Using $P = \dfrac{nRT}{V}$:
$$\frac{P_2}{P_1} = \frac{1.25n\times2000/(2V_1)}{n\times250/V_1} = \frac{1.25\times1000}{250} = 5$$
Solution by Sreeraj P, M.Sc Physics