JEE Advanced 2023 — Paper 1 — Question 42

In a one-litre flask, 6 moles of A undergoes the reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{P}$ (g). The progress of product formation at two temperatures (in Kelvin), $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$, is shown in the figure: If $T_{1}=2 T_{2}$ and $\left(\Delta G_{2}^{\theta}-\Delta G_{1}^{\theta}\right)=R T_{2} \ln x$, then the value of $x$ is $\ldots .$. [ $\left[\Delta G_{1}^{\theta}\right.$ and $\Delta G_{2}^{\theta}$ are standard Gibb's free energy change for the reaction at temperatures $T_{1}$ and $T_{2}$, respectively.]