JEE Advanced · 2021 · 03 Oct 2021 · Paper 1 · Chemical Thermodynamics

For the reaction $\mathbf{X}(\mathrm{s})\rightleftharpoons \mathbf{Y}(\mathrm{s})+\mathbf{Z}(\mathrm{g})$, the plot of $\ln \frac{{\mathrm{p}}_{\mathrm{z}}}{{\mathrm{p}}^{\ominus }}$ versus $\frac{10^4}{T}$ is given below (in solid line), where ${\mathrm{p}}_{\mathrm{z}}$ is the pressure (in bar) of the gas $\mathbf{Z}$ at temperature $T$ and ${\mathrm{P}}^{\theta }=1$ bar.

(Given, $\frac{\mathrm{d}(\ln \mathrm{K})}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\ominus }}{\mathrm{R}}$, where the equilibrium constant, $\mathrm{K}=\frac{{\mathrm{p}}_{\mathrm{z}}}{{\mathrm{p}}^{\ominus }}$ and the gas constant, $\mathrm{R}=8.314$ ${\mathrm{J}\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$)

The value of $\Delta {\mathrm{S}}^{\ominus }$ (in ${\mathrm{J}\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$) for the given reaction, at 1000 K is ____.