For the reaction, X (s) rightleftharpoons Y (s)+ Z (g) , the plot of ln frac p Z p θ versus frac 10 4 T is given below (in solid line), where p Z is the pressure (in bar) of the gas Z at temperature T and p θ =1 bar. ln frac p Z p θ (Given, frac d (ln K) d (1/T ) =-frac Δ H θ R , where the equilibrium constant, K=frac p z p α and the gas constant, R =8.314 J K -1 mol -1 ) The value of \!\!Δ\!\! S ominus (in J K -1 \!\! \!\! mo l -1 ) for the given reaction, at 1000 K is

Chemistry · Chemical Kinetics

JEE Advanced 2021 — Paper 1 — Question 41

For the reaction, $\mathbf{X}(s) \rightleftharpoons \mathbf{Y}(s)+\mathbf{Z}(g)$ , the plot of $\ln \frac{p_{\mathbf{Z}}}{p^{\theta}}$

versus $\frac{10^{4}}{T}$ is given below (in solid line), where $p_{\mathbf{Z}}$ is the pressure (in bar) of the gas $\mathbf{Z}$ at temperature

$T$ and $p^{\theta}=1$ bar. $\ln \frac{p_{Z}}{p^{\theta}}$ (Given, $\frac{\mathrm{d}(\ln K)}{\mathrm{d}\left(\frac{1}{T}\right)}=-\frac{\Delta H^{\theta}}{R}$ ,

where the equilibrium constant, $K=\frac{p_{z}}{p^{\alpha}}$ and the gas constant, $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

The value of $\text{ }\!\!\Delta\!\!\text{ }{{S}^{\ominus }}$ (in $\text{J}{{\text{K}}^{-1}}\text{ }\!\!~\!\!\text{ mo}{{\text{l}}^{-1}}$ ) for the given reaction, at 1000 K is

Answer: 141.34

Numerical answer — enter this value.

Step-by-step solution

Putting the value of $\text{ }\!\!\Delta\!\!\text{ }{{\text{H}}^{0}}$ in equation (2), we get $-3=-\left( \frac{2\text{R}\times {{10}^{4}}}{{{10}^{4}}\text{R}} \right)\times \frac{{{10}^{4}}}{7}+\frac{\text{ }\!\!\Delta\!\!\text{ }{{\text{S}}^{0}}}{\text{R}}$ $-3=-2R\times \frac{{{10}^{4}}}{T}+\frac{\text{ }\!\!\Delta\!\!\text{ }{{S}^{0}}}{R}$ $-3=-2\times \frac{{{10}^{4}}}{1000}+\frac{\text{ }\!\!\Delta\!\!\text{ }{{S}^{0}}}{R}$ $-3=-20+\frac{\text{ }\!\!\Delta\!\!\text{ }{{S}^{0}}}{R}$ $\therefore \frac{\text{ }\!\!\Delta\!\!\text{ }{{S}^{0}}}{R}=17$ $\therefore \text{ }\!\!\Delta\!\!\text{ }{{\text{S}}^{0}}=17\times 8.314=141.34\text{J}{{\text{K}}^{-1}}\text{ }\!\!~\!\!\text{ mo}{{\text{l}}^{-1}}$

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Exam: JEE Advanced 2021
Paper: Paper 1
Subject: Chemistry
Chapter: Chemical Kinetics
Topic: Arrhenius Equation

The value of standard enthalpy, Delta H^ominus ( inkJmo l^-1 ) for the given reaction is .

Answer: 141.34

Step-by-step solution

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