Search any question & find its solution
Question:
Answered & Verified by Expert
The value of $\log _{10} K$ for a reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$ is
(Given : $\Delta_{\mathrm{r}} \mathrm{H}_{298 \mathrm{O}}^{\circ}=-54.07 \mathrm{~kJ} \mathrm{~mol}^{-1}$,
$\Delta_{\mathrm{r}} \mathrm{S}_{298 \mathrm{~K}}^{\circ}=10 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ and $\mathrm{R}=8.314 \mathrm{JK}^{-1}$
$\mathrm{mol}^{-1}$;
$2.303 \times 8.314 \times 298=5705)$
Options:
(Given : $\Delta_{\mathrm{r}} \mathrm{H}_{298 \mathrm{O}}^{\circ}=-54.07 \mathrm{~kJ} \mathrm{~mol}^{-1}$,
$\Delta_{\mathrm{r}} \mathrm{S}_{298 \mathrm{~K}}^{\circ}=10 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$ and $\mathrm{R}=8.314 \mathrm{JK}^{-1}$
$\mathrm{mol}^{-1}$;
$2.303 \times 8.314 \times 298=5705)$
Solution:
1312 Upvotes
Verified Answer
The correct answer is:
10
$$
\begin{aligned}
& \text { } \mathrm{A} \rightleftharpoons \mathrm{B} \\
& \Delta G^{\circ}=\Delta H^{\circ}-\mathrm{T} \Delta S^{\circ} \\
& \Delta G^{\circ}=-2.303 \mathrm{RT} \log _{10} \mathrm{~K} \\
& -2.303 \mathrm{RT} \log _{10} \mathrm{~K}=\Delta H^{\circ}-T \Delta S^{\circ} \\
& 2.303 \mathrm{RT} \log _{10} \mathrm{~K}=T \Delta S^{\circ}-\Delta H^{\circ} \\
& \log _{10} \mathrm{~K}=\frac{T \Delta S^{\circ}-\Delta H^{\circ}}{2.303 R T} \\
& =\frac{298 \times 10+54.07 \times 1000}{2.303 \times 8.314 \times 298} \\
& =9.998 \approx 10 \\
&
\end{aligned}
$$
\begin{aligned}
& \text { } \mathrm{A} \rightleftharpoons \mathrm{B} \\
& \Delta G^{\circ}=\Delta H^{\circ}-\mathrm{T} \Delta S^{\circ} \\
& \Delta G^{\circ}=-2.303 \mathrm{RT} \log _{10} \mathrm{~K} \\
& -2.303 \mathrm{RT} \log _{10} \mathrm{~K}=\Delta H^{\circ}-T \Delta S^{\circ} \\
& 2.303 \mathrm{RT} \log _{10} \mathrm{~K}=T \Delta S^{\circ}-\Delta H^{\circ} \\
& \log _{10} \mathrm{~K}=\frac{T \Delta S^{\circ}-\Delta H^{\circ}}{2.303 R T} \\
& =\frac{298 \times 10+54.07 \times 1000}{2.303 \times 8.314 \times 298} \\
& =9.998 \approx 10 \\
&
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.