At 300 K . the $E_{ ext {cell }}^{\circ}$ of $\mathrm{A}(\mathrm{~s})+\mathrm{B}^{2+}(\mathrm{aq}) ightleftharpoons \mathrm{A}^{2+}(\mathrm{aq})+\mathrm{B}(\mathrm{~s})$ is 1.0 V . If $\Delta_r S^{\circ}$ of this reaction is $100 \mathrm{JK}^{-1}$, what is $\Delta_{\mathrm{r}}…

Question

At 300 K . the $E_{	ext {cell }}^{\circ}$ of $\mathrm{A}(\mathrm{~s})+\mathrm{B}^{2+}(\mathrm{aq}) ightleftharpoons \mathrm{A}^{2+}(\mathrm{aq})+\mathrm{B}(\mathrm{~s})$ is 1.0 V . If $\Delta_r S^{\circ}$ of this reaction is $100 \mathrm{JK}^{-1}$, what is $\Delta_{\mathrm{r}} \mathrm{H}^{\circ}$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of this reaction?( $\mathrm{F}=96500 \mathrm{Cmol}^{-1}$ )

Aicharya · Accepted Answer

Given, $\begin{aligned} & \Delta_{\mathrm{r}} \mathrm{~S}^{\circ}=100 \mathrm{JK}^{-1} \mathrm{~mol}^{-1} \ & \mathrm{E}_{\mathrm{cell}}^{\circ}=1.0 \mathrm{~V} \ & \mathrm{n}=2 \ & \Delta \mathrm{G}^{\circ}=-\mathrm{nFE}^{\circ} \ &=-2 	imes 96500 	imes 1 \mathrm{~J} \mathrm{~mol}^{-1} \ &=-193 \mathrm{~kJ} \mathrm{~mol}^{-1} \ & 	herefore \quad \Delta \mathrm{G}^{\circ}=\Delta \mathrm{H}^{\circ}-\mathrm{T} \Delta \mathrm{~S}^{\circ} \ & \Delta \mathrm{H}^{\circ}=\Delta \mathrm{G}+\mathrm{T} \Delta \mathrm{~S} \ &=-193+\frac{300 	imes 100}{1000} \ &=-193+30 \ & \Delta \mathrm{H}^{\circ}=-163 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}$

At 300 K . the $E_{\text {cell }}^{\circ}$ of $\mathrm{A}(\mathrm{~s})+\mathrm{B}^{2+}(\mathrm{aq})…

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