Question

Consider an electrochemical cell: $A\left(s\right)\left|A^{n+}\left(aq,2M\right)\right|\left|B^{2n+}\left(aq,1M\right)\right|B\left(s\right).$ The value of $\Delta H^{\theta }$ for the cell reaction is twice that of $\Delta G^{\theta }$ at $300K$. If the emf of the cell is zero, the $\Delta S^{\theta }$ (in $J{K}^{-1}mo{l}^{-1}$) of the cell reaction per mole of $B$ formed at $300K$ is ____.
(Given: $ln(2)$ = $0.7,R$ (universal gas constant) = $8.3J{K}^{-1}mo{l}^{-1}$. $H,S$ and $G$ are enthalpy, entropy and Gibbs energy, respectively.)

Answer 1

Answer: -11.62

$A(s)\left|A^{\ln }(aq.2M)\right|\left|B^{+2a}(aq,1M)\right|B(s)$
$\Delta H^{\circ }=2\Delta G_0^0$
$E_{\text{cell }}=0$
Cell $RxA\to A^{+n}+n{e}^{-}\times 2$
$B^{+2n}+2n{e}^{-}\to B(s)$
$2A(s)+B_{1M}{}^{+2n}(aq)\to 2A_{2M}{}^{+n}(aq)+B(s)$
$\Delta G=\Delta G^{\circ }+RT\ln \frac{{\left[A^{+n}\right]}^2}{\left[B^{+2n}\right]}$
$\Delta G^{\circ }=-RT\ln \frac{{\left[A^{+n}\right]}^2}{\left[B^{+2n}\right]}$
$=-RT\cdot \ln \frac{2^2}{1}=-RT\cdot \ln 4$
$\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$
$\Delta G^{\circ }=2\Delta G^{\circ }T\Delta S^{\circ }$
$\Delta S^{\circ }=\frac{\Delta G^{\circ }}{T}=\frac{RT\ln 4}{T}$
$=-8.3\times 2\times 0.7=11.62J/K.mol$