Question

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

Answer 1

$A\left(s\right)|A^{n+}(aq,2M)||B^{2n+}(aq,1M)|B\left(s\right)$
$2A\left(s\right)\to 2A^{n+}+2n{e}^{-}$
$B^{2n+}+2n{e}^{-}\to B\left(s\right)$
$2A\left(s\right)+B^{2n+}\to 2A^{n+}+B\left(s\right)$
$Q=\frac{[A^{n+}{]}^2}{B^{2n+}}=\frac{2\times 2}{1}=4$
$\Delta G^{\circ }=\Delta H^{\circ }-T\Delta S^{\circ }$
$\Delta H^{\circ }=2\Delta G^{\circ }$
$E_{cell}^0=\frac{RT}{2nF}ln4$
$\Delta G^{\circ }=-2n\times F\times \frac{RT}{2nF}ln4$
$\Delta G^{\circ }=-RTln4$
$\Delta S^{\circ }=\frac{\Delta H^0-\Delta G^0}{T}=\frac{\Delta G^{\circ }}{T}=-\frac{RTln4}{T}$
$\Delta S^{\circ }=-8.314\times 1.4$
$=-11.62Jmo{l}^{-1}{K}^{-1}$