Question

Consider an electrochemical cell: $A(s)\left|A^{n+}(aq,2M)\right|\left|B^{2n+}(aq,1M)\right|B(s).$ The value of $\Delta H^o$ for the cell reaction is twice that of $\Delta G^o$ at $300K$. If the emf of the cell is zero, the $\Delta S^{\Theta }\left(inJK-1mo{1}^{-1}\right)$ of the cell reaction per mole of $B$ formed at $300K$ is

(Given: $\ln (2)=0.7,R=8.3J{K}^{-1}mo{l}^{-1}.H,S$ and G are enthalpy, entropy and Gibbs energy, respectively.)

Answer 1

Answer: -11.60

$A(s)\left|A^{+n}(aq\cdot 2M)\right|\left|B^{+2n}(aq\cdot 1M)\right|B(s)$

$\Delta H^0=2\Delta G^0{E}_{\text{cell }}=0$

$\mathrm{Cell}RxA\to A^{+n}+n{e}^{-}]\times 2$

$B^{+2n}+2n{e}^{-}\to B(s)$

$2A(s)+B_{1M}^{+2n}(aq)\to 2A_{2M}^{+n}(aq)+B(s)$

$\Delta G=\Delta G^o+RT\ln \frac{{\left[A^{+n}\right]}^2}{\left[B^{+2n}\right]}$

$\Delta G^0=-RT\ln \frac{{\left[A^{+n}\right]}^2}{\left[B^{+2n}\right]}=-RT\times \ln \frac{2^2}{1}=-RT\ln 4$

$\Delta G^0=\Delta H^0-T\Delta S^0$

$\Delta G^0=2\Delta G^0-T\Delta S^0$

$\Delta S^0=\frac{\Delta G^0}{T}=-\frac{RTln4}{T}$

$=-8.3\times 2\times 0.7=-11.6J/Kmo{l}^{-1}$