Question

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

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

Answer 1

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

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

$\left.\operatorname{Cell} R x A \rightarrow A^{+n}+n e^{-}\right] \times 2$

$B ^{+2 n }+2 ne ^{-} \rightarrow B ( s )$

$2 A ( s )+ B _{1 M }^{+2 n }( aq ) \rightarrow 2 A _{2 M }^{+ n }( aq )+ B ( s )$

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

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

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

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

$\Delta S ^{0}=\frac{\Delta G ^{0}}{ T }=-\frac{ RTln 4}{ T }$

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