Question

For the cell reaction,
$Mg(s)+2A{g}^{+}(aq)\rightleftharpoons M{g}^{2+}(aq)+2Ag(s)$
$E_{\text{cell }}^o$ is $3.17V$ at $298K$. The value of $E_{\text{cell }},\Delta G^{\circ }$ and $Q$ at $A{g}^{+}$and $M{g}^{2+}$ concentrations of $0.001$ $M$ and $0.02M$ respectively are :

• A. $3.04V,-605.8kJmo{l}^{-1},20000$
• B. $3.04V,611.8kJmo{l}^{-1},20000$
• C. $3.13V,-604kJmo{l}^{-1},20$
• D. $3.04V,-611.8kJ,20000$

Answer 1

Answer: (D)

$Mg(s)+2A{g}^{+}(aq)\rightleftharpoons M{g}^{+2}(aq)+2Ag(s)$
$E_{cell}=E_{\text{cell }}^{\circ }-\frac{0.0591}{n}\log \frac{\left[M{g}^{+2}\right]}{{\left[A{g}^{+}\right]}^2}$
$E_{cell}=3.17-\frac{0.0591}{2}\log \frac{\left(2\times 10^{-2}\right)}{{\left(10^{-3}\right)}^2}$
$E_{\text{cell }}=3.17-\frac{0.0591}{2}\times 4.3$
$=3.17-0.129$
$=3.04volt$
$\Delta G^{\circ }=-nF{E}_{\text{cell }}^{\circ }$
$=-2\times 96500\times 3.17$
$=-611.8kJ$
$Q=\frac{\left[M{g}^{2+}\right]}{{\left[A{g}^{+}\right]}^2}=20000$
$Q=20000$