Chemistry - Electrochemistry Question with Solution | TestHub

$\text{A(s)}\text{|}{\text{A}}^{\text{+n}}\text{(aq}\text{.}\text{2}\text{M)}\text{||}{\text{B}}^{\text{+2n}}\text{(aq}\text{.}\text{1}\text{M)}\text{|}\text{B(s)}$
${\text{ΔH}}^{\text{o}}\text{=}{\text{2ΔG}}^{\text{o}}{\text{ E}}_{\text{cell}}\text{=}\text{0}$
$\text{Cell}\text{Reaction\hspace{0.33em}}\text{A}\to {\text{A}}^{\text{+n}}+{\text{ne}}^{-}\times 2$
${\text{B}}^{\text{+2n}}+\text{2}{\text{ne}}^{-}\to \text{B(s)}$
$\text{2}\text{A(s)}+\underset{1\text{M}}{{\text{B}}^{\text{+2n}}}\text{(aq)}\to \underset{\text{2}\text{M}}{\text{2}{\text{A}}^{\text{+n}}}\text{(aq)}+\text{B(s)}$
$\text{ΔG}\text{=}{\text{ΔG}}^o\text{+}\text{RT}\text{ln}\frac{{\left[{\text{A}}^{\text{+n}}\right]}^{\text{2}}}{\left[{\text{B}}^{\text{+2n}}\right]}$
${\text{ΔG}}^{\text{o}}\text{=}-\text{RT}\text{ln}\frac{{\left[{\text{A}}^{\text{+n}}\right]}^{\text{2}}}{\left[{\text{B}}^{\text{+2n}}\right]}\text{=}-\text{RT}\text{×}\text{ln}\frac{{\text{2}}^{\text{2}}}{\text{1}}\text{=}-\text{RT}\text{ln4}$
${\text{ΔG}}^{\text{o}}\text{=}{\text{ΔH}}^{\text{o}}-{\text{TΔS}}^{\text{o}}$
${\text{ΔG}}^{\text{o}}\text{=}{\text{2ΔG}}^{\text{o}}-{\text{TΔS}}^{\text{o}}$
${\text{ΔS}}^{\text{o}}\text{=}\frac{{\text{ΔG}}^{\text{o}}}{\text{T}}\text{=}-\frac{\text{RT}\text{ln4}}{\text{T}}$
$\text{=}-\text{8}\text{.3}\text{×}\text{2}\text{×}\text{0}\text{.7}\text{=}-\text{11}\text{.62\hspace{0.33em}}\text{J/K}{\text{mol}}^{-1}$