Question
Write the cell representation and calculate equilibrium constant for the following redox reaction:
$Ni _{( s )}+2 Ag _{( aq )}^{+}(1 M ) \longrightarrow Ni ^{2+}{ }_{\text {(aq) }}(1 M )+2 Ag _{\text {(s) }}$ at $25^{\circ} C ; E _{ Ni }^0=-0.25 V$ and $E _{ Ag }^0=0.799 V$

Answer

$N i_{(s)}+2 A g_{(a q)}^{+}(1 M) \rightarrow N i_{(a q)}^{2+}(1 M)+2 A g_{(s)}$ at $25^{\circ} C$
$E_{n i}^{+}=-0.25 V$ and $E_{A g}^{+}=0.799 V$
Cell representation :
$N i_{(s)}\left|N i_{(a q)}^{2+}(1 M)\right|\left|A g_{a q}^{+}(1 M)\right| A g(s)$
Calculation of equilibrium constant
$E_{\text {cell }}^{\circ}=\frac{0.0592}{n} \log _{10} K$
$E_{\text {cell }}^{\circ}=E_{ Ag }^{\circ}-E_{ Ni }^{\circ}$
=0.799-(-0.25)=1.049 V
Hence $1.049=\frac{0.0592}{2} \log _{10} K$
$\log _{10} K=\frac{1.049 \times 2}{0.0592}=35.44$
$K=$ anti $\log (35.44)$
$=2.754 \times 10^{35}$

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