Question
Calculate cell potential of following given cell at 298 K temperature.
$\begin{array}{l} Mg _{( s )}\left| Mg ^{2+}{ }_{(0.001 M )} \| Cl _{(0.02 M )}^{-}\right| Cl _{2(B \mid ba )}\left| Pt _{( s )}\right| \\ E _{ Mg ^{2+ Mg }}^0=-2.36 V \\ E _{ Cl _2 / G =}^0=1.36 V\end{array}$

Answer

⇒ $Mg ( s )\left| Mg ^{2+}(0.001 M ) \| Cu ^{2+}(0.0001 M )\right| Cu ( s )$
cell reaction $: Mg ( s )+ Cu ^{2+}( aq ) \rightarrow Mg ^{2+}( aq )+ Cu ( s )( n =2)$
$E _{\text {cell }}^0= E _{ Cu 2+\mid Cu }^0- E _{ Mg 2+\mid Mg }^0$
$=0.34-(-2.36)$
$=2.70 V$
$E _{\text {cell }}= E _{\text {cell }}^0-\frac{0.059}{ n } \log \frac{\left[ Mg ^{2+}\right]}{\left[ Cu ^{2+}\right]}$
$=2.70 \times \frac{0.059}{2} \log \frac{0.001}{0.0001}$
$=2.70-0.0295$
$E _{\text {cell }}=2.67 V$

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