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Calculate the standard free energy change for the given reaction.

\(\mathrm{Ni + Cu^{2+} \to Ni^{2+} + Cu}\)

[ Given: \(E^\circ_{\mathrm{Ni^{2+}/Ni}} = -0.25\) V; \(E^\circ_{\mathrm{Cu^{2+}/Cu}} = 0.34\) V ]

  • A.\(56935\ \mathrm{J\,mol^{-1}}\)
  • B.\(-56935\ \mathrm{J\,mol^{-1}}\)
  • C.\(-113870\ \mathrm{J\,mol^{-1}}\)
  • D.\(113870\ \mathrm{J\,mol^{-1}}\)

Answer: C

The cell potential is the reduction potential of the cathode minus that of the anode. Copper is reduced and nickel is oxidised, so


\[ E^\circ_{cell} = 0.34 - (-0.25) = 0.59\ \text{V} \]


Two electrons are transferred (\(n = 2\)), and the Faraday constant is 96500 C/mol.


\[ \begin{aligned} \Delta G^\circ = -nFE^\circ \\ &= -2 \times 96500 \times 0.59 \\ &= -113870\ \text{J mol}^{-1} \end{aligned} \]


The sign is negative because the reaction is spontaneous. The value \(-56935\) comes from using \(n = 1\) and the positive values from the wrong sign. The answer is option C.

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