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Gibb's Energy and Nernst Equation

The standard ...

Question

The standard reduction potential of $C u^{2 +} / C u$ and $C u^{2 +} / C u^{+}$ are $0.337$ and $0.153 V$ respectively. The standard electrode potential of $C u^{+} / C u$ half cell is:

A

0.184 V

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B

0.827 V

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C

0.521 V

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D

0.490 V

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Solution

The correct option is C $0.521 V$
$C u^{2 +} + 2 e^{-} \to C u; △ G_{1} \to (1) C u^{2 +} + e^{-} \to C u^{+}; △ G_{2} \to (2)$
Subtracting (2) from (1) we get
$C u^{+} + e^{-} \to C u; △ G_{3} N o w, Δ G_{3} = - n F E_{3} \Rightarrow Δ G_{3} = Δ G_{1} - Δ G_{2}$
$\Rightarrow - F E_{3} = - 2 F E_{1} - (- F E_{2}) \Rightarrow E_{3} = 2 E_{1} - E_{2} \Rightarrow E_{3} = 2 \times 0.337 - 0.153 = 0.521 V$

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