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Cu + aq is un...

Question

${C u}^{+} (a q)$ is unstable in solution and undergoes simultaneous oxidation and reduction, according to the reaction
$2 {C u}^{+} (a q) ⇌ {C u}^{2 +} (a q) + C u (s)$
Choose correct $E$ for above reaction if
$E_{{C u}^{2 +} / C u} = 0.34 V$ and $E_{{c u}^{2 +} / {C u}^{+}} = 0.15 V$

A

- 0.38 V

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B

+ 0.49 V

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C

+ 0.38 V

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D

- 0.19 V

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Solution

The correct option is D $+ 0.38 V$
From given data (From $Δ G = - n E F$ )
(i) $C u (s) ⟶ {C u}^{2 +} (a q) + 2 e^{-} \cdot Δ G_{1} = - 2 \times (- 0.34) \times F$
(ii) ${C u}^{2 +} (a q) + e^{-} ⟶ {C u}^{+} (a q) \cdot Δ G_{2} = - 1 \times (0.15) F$
On addition
$C u (s) ⟶ {C u}^{+} (a q) + e^{-} \cdot Δ G_{3} = - 1 \times E \times E$
$Δ G_{3} = Δ G_{1} + Δ G_{2}$
$= (- 2 \times - 0.34 \times F) + (- 1 \times 0.15 \times F)$
$= + 0.68 F - 0.15 F = 0.53 F$
or $E = - 0.53 V$

Reaction,
$2 {C u}^{+} (a q) ⇌ {C u}^{2 +} (a q) + C u (s)$
$E =$ ?
So, ${C u}^{+} (a q) + e^{-} ⇌ C u (s),$
$E = + 0.53 V$
${C u}^{+} (a q) ⇌ {C u}^{2 +} (a q) + e^{-};$
$E = - 0.15 V$
$2 {C u}^{+} (a q) ⇌ {C u}^{2 +} (a q) + C u (s),$
$E = + 0.38 V$

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