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The emf of the following three galvanic cells:
1) $Zn / {Zn}^{2 +} (1 M) | | {Cu}^{2 +} (1 M) / Cu$
2) $Zn / {Zn}^{2 +} (0 .1 M) | | {Cu}^{2 +} (M) / Cu$
3) $Zn / {Zn}^{2 +} (1 M) | | {Cu}^{2 +} (0 .1 M) / Cu$
are represented by $E_{1}, E_{2}, E_{3}$ . Which of the following statement is true?

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$E_{3} > E_{1} > E_{2}$

$E_{2} > E_{1} > E_{3}$

$E_{3} > E_{2} > E_{1}$

$E_{1} > E_{2} > E_{3}$

answer is D.

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Detailed Solution

$E_{cell} = E_{cell}^{o} - \frac{2 .303 RT}{nF} \log \frac{[{Zn}^{2 +}]}{[{Cu}^{2 +}]}$

$E_{1} = E_{cell}^{o} - \frac{2 .303 RT}{2 F} \log \frac{1}{1}$

$E_{1} = E_{cell}^{o}$

$\begin{array}{l} E_{2} = E_{cell}^{0} - \frac{2 .303 RT}{2 F} \log \frac{0 .1}{1 .0} \\ E_{3} = E_{cell}^{0} - \frac{2 .303}{2 F} \log \frac{1}{0 .1} \\ ∴ E_{2} > E_{1} > E_{3} \end{array}$

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