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Gibb's Energy and Nernst Equation

The emf of th...

Question

The emf of the three galvanic cells:
(i) $Z n | Z n^{2 +} (1 M) | | C u^{2 +} (1 M) | C u$
(ii) $Z n | Z n^{2 +} (0.1 M) | | C u^{2 +} (1 M) | C u$
(iii) $Z n | Z n^{2 +} (1 M) | | C u^{2 +} (0.1 M) | C u$
are represented by $E_{1}$ , $E_{2}$ and $E_{3}$ respectively. Which of the following is true?

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is D $E_{2} > E_{1} > E_{3}$
$Z n + C u^{2 +} \to Z n^{2 +} + C u$
$E_{cell} = E_{cell}^{\circ} - \frac{R T}{n F} ln \frac{[Z n^{+ 2}]}{[C u^{+ 2}]}$

So higher the value of $\frac{[Z n^{+ 2}]}{[C u^{+ 2}]}$ , lower will be the value of $E_{cell}$ .

(i) $\frac{[Z n^{+ 2}]}{[C u^{+ 2}]} = 1$

(ii) $\frac{[Z n^{+ 2}]}{[C u^{+ 2}]} = \frac{0.1}{1} = 0.1$

(iii) $\frac{[Z n^{+ 2}]}{[C u^{+ 2}]} = \frac{1}{0.1} = 10$

$∴ E_{2} > E_{1} > E_{3}$

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