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Nernst Equation

Below given a...

Question

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

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

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

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

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

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Solution

The correct option is D $E_{2} > E_{1} > E_{3}$
Nernst equation is $E = E ° - \frac{R T}{n F} l n Q$
Where,
E = potiential difference
E°= potiential difference at standard conditions.
Q=reaction quotient.

Give reaction is; $Z n (s) + {C u}^{2 +} \to {Z n}^{2 +} + C u (s)$
Here, $Q = \frac{[{Z n}^{2 +}]}{[{C u}^{2 +}]}$
n = no.of electrons transferred = 2

1. $Z n | Z n^{2 +} (1 M) | | C u^{2 +} (1 M) | C u$

$Q = \frac{1 M}{1 M} = 1$

$E_{1} = E^{o} - \frac{0.059}{n} \times l o g (Q) = E^{o} - \frac{0.059}{n} \times l o g (1) = E^{o}$ .
2. $Z n | Z n^{2 +} (0.1 M) | | C u^{2 +} (1 M) | C u$

$Q = \frac{0.1}{1} = 0.1$

$E_{2} = E^{o} - \frac{0.059}{n} \times l o g Q = E^{o} - \frac{0.059}{n} \times l o g 0.1 = E^{o} + 0.0295$ .

3. $Z n | Z n^{2 +} (1 M) | | C u^{2 +} (0.1 M) | C u$

$Q = \frac{1 M}{0.1 M} = 10$

$E_{3} = E ° - \frac{0.059}{n} \times l o g Q = E^{o} - \frac{0.059}{n} \times l o g 10 = E^{o} - 0.0295$ .

The order of potential differences is $E_{2} > E_{1} > E_{3}$ .

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