$Z n ∣ ∣ ∣ \begin{matrix} Z n (N O_{3})_{2} (a q) 100 m L, 1 M \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} C u (N O_{3})_{2} (a q) 100 m L, 1 M \end{matrix} ∣ ∣ ∣ C u$
The following galvanic cell was operated as an electrolytic cell using Cu as anode and Zn as cathode. A current of 0.48 ampere was passed for 10 hour and then the cell was allowed to function as galvanic cell. The e.m.f. of the cell at 25 $^{o}$ C is (write the nearest integer value) :
Assume that the only electrode reactions occurring were those involving $C u / c u^{2 +}$ and $Z n / Z n^{2 +}$ , Given
$E_{C u^{2 +}, C u}^{o} = 0.34 V$ and $E_{Z n, Z n^{2 +}}^{o} = - 0.76 V$

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Solution

During electrolysis some Zn will discharge and some $C u^{2 +}$ will pass in solution
Thus, $\frac{m}{E} = \frac{0.48 \times 10 \times 60 \times 60}{96500} = 0.18$
or Mole of $C u^{2 +}$ formed $=$ Mole of $Z n^{2 +}$ deposited $=$ 0.09
or m mole of $C u^{2 +}$ formed $=$ m mole of $Z n^{2 +}$ deposited $=$ 90
$∴$ m mole of $Z n^{2 +}$ left $= 100 \times 1 - 90 = 10$
m mole of $C u^{2 +}$ left $= 100 \times 1 + 90 = 190$
Both are present in 100 mL solution of each.
Now, $E_{c e l l} = E_{O P_{Z n / Z n^{2 +}}}^{o} + E_{R P_{C u^{2 +} / C u}}^{o} + \frac{0.059}{2} l o g_{10} \frac{[C u^{2 +}]}{[Z n^{2 +}]}$
$= 0.76 + 0.34 + \frac{0.059}{2} l o g_{10} \frac{190}{10}$
$E_{c e l l} = 1.137 V$

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