At what concentration of ${C u}^{2 +}$ in a solution of $C u {S O}_{4}$ will the electrode potential be zero at $25^{0} C$ ?
Given: $E^{0} (C u / {C u}^{2 +}) = - 0.34 V$

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Solution

${C u}^{2 +} + 2 e^{-} \to C u E_{c e l l} = 0.34$
$E_{c e l l} = E^{0} - \frac{0.059}{n} l o g ⎡ ⎢ ⎢ ⎣ \frac{1}{({C u}^{2 +})} ⎤ ⎥ ⎥ ⎦$
$0 = + 0.34 - \frac{0.059}{2} l o g [\frac{1}{{C u}^{2 +}}]$
$\frac{0.34 \times 2}{0.059} = l o g (\frac{1}{{C u}^{2 +}})$
$11.52 = l o g (\frac{1}{{C u}^{2 +}})$
$10^{11.52} = 1 / {C u}^{2 +}$
$({C u}^{2 +}) = 3.01 \times 10^{- 12}$

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