Write Nernst equation for Daniel cell at equilibrium condition and derive relationship between $E_{(c e l l)}^{o}$ and equilibrium constant $(K_{c})$ .

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Solution

Nernst equation for Daniel cell at equilibrium condition:
$E_{c e l l} = E_{c e l l}^{o} - \frac{0.0592}{n} l o g K$
$E_{c e l l} = E_{c e l l}^{o} - \frac{0.0592}{2} l o g \frac{[Z n^{2 +}]}{[C u^{2 +}]}$
Relationship between $E_{c e l l}^{o}$ and equilibrium constant ( $K_{c}$ ).
$Δ G^{0} = - n F E_{c e l l}^{o}$ ....(1)
$Δ G^{0} = - R T l n K$ ....(2)
From (1) and (2)
$- n F E_{c e l l}^{o} = - 2.303 R T l o g K$

$E_{c e l l}^{o} = \frac{2.303 R T}{n F} l o g K$

At $25^{o} C$ ,
$\frac{2.303 R T}{F} = 0.0592$
Hence, $E_{c e l l}^{o} = \frac{0.0592}{n} l o g K$

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