For a cell involving one electron, $\mathrm{E}{°}_{\text{cell }}=0.59 \mathrm{V}\text{ at }298 \mathrm{K},$ the equilibrium constant for the cell reaction is

$\text{ [Given that }\underset{¯}{2.303\mathrm{RT}}=0.059 \mathrm{V}\mathrm{atT}=298 \mathrm{K}]$

$\text{According to Nernst equation, }{E}_{cell}=E_{cell}-\frac{0.059}{n}\log Q_c$$$

${\text{At equilibrium E}}_{cell}=0,\therefore Q_c=K_c$

$E_{cell}=\frac{0.059}{n}\log K_c\Rightarrow 0.59=\frac{0.059}{1}\log K_c$

$K_c=\text{antilog 10}\Rightarrow {\text{K}}_c=1\times {10}^{10}$