The relationship between the standard emf of a cell ($E^\ominus_{\text{cell}}$) and the equilibrium constant ($K_c$) for the cell reaction is given by the Nernst equation at equilibrium:

$E^\ominus_{\text{cell}} = \frac{2.303 RT}{nF} \log K_c$

Given: $E^\ominus_{\text{cell}} = 0.59 \text{ V}$ $n = 1$ (since the cell involves one electron) $\frac{2.303 RT}{F} = 0.059 \text{ V}$

Substituting these values into the equation: $0.59 = \frac{0.059}{1} \log K_c$ $\log K_c = \frac{0.59}{0.059} = 10$

Taking the antilog of both sides: $K_c = 10^{10} = 1.0 \times 10^{10}$