Calculate the \( \Delta G^\circ \) and \( \log K_c \) for the following cell reaction:
\(\text{Fe (s)} + \text{Ag}^+ (aq) \rightleftharpoons \text{Fe}^{2+} (aq) + \text{Ag (s)}\)
Given: \( E^\circ_{\text{Fe}^{2+}/\text{Fe}} = -0.44 \, \text{V}, E^\circ_{\text{Ag}^+/ \text{Ag}} = +0.80 \, \text{V} \)
\( 1 F = 96500 \, \text{C mol}^{-1} \)