Chemistry Question from JEE Main 2023 · 30 January, Shift 1

Consider the cell $\text{Pt}(s) \mid \text{H}_2 (g, 1 \, \text{atm}) \mid \text{H}^+ (aq, 1\,\text{M}) \mid\mid \text{Fe}^{3+} (aq) , \text{Fe}^{2+} (aq) \mid\mid \text{Pt}(s).$ When the potential of the cell is $0.712 \, \text{V}$ at $298 \, \text{K}$, the ratio $\frac{[Fe^{2+}]}{[Fe^{3+}]}$ is _____. (Nearest integer)

Given: $\text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}, \quad E^\circ_{Fe^{3+}|Fe^{2+}} = 0.771 \, V.$ $\frac{2.303RT}{F} = 0.06 \, V.$