$\mathrm{Pt}(\mathrm{s}) \mathrm{H}_2(\mathrm{~g})(1 \mathrm{bar})\left|\mathrm{H}^{+}(\mathrm{aq})(1 \mathrm{M})\right|\left|\mathrm{M}^{3+}(\mathrm{aq}), \mathrm{M}^{+}(\mathrm{aq})\right| \mathrm{Pt}(\mathrm{s})$ $$ \text { The Ecell for the given cell is } 0.1115 \mathrm{~V} \text { at } 298 \mathrm{~K} \text { when } \frac{\left[\mathrm{M}^{+}(\mathrm{aq})\right]}{\left[\mathrm{M}^{3+}(\mathrm{aq})\right]}=10^{\mathrm{a}} \text {. The value of } \mathrm{a} \text { is } $$ $$ \text { Given: } \mathrm{E}_{\mathrm{M}^{3+} / \mathrm{M}^{+}}^{\ominus}=0.2 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V} $$