What is the standard reduction potential E o for Fe 3 + → Fe ? Given that: Fe 2 + + 2 e - → Fe ;…

$\left(\mathrm{i}\right) {\mathrm{Fe}}^{3+}\to \mathrm{Fe}$ ${\mathrm{E}}_1^{\mathrm{o}}$;

$\text{'}\mathrm{n}\text{'}$ factor$=3$

${\text{ΔG}}_1^{\circ }=-3\mathrm{\hspace{0.17em}}\times \mathrm{F}\times {\mathrm{E}}_1^{\mathrm{o}}$

$\left(\mathrm{ii}\right) {\mathrm{Fe}}^{3+}+{\mathrm{e}}^{-}\to {\mathrm{Fe}}^{2+}$${\mathrm{E}}_2^{\mathrm{o}}$; $0.77$

$\text{'}\mathrm{n}\text{'}$ factor$=1$

$∆{\mathrm{G}}_2^{\circ }=-1\times \mathrm{F}\times 0.77$

$\left(\mathrm{iii}\right) {\mathrm{Fe}}^{2+}+2{\mathrm{e}}^{-}\to \mathrm{Fe}$ ${\mathrm{E}}_3^{\mathrm{o}}=-0.47$ 

$\text{'}\mathrm{n}\text{'}$ factor$=2$

$∆{\mathrm{G}}_3^{\circ }=-2\times \mathrm{F}\times -0.47$

${\mathrm{\Delta G}}_1={\mathrm{\Delta G}}_2+{\mathrm{\Delta G}}_3$

$-3{\mathrm{FE}}_{{}^1}^{\mathrm{o}}=\left(-1\times 0.77\times \mathrm{F}\right)+\left(2\times 0.47\times \mathrm{F}\right)$

${\text{-E}}_{{}^1}^{\mathrm{o}}=\frac{\left[\left(2\times 0.47\right)+\left(-0.77\right)\right]\mathrm{F}}{3\mathrm{F}}=0.057 \mathrm{V}$

${\text{E}}_{{}^1}^{\mathrm{o}}=-\mathrm{\hspace{0.17em}}0.057 \mathrm{V}$