The reduction potential E 0 , in V of MnO 4 - aq / Mn s is [Given: E MnO 4 - aq / MnO 2 s o = 1 . 68  …

Given

(1) ${\mathrm{MnO}}_4^{-}\left(\mathrm{aq}\right)+4{\mathrm{H}}^{+}+3\mathrm{e}⟶{\mathrm{MnO}}_2\left(\mathrm{s}\right)+2{\mathrm{H}}_2\mathrm{O}$; $\mathrm{E}°=1.68 \mathrm{V}$

${\mathrm{\Delta G}}_1°=-3 \mathrm{F}\left(1.68\right)=-5.04 \mathrm{F}$

(2) ${\mathrm{MnO}}_2\left(\mathrm{s}\right)+4{\mathrm{H}}^{+}+2\mathrm{e}⟶{{\mathrm{Mn}}^{2+}}_{\left(\mathrm{aq}\right)} +2{\mathrm{H}}_2\mathrm{O}$; $\mathrm{E}°=1.21 \mathrm{V}$

${\mathrm{\Delta G}}_2°=-2 \mathrm{F}\left(1.21\right)=-2.42 \mathrm{F}$

(3) ${\mathrm{Mn}}^{2+}\left(\mathrm{aq}\right)+2\mathrm{e}⟶\mathrm{Mn}\left(\mathrm{s}\right)$; $\mathrm{E}°=-1.03 \mathrm{V}$

${\mathrm{\Delta G}}_3°=-2 \mathrm{F}\left(-1.03\right)=+2.06 \mathrm{F}$

Adding $\left(1\right),\left(2\right)$ and $\left(3\right)$,

${\mathrm{MnO}}_4^{-}\left(\mathrm{aq}\right)+8{\mathrm{H}}^{+}+7\mathrm{e}⟶\mathrm{Mn}\left(\mathrm{s}\right)+4{\mathrm{H}}_2\mathrm{O}$

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

$=\left(-5.04-2.42+2.06\right)\mathrm{F}$

$-7 \mathrm{FE}°=-5.40 \mathrm{F}$

$\mathrm{E}°=0.77 \mathrm{V}$