# EMF of a disproportionation reaction

## Homework Statement

Consider the following sequence of reactions occuring in the acid medium. All emf (standard) are measured at $25^{\circ} C$ and expressed in volt unit:
$$MnO_4^-\stackrel{0.564}{\rightarrow}MnO_4^{2-}\stackrel{2.26}{\rightarrow}MnO_2\stackrel{0.95}{\rightarrow}Mn^{3+} \stackrel{1.51}{\rightarrow}Mn^{2+}\stackrel{-1.18}{\rightarrow}Mn$$
Determine the standard emf of the following reaction:
$$3MnO_4^{2-}+4H^+ \rightarrow MnO_2(s)+2MnO_4^-+2H_2O$$

## The Attempt at a Solution

$$MnO_4^{2-}+4H^++2e^- \rightarrow MnO_2+2H_2O \,\,\,\, \Delta G^{\circ}=-4.52F$$
$$MnO_4^{2-}\rightarrow MnO_4^{-}+e^- \,\,\,\, \Delta G^{\circ}=+0.564F$$
Multiplying the second equation by two and adding with the first, I get the equation presented in the problem and $\Delta G^{\circ}=-3.392F$. Let E be the emf of the resulting reaction, then $\Delta G^{\circ}$ is also equal to $-2FE$. Equating and solving for E, I get $E=1.696 V$ which is incorrect.

Any help is appreciated. Thanks!