What is the standard electrode potential for the electrode, `MnO_4^-//MnO_2` in an acid solution?
`E_(MnO_4^-,Mn^(2+))^@=1.51 V, E_(MnO_2,Mn^(2+))^@=1.23V`

Explanation

`MnO_4^(-) +8H^+ +5e to Mn^(2+)+4H_2O , E^@=1.51 ` volts
`therefore Delta G^@=-5(1.51 ) F=-7.55 F`
`MnO_2+ 4H^+ +2e to Mn^(2+) +2H_2O, E^@=1.23` volts
`therefore Delta G^@=-2(1.23) F=-2.46 F`
On subtracting
`MnO_4^(-) -MnO_2 +4H^+ +3e to 2H_2O`,
`Delta G^@=-7.55 F-(2.46) =-5.09 F`
or `MnO_4^(-) +4H^+ +3e to MnO_2+ 2H_2O, Delta G^@=-5.09F`
`therefore E_(MnO_4^-,MnO_2)^@= (Delta G^@)/(-nF)=(-5.09 F)/(-3F)=1.70` volts