Given `E_(Mn^(7+)//M^(n+))^(@)` and `E_(Mn^(4+)//M^(2+))^(@)` are `1.51 V` and `1.23 V`. Calculate `E_(Mn^(7+)//M^(n+))^(@)`.

Explanation

Given: `MnO_(4)^(-)+8H^(+)+5e rarr Mn^(2+)+4H_(2)O`,
`E_(1)^(@) = 1.51 V` …(1)
`MnO_(2)+4H^(+)+2e rarr Mn^(2+)+2H_(2)O`,
`E_(2)^(@) = 1.23 V` …(2)
or `Mn^(2+)+2H_(2)O rarr MnO_(2)+4H^(+)+2e`,
`E_(3)^(@) = -1.23 V` …(3)
On adding (1) and (3) we get
`MnO_(4)^(-)+4H^(+)+3e rarr MnO_(2)+2H_(2)O`
`DeltaG_(4)^(@) = DeltaG_(1)^(@)+DeltaG_(3)^(@)`
`3 xx E_(4)^(@)F = 5 xx E_(1)^(@)F + 2 xx (E_(3)^(@)) xx F`
or ` E_(4)^(@) = (5E_(1)^(@) + 2E_(3)^(@))/(3) = (5 xx 1.51 + 2 xx (-123))/(3)`
`= (5.09)/(3) = 1.70 V`