The Nearst Equation: Calcualte the nonstandard electrode potential, `E`, for the `Fe^(3+)//Fe^(2+)` electrode when the concentration of `Fe^(2+)` is exactly firve time that of `Fe^(3+)`
Strategy: The Nearst equation helps us calculate electrode potentials for concentrations other than one molar. The Tabulation of standard electrode potentials gives us the value of `E^(@)` for the reduction half-reaction. Use the balanced half-reaction and the given concentration ratio to calculate the value of `Q`. Finally substitude this into the Nearst equation with `n` equal to the number of moles of elecrons involved in the half-reaction.

Explanation

The reduction half-reaction is
`Fe^(3+)(aq.) + e^(-) rarr Fe^(2+)(aq.)E_(Fe^(3+)//Fe^(2+)) = + 0.77V`
Calculating the value of `Q` by using the fact that the concentration of `Fe^(2+)` is five times that of `Fe^(3+)`:
`Q = ["Red"]^(b)/["Ox"]^(a) = C_(Fe^(2+))/C_(Fe^(3+)) = (5C_(Fe^(3+)))/(C_(Fe^(3+))) = 5`
The balanced half-cell reaction shows one mole of electrons, or `n = 1`. Putting values into the Nearst equation,
`E_(Fe^(3+)//Fe^(2+))^(@) = E_(Fe^(3+)//Fe^(2+))^(@) - (0.0592 V)/(n) log Q`
`= +0.77 V - (0.0592 V)/(1) log 5`
`= 0.77 V - 0.04 V`
`= + 0.73`