A question which sometimes arises is why, if the reduction potentials of copper(II) to copper(I) and copper(I) to copper metal are added, the result is not the same as the reduction potential of copper(II) to copper metal?

As is often the case, the explanation can only be given in terms of free energy changes.

The relationship between the free energy change ΔG and the potential of an electrochemical cell is

ΔG = -nFE^o

where F is the Faraday constant, 96485 C mol^-1 – the charge on a mole of electrons – and n is the number of electrons transferred in the reaction. Note this is the moles of electrons per mole of reaction, not the total number, which would be pretty big!

The electrode potentials do not, indeed, add up; however the free energy changes do. This is shown below; the free energy change for the conversion of Cu²⁺ to Cu is the same as that for the conversion of Cu²⁺ to Cu⁺ plus that of Cu⁺ to Cu.