# Formulaes and Remarks relating to unified reducity

The defintion of the pe_{abs} is:

The pe_{abs} can be calculated without the knowledge of the absolute chemical potential of the electron. The reason can be found by considering the Born-Fajans-Haber cycle (BFHC) of the H_{2}-electrolysis where in equilibrium the electron can adopt any arbitrary state.

From the BFHC follows that only the Standard Gibbs energy of solvation of the proton is needed to calculate the pe_{abs} of the system H^{+}/H_{2}:

Since the first term contains the Standard Gibbs energies of formation and ionization of the hydrogen atom it is solvent independent. The second and third term are activity dependent terms whereby pH_{S} is the pH value in the pH scale of the solvent S. For the calculation of pH_{S} see “Formulas and remarks to pH_{abs}”.

Other redox systems than H^{+}/H_{2} demand their own BFHC resulting in individual but constant first terms and activity depending terms, e.g. for the system M^{+}/M:

Resulting in:

where p*K*_{M} is assigned to the Gibbs energy of formation and ionization, resp. In this way any redox system can be implemented into the pe_{abs} scale.

The pe_{abs} value can be converted into the conventional Volt scale via:

With equation (4) one can determine the pe_{abs} via *E*°_{abs}(M^{z+}/M,S) which is the redox potential of the system M^{z+}/M in the solvent S within the unified potential scale:

with *E*°_{S}(M^{z+}/M,S) is the redox potential of the system M^{z+}/M in the solvent S in the potential scale of S (i.e. vs. SHE in S) and *E*°_{abs}(H^{+}/H_{2},S) is the SHE in S within the unified potential scale. *E*°_{S}(M^{z+}/M,S) can be obtained directly by the Gibbs energies of transfer:

The zero point of the absolute pe scale pe_{abs} 0 is assigned to the ideal electron gas at 1 bar and 298.15 K. Here the chemical potential of the electron is 0 kJ mol^{−1}.