The values below are standard apparent reduction potentials (E°') for electro-biochemical half-reactions measured at 25 °C, 1 atmosphere and a pH of 7 in aqueous solution.
[1][2] The actual physiological potential depends on the ratio of the reduced (Red) and oxidized (Ox) forms according to the Nernst equation and the thermal voltage.
When an oxidizer (Ox) accepts a number z of electrons ( e−) to be converted in its reduced form (Red), the half-reaction is expressed as: The reaction quotient (Qr) is the ratio of the chemical activity (ai) of the reduced form (the reductant, aRed) to the activity of the oxidized form (the oxidant, aox).
It is equal to the ratio of their concentrations (Ci) only if the system is sufficiently diluted and the activity coefficients (γi) are close to unity (ai = γi Ci): The Nernst equation is a function of Qr and can be written as follows:
At chemical equilibrium, the reaction quotient Qr of the product activity (aRed) by the reagent activity (aOx) is equal to the equilibrium constant (K) of the half-reaction and in the absence of driving force (ΔG = 0) the potential (Ered) also becomes nul.
Solving the Nernst equation for the half-reaction of reduction of two protons into hydrogen gas gives: In biochemistry and in biological fluids, at pH = 7, it is thus important to note that the reduction potential of the protons ( H+) into hydrogen gas H2 is no longer zero as with the standard hydrogen electrode (SHE) at 1 M H+ (pH = 0) in classical electrochemistry, but that
and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram (
For a half cell equation, conventionally written as a reduction reaction (i.e., electrons accepted by an oxidant on the left side): The half-cell standard reduction potential
is the standard Gibbs free energy change, z is the number of electrons involved, and F is Faraday's constant.
) (without {H+} already isolated apart in the last term as h pH) expressed here above with activities { } becomes: It allows to reorganize the Nernst equation as: Where
is the formal standard potential independent of pH including the activity coefficients.
Is it simply: This requires thus to dispose of a clear definition of the considered reduction potential, and of a sufficiently detailed description of the conditions in which it is valid, along with a complete expression of the corresponding Nernst equation.
Were also the reported values only derived from thermodynamic calculations, or determined from experimental measurements and under what specific conditions?
Without being able to correctly answering these questions, mixing data from different sources without appropriate conversion can lead to errors and confusion.
of the half-reaction at unity concentration ratio of the oxidized and reduced species (i.e., when Cred/Cox = 1) under given conditions.
The formal reduction potential makes possible to more simply work with molar or molal concentrations in place of activities.
[4] If any small incremental change of potential causes a change in the direction of the reaction, i.e. from reduction to oxidation or vice versa, the system is close to equilibrium, reversible and is at its formal potential.
When the formal potential is measured under standard conditions (i.e. the activity of each dissolved species is 1 mol/L, T = 298.15 K = 25 °C = 77 °F, Pgas = 1 bar) it becomes de facto a standard potential.
[5] According to Brown and Swift (1949), "A formal potential is defined as the potential of a half-cell, measured against the standard hydrogen electrode, when the total concentration of each oxidation state is one formal".
, and because they depend on experimental conditions such as temperature, ionic strength, and pH,
cannot be referred as an immuable standard potential but needs to be systematically determined for each specific set of experimental conditions.
[5] Formal reduction potentials are applied to simplify results interpretations and calculations of a considered system.
Their relationship with the standard reduction potentials must be clearly expressed to avoid any confusion.
The main factor affecting the formal (or apparent) reduction potentials
To determine approximate values of formal reduction potentials, neglecting in a first approach changes in activity coefficients due to ionic strength, the Nernst equation has to be applied taking care to first express the relationship as a function of pH.
The second factor to be considered are the values of the concentrations taken into account in the Nernst equation.
When using, or comparing, several formal (or apparent) reduction potentials they must also be internally consistent.
When working at the frontier between inorganic and biological processes (e.g., when comparing abiotic and biotic processes in geochemistry when microbial activity could also be at work in the system), care must be taken not to inadvertently directly mix standard reduction potentials (
Definitions must be clearly expressed and carefully controlled, especially if the sources of data are different and arise from different fields (e.g., picking and directly mixing data from classical electrochemistry textbooks (
For example, in a two electrons couple like NAD+:NADH the reduction potential becomes ~ 30 mV (or more exactly, 59.16 mV/2 = 29.6 mV) more positive for every power of ten increase in the ratio of the oxidised to the reduced form.