Table of standard reduction potentials for half-reactions important in biochemistry

The values below are standard apparent reduction potentials for electro-biochemical half-reactions measured at 25 °C, 1 atmosphere and a pH of 7 in aqueous solution.
The actual physiological potential depends on the ratio of the reduced and oxidized forms according to the Nernst equation and the thermal voltage.
When an oxidizer accepts a number z of electrons to be converted in its reduced form, the half-reaction is expressed as:
The reaction quotient is the ratio of the chemical activity of the reduced form to the activity of the oxidized form. It is equal to the ratio of their concentrations only if the system is sufficiently diluted and the activity coefficients are close to unity :
The Nernst equation is a function of and can be written as follows:
At chemical equilibrium, the reaction quotient of the product activity by the reagent activity is equal to the equilibrium constant of the half-reaction and in the absence of driving force the potential also becomes nul.
The numerically simplified form of the Nernst equation is expressed as:
Where is the standard reduction potential of the half-reaction expressed versus the standard reduction potential of hydrogen. For standard conditions in electrochemistry the standard reduction potential of hydrogen is fixed at zero by convention as it serves of reference. The standard hydrogen electrode, with = 1 M works thus at a pH = 0.
At pH = 7, when = 10⁻⁷ M, the reduction potential of differs from zero because it depends on pH.
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 into hydrogen gas is no longer zero as with the standard hydrogen electrode at 1 M in classical electrochemistry, but that versus the standard hydrogen electrode.
The same also applies for the reduction potential of oxygen:
For, = 1.229 V, so, applying the Nernst equation for pH = 7 gives:
For obtaining the values of the reduction potential at pH = 7 for the redox reactions relevant for biological systems, the same kind of conversion exercise is done using the corresponding Nernst equation expressed as a function of pH.
The conversion is simple, but care must be taken not to inadvertently mix reduction potential converted at pH = 7 with other data directly taken from tables referring to SHE.

Expression of the Nernst equation as a function of pH

The 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 :
The half-cell standard reduction potential is given by
where is the standard Gibbs free energy change, is the number of electrons involved, and is Faraday's constant. The Nernst equation relates pH and :
where curly braces indicate activities, and exponents are shown in the conventional manner.
This equation is the equation of a straight line for as a function of pH with a slope of volt.
This equation predicts lower at higher pH values. This is observed for the reduction of O₂ into H₂O, or OH⁻, and for reduction of H⁺ into H₂.

Formal standard reduction potential combined with the pH dependency

To obtain the reduction potential as a function of the measured concentrations of the redox-active species in solution, it is necessary to express the activities as a function of the concentrations.
Given that the chemical activity denoted here by is the product of the activity coefficient γ by the concentration denoted by : a_i = γ_i·C_i, here expressed as = γ_x and ^x = ^x ^x and replacing the logarithm of a product by the sum of the logarithms, the log of the reaction quotient 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.
Combining directly with the last term depending on pH gives:
For a pH = 7:
So,
It is therefore important to know to what exact definition does refer the value of a reduction potential for a given biochemical redox process reported at pH = 7, and to correctly understand the relationship used.
Is it simply:

calculated at pH 7,
, a formal standard reduction potential including the activity coefficients but no pH calculations, or, is it,
, an apparent formal standard reduction potential at pH 7 in given conditions and also depending on the ratio.

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.

Determination of the formal standard reduction potential when 1

The formal standard reduction potential can be defined as the measured reduction potential of the half-reaction at unity concentration ratio of the oxidized and reduced species under given conditions.
Indeed:
as,, when,
because, and that the term is included in.
The formal reduction potential makes possible to more simply work with molar or molal concentrations in place of activities. Because molar and molal concentrations were once referred as formal concentrations, it could explain the origin of the adjective formal in the expression formal potential.
The formal potential is thus the reversible potential of an electrode at equilibrium immersed in a solution where reactants and products are at unit concentration. 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 it becomes de facto a standard potential. According to Brown and Swift, "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".
The activity coefficients and are included in the formal potential, 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.
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.

Main factors affecting the formal (or apparent) standard reduction potentials

The main factor affecting the formal reduction potentials in biochemical or biological processes is the pH. 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. To define a formal reduction potential for a biochemical reaction, the pH value, the concentrations values and the hypotheses made on the activity coefficients must always be clearly indicated. When using, or comparing, several formal reduction potentials they must also be internally consistent.
Problems may occur when mixing different sources of data using different conventions or approximations. When working at the frontier between inorganic and biological processes, care must be taken not to inadvertently directly mix standard reduction potentials with formal reduction potentials. Definitions must be clearly expressed and carefully controlled, especially if the sources of data are different and arise from different fields and microbiology textbooks.

Example in biochemistry

For example, in a two electrons couple like : the reduction potential becomes ~ 30 mV more positive for every power of ten increase in the ratio of the oxidised to the reduced form.

Some important apparent potentials used in biochemistry

Half-reaction	E°'	E' Physiological conditions	References and notes
	−0.58		Many carboxylic acid: aldehyde redox reactions have a potential near this value
2 + 2 →	−0.41		Non-zero value for the hydrogen potential because at pH = 7, = 10⁻⁷ M and not 1 M as in the standard hydrogen electrode, and that:
→ NADPH	−0.320	−0.370	The ratio of :NADPH is maintained at around 1:50. This allows NADPH to be used to reduce organic molecules
→ NADH	−0.320	−0.280	The ratio of :NADH is maintained at around 30:1. This allows to be used to oxidise organic molecules
FAD + 2 + 2 →	−0.22		Depending on the protein involved, the potential of the flavine can vary widely
Pyruvate + 2 + 2 → Lactate	−0.19
Oxaloacetate + 2 + 2 → Malate	−0.17		While under standard conditions malate cannot reduce the more electronegative NAD⁺:NADH couple, in the cell the concentration of oxaloacetate is kept low enough that Malate dehydrogenase can reduce NAD⁺ to NADH during the citric acid cycle.
Fumarate + 2 + 2 → Succinate	+0.03
	+0.30		Formation of hydrogen peroxide from oxygen
	+0.82		In classical electrochemistry, E° for = +1.23 V with respect to the standard hydrogen electrode. At pH = 7,
+ → P680	~ +1.0		Half-reaction independent of pH as no is involved in the reaction