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 same also applies for the reduction potential of oxygen:

:

For , <math>E^{\ominus}_\text{red}</math> = 1.229 V, so, applying the Nernst equation for pH = 7 gives:

: <math>E_\text{red} = E^{\ominus}_\text{red} - 0.05916 \ pH</math>

: <math>E_\text{red} = 1.229 - \left(0.05916 \ \text{×} \ 7\right) = 0.815 \ V</math>

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 (pH = 0).

Expression of the Nernst equation as a function of pH

The <math>E_h</math> 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):

: <math chem>a \, A + b \, B + h \, \ce{H+} + z \, e^{-} \quad \ce{<=>} \quad c \, C + d \, D</math>

The half-cell standard reduction potential <math>E^{\ominus}_\text{red}</math> is given by

: <math>E^{\ominus}_\text{red} (\text{volt}) = -\frac{\Delta G^\ominus}{zF}</math>

where <math>\Delta G^\ominus</math> is the standard Gibbs free energy change, is the number of electrons involved, and is Faraday's constant. The Nernst equation relates pH and <math>E_h</math>:

: <math>E_h = E_\text{red} = E^{\ominus}_\text{red} - \frac{0.05916}{z} \log\left(\frac{\{C\}^c\{D\}^d}{\{A\}^a\{B\}^b}\right) - \frac{0.05916\,h}{z} \text{pH}</math> &nbsp;

where curly braces {&nbsp;} indicate activities, and exponents are shown in the conventional manner.<br />This equation is the equation of a straight line for <math>E_h</math> as a function of pH with a slope of <math>-0.05916\,\left(\frac{h}{z}\right)</math> volt (pH has no units).

This equation predicts lower <math>E_h</math> at higher pH values. This is observed for the reduction of O<sub>2</sub> into H<sub>2</sub>O, or OH<sup>−</sup>, and for reduction of H<sup>+</sup> into H<sub>2</sub>.

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.

: <math>E_h = E_\text{red} = E^{\ominus}_\text{red} - \frac{0.05916}{z} \log\left(\frac{\{C\}^c\{D\}^d}{\{A\}^a\{B\}^b}\right) - \frac{0.05916\,h}{z} \text{pH}</math>

Given that the chemical activity denoted here by {&nbsp;} is the product of the activity coefficient γ by the concentration denoted by [&nbsp;]: a<sub>i</sub> = γ<sub>i</sub>·C<sub>i</sub>, here expressed as {X} = γ<sub>x</sub> [X] and {X}<sup>x</sup> = (γ<sub>x</sub>)<sup>x</sup> [X]<sup>x</sup> and replacing the logarithm of a product by the sum of the logarithms (i.e., log (a·b) = log a + log b), the log of the reaction quotient (<math>Q_r</math>) (without {H<sup>+</sup>} already isolated apart in the last term as h pH) expressed here above with activities {&nbsp;} becomes:

: <math>\log\left(\frac{\{C\}^c\{D\}^d}{\{A\}^a\{B\}^b}\right) = \log\left(\frac{\left({\gamma_\text{C\right)^c \left({\gamma_\text{D\right)^d}{\left({\gamma_\text{A\right)^a \left({\gamma_\text{B\right)^b}\right)+ \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right)</math>

It allows to reorganize the Nernst equation as:

: <math>E_h = E_\text{red} = \underbrace{\left(E^{\ominus}_\text{red} - \frac{0.05916}{z} \log\left(\frac{\left({\gamma_\text{C\right)^c \left({\gamma_\text{D\right)^d}{\left({\gamma_\text{A\right)^a \left({\gamma_\text{B\right)^b}\right)\right)}_{E^{\ominus '}_\text{red - \frac{0.05916}{z} \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right) - \frac{0.05916\,h}{z} \text{pH}</math>

: <math>E_h = E_\text{red} = E^{\ominus '}_\text{red} - \frac{0.05916}{z} \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right) - \frac{0.05916\,h}{z} \text{pH}</math>

Where <math>E^{\ominus '}_\text{red}</math> is the formal standard potential independent of pH including the activity coefficients.

Combining <math>E^{\ominus '}_\text{red}</math> directly with the last term depending on pH gives:

: <math>E_h = E_\text{red} = \left(E^{\ominus '}_\text{red} - \frac{0.05916\,h}{z} \text{pH} \right)- \frac{0.05916}{z} \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right)</math>

For a pH = 7:

: <math>E_h = E_\text{red} = \underbrace{\left(E^{\ominus '}_\text{red} - \frac{0.05916\,h}{z} \text{× 7} \right)}_{E^{\ominus '}_\text{red apparent at pH 7 - \frac{0.05916}{z} \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right)</math>

So,

: <math>E_h = E_\text{red} = E^{\ominus '}_\text{red apparent at pH 7} - \frac{0.05916}{z} \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right)</math>

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:

  • <math>E_h = E_\text{red}</math> calculated at pH 7 (with or without corrections for the activity coefficients),
  • <math>E^{\ominus '}_\text{red}</math>, a formal standard reduction potential including the activity coefficients but no pH calculations, or, is it,
  • <math>E^{\ominus '}_\text{red apparent at pH 7}</math>, an apparent formal standard reduction potential at pH 7 in given conditions and also depending on the ratio <math>\frac{h} {z} = \frac{\text{(number of involved protons) {\text{(number of exchanged electrons)</math>.

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 <math>E^{\ominus '}_\text{red}</math> can be defined as the measured reduction potential <math>E_\text{red}</math> of the half-reaction at unity concentration ratio of the oxidized and reduced species (i.e., when 1) under given conditions.

Indeed:

as, <math>E_\text{red} = E^{\ominus}_\text{red}</math>, when <math>\frac{a_\text{red {a_\text{ox = 1</math>,

: <math>E_\text{red} = E^{\ominus'}_\text{red}</math>, when <math>\frac{C_\text{red {C_\text{ox = 1</math>,

because <math>\ln{1} = 0</math>, and that the term <math>\frac{\gamma_\text{red {\gamma_\text{ox</math> is included in <math>E^{\ominus '}_\text{red}</math>.

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 (i.e. the activity of each dissolved species is 1&nbsp;mol/L, T = 298.15 K = 25&nbsp;°C = 77&nbsp;°F, = 1 bar) it becomes de facto a standard potential. 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".

The activity coefficients <math>\gamma_{red}</math> and <math>\gamma_{ox}</math> are included in the formal potential <math>E^{\ominus '}_\text{red}</math>, and because they depend on experimental conditions such as temperature, ionic strength, and pH, <math>E^{\ominus '}_\text{red}</math> cannot be referred as an immuable standard potential but needs to be systematically determined for each specific set of experimental conditions. While under standard conditions malate cannot reduce the more electronegative NAD<sup>+</sup>:NADH couple, in the cell the concentration of oxaloacetate is kept low enough that Malate dehydrogenase can reduce NAD<sup>+</sup> to NADH during the citric acid cycle.

|-

| align="center" | Fumarate + 2 + 2 → Succinate

| align="center" | +0.03

|

|

|-

| align="center" |

| align="center" | +0.30

|

|Formation of hydrogen peroxide from oxygen

|-

| align="center" |

| align="center" | +0.82

|

|In classical electrochemistry, <br />E° for = +1.23 V with respect to the standard hydrogen electrode (SHE). At pH = 7,

|-

| align="center" | + → P680

| align="center" | ~ +1.0

|

|Half-reaction independent of pH as no is involved in the reaction

|}

See also

  • Nernst equation
  • Electron bifurcation
  • Pourbaix diagram
  • Reduction potential
  • Dependency of reduction potential on pH
  • Standard electrode potential
  • Standard reduction potential
  • Standard reduction potential (data page)
  • Standard state

References

Bibliography

;Electrochemistry

;Bio-electrochemistry

;Microbiology