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Apparent (formal) standard reduction potential $(E°')$ in biochemistry
Relationship of $E_{h}$ as a function of pH


 * $$E_h = E_\text{red} = E^{\ominus}_\text{red} - \frac{0.05916}{n} \log\left(\frac{\{C\}^c\{D\}^d}{\{A\}^a\{B\}^b}\right) - \frac{0.05916\,h}{n} \text{pH}$$

where curly brackets indicate activities, and exponents are shown in the conventional manner. This equation is the equation of a straight line for $$E_h$$ as a function of pH with a slope of $$-0.05916\,h/n$$ volt (pH has no units). This equation predicts lower $$E_h$$ at higher pH values.

Standard reduction potential $(E°)$ with activity coefficients
Similarly to equilibrium constants, activities are always measured with respect to the standard state (1 mol/L for solutes, 1 atm for gases, and T = 298.15 K, i.e., 25 °C or 77 °F). The chemical activity of a species $i$, $a_{i}$, is related to the measured concentration $C_{i}$ via the relationship $a_{i} = γ_{i} C_{i}$, where $γ_{i}$ is the activity coefficient of the species $i$. Because activity coefficients tend to unity at low concentrations, activities in the Nernst equation are frequently replaced by simple concentrations.

Taking into account the activity coefficients ($$\gamma$$) the Nernst equation becomes:

$$E_\text{red} = E^\ominus_\text{red} - \frac{RT}{zF} \ln\left(\frac{\gamma_\text{Red}}{\gamma_\text{Ox}}\frac{C_\text{Red}}{C_\text{Ox}}\right)$$

$$E_\text{red} = E^\ominus_\text{red} - \frac{RT}{zF} \left(\ln\frac{\gamma_\text{Red}}{\gamma_\text{Ox}} + \ln\frac{C_\text{Red}}{C_\text{Ox}}\right)$$

$$E_\text{red} = \left(E^\ominus_\text{red} - \frac{RT}{zF} \ln\frac{\gamma_\text{Red}}{\gamma_\text{Ox}}\right) - \frac{RT}{zF} \ln\frac{C_\text{Red}}{C_\text{Ox}}$$

Where the first term $$\left(E^\ominus_\text{red} - \frac{RT}{zF} \ln\frac{\gamma_\text{Red}}{\gamma_\text{Ox}}\right)$$ is denoted $$E^{\ominus '}_\text{red}$$ and called the formal reduction potential, so that: $$E_\text{red}=E^{\ominus '}_\text{red} - \frac{RT}{zF} \ln\frac{C_\text{Red}}{C_\text{Ox}}$$

Or more simply, using the math code for inserting an underbrace to more easily denote the first term $$E^{\ominus '}_\text{red}$$:

$$E_\text{red} = \underbrace{\left(E^\ominus_\text{red} - \frac{RT}{zF} \ln\frac{\gamma_\text{Red}}{\gamma_\text{Ox}}\right)}_{E^{\ominus '}_\text{red}} - \frac{RT}{zF} \ln\frac{C_\text{Red}}{C_\text{Ox}}$$

Where the first term including the activity coefficients ($$\gamma$$) is denoted $$E^{\ominus '}_\text{red}$$ and called the formal reduction potential, so that $$E_\text{red}$$ can be directly expressed as a function of $$E^{\ominus '}_\text{red}$$ and the concentrations in the simplest form of the Nernst equation: $$E_\text{red}=E^{\ominus '}_\text{red} - \frac{RT}{zF} \ln\frac{C_\text{Red}}{C_\text{Ox}}$$

Formal standard reduction potential
Thus, when the activity coefficients are far from unity and can no longer be simply neglected, it can be convenient to introduce the notion of the "so-called" standard formal reduction potential ($$E^{\ominus '}_\text{red}$$) which is related to the standard reduction potential as follows: $$E^{\ominus '}_\text{red}=E^{\ominus}_\text{red}-\frac{RT}{zF}\ln\frac{\gamma_\text{Red}}{\gamma_\text{Ox}}$$ So that the Nernst equation for the half-cell reaction can be correctly formally written in terms of concentrations as: $$E_\text{red}=E^{\ominus '}_\text{red} - \frac{RT}{zF} \ln\frac{C_\text{Red}}{C_\text{Ox}}$$

Formal standard reduction potential combined with the pH dependency

 * ---Début du brouillon---


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

Avec la transformation progressive de l'équation ci-dessus par petites étapes afin de pouvoir s'y retrouver lentement:


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

A laquelle, il faut évidemment encore rajouter le terme suivant : $$ - \frac{0.05916}{z} \log\left(\frac{\left({\gamma_\text{C}}\right)^c \left({\gamma_\text{D}}\right)^d}{\left({\gamma_\text{A}}\right)^a \left({\gamma_\text{B}}\right)^b}\right)$$

Expressing the activity (ai = γi·Ci) as a function of the concentration taking into account the activity coefficients:

with {X} = γx [X] and {X}x = (γx)x [X]x and reorganising the equation taking into account that the logarithm of a product is the sum of the logarithms (i.e., log (a·b) = log a + log b), the Nernst equation becomes:

_________________________________________________________________________________
 * ---Fin du brouillon---

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.


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

Given that the chemical activity denoted here by { } is the product of the activity coefficient γ by the concentration denoted by [ ]: ai = γi·Ci, here expressed as {X} = γx [X] and {X}x = (γx)x [X]x 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 ($$Q_r$$) expressed here above with activities { } becomes:


 * $$\log\left(\frac{\{C\}^c\{D\}^d}{\{A\}^a\{B\}^b}\right) = \log\left(\frac{\left({\gamma_\text{C}}\right)^c \left({\gamma_\text{D}}\right)^d}{\left({\gamma_\text{A}}\right)^a \left({\gamma_\text{B}}\right)^b}\right)+ \log\left(\frac{\left[C\right]^c\left[D\right]^d}{\left[A\right]^a\left[B\right]^b}\right)$$

It allows to reorganize the Nernst equation as:


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


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

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

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


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

For a pH = 7:


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

So,


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

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

Haber-Weiss chain reaction
The main finding of Haber and Weiss was that hydrogen peroxide (H2O2) is decomposed by a chain reaction.

The Haber-Weiss reaction chain proceeds by successive steps: (i) initiation, (ii) propagation and (iii) termination.

The chain is initiated by the Fenton reaction:


 * Fe2+ + H2O2 → Fe3+ + HO– + HO•    (step 1: initiation)

Then, the reaction chain propagates by means of two successive steps:


 * HO• + H2O2 → H2O + O2•– + H+       (step 2: propagation)


 * O2•– + H+ + H2O2 → O2 + HO• + H2O   (step 3: propagation)

Finaly, the chain is terminated when the hydroxyl radical is scavenged by a ferrous ion:


 * Fe2+ + HO• + H+ → Fe3+ + H2O        (step 4: termination)

Hydroperoxyl and superoxide radicals
With time, various chemical notations for the hydroperoxyl (perhydroxyl) radical coexist in the literature. Haber, Wilstätter and Weiss simply wrote HO2 or O2H, but sometimes HO2• or •O2H can also be found to stress the radical character of the species.

The hydroperoxyl radical is a weak acid and gives rise to the superoxide radical (O2•–) when it loses a proton:


 * HO2 → H+ + O2–


 * sometimes also written as:


 * HO2• → H+ + O2•–

A first pKa value of 4.88 for the dissociation of the hydroperoxyl radical was determined in 1970. The presently accepted value is 4.7.

Scientific methods and model validation
Oreskes worked on scientific methods, in particular model validation in the earth sciences. In 1999 she participated as a consultant to the US Nuclear Waste Technical Review Board for developing a repository safety strategy for the Yucca Mountain project, with special attention to model validation.

Havar alloy
The composition of Havar alloy is given in the next table.