Biochemistry - The Chemical Reactions of Living Cells Volume 1 - D. Metzler 1980

Energetics of Biochemical Reactions
Electrode potentials and free energy change for oxidation-reduction reactions
Measurement of electrode potentials

To measure an electrode potential, it is necessary that the oxidizing agent of a conjugated redox pair can be reduced by a flow of electrons [Equation (3-62)] "flowing off" The surface of an electrode, which in many cases is coated with a layer of specially treated platinum.

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Equation (3-62) describes the reaction occurring at a single electrode. An electrochemical Cell has two electrodes, and the overall reaction is the sum of two half-reactions. The electrode potential of a given half-reaction is determined by measuring the electromotive force generated by a cell in which one of the half-reactions takes place at a standard electrode with a known potential. Fig. 3-3 schematically depicts the experimental setup for measuring electrode potentials. The standard hydrogen electrode consists of a platinum rod enclosed in a Glass tube through which hydrogen gas is supplied at a pressure of 1 atm. The electrode is immersed in a solution containing hydrogen ions at unit activity (a_H+ = 1). The potential of this electrode is conventionally set to zero. In practice, a calomel electrode or another electrode with a precisely known, constant potential is most frequently used as a standard electrode. The circuit between the solutions into which the electrodes are immersed is completed by a bridge filled with an electrolyte. In the half-cell under study, the reaction described by Equation (3-62) takes place On the surface of another electrode (usually platinum). The potential difference between the two electrodes is controlled by a potentiometer. By subtracting the potential of the standard electrode from this potential difference, the electrode potential of the redox pair under investigation is obtained. It is essential that the electrode reaction of interest be fully reversible. By adjusting the potentiometer slider so that the electromotive force (emf) of the system under study is exactly balanced by an external voltage source, it is possible to make the current through The Cell equal to zero. If the reaction is reversible, a slight change in voltage will cause a current to flow through the cell. Increasing or decreasing the voltage makes it possible to reverse the direction of the current.

FIG. 3-3. Apparatus for measuring electrode potentials. The equations for the reactions occurring in each half-cell are given at the bottom. The maximum electrical work that such a cell can perform on its surroundings is equal to —∆C = nEF, where E = V₂—V₁ (the potential difference measured with a potentiometer). If substance A, reacting with H₂, is reduced to AH₂, the electrons in the external circuit will flow in the direction indicated in the figure. In this process, reduction of A will occur in the right half-cell, while H₂ will be oxidized to H⁺ in the left half-cell. Protons will flow from left to right through the bridge filled with gel saturated with electrolyte, acting as charge carriers in the internal circuit.

Reaction reversibility does not hold for all redox pairs. This is especially true for Organic compounds: for example, for the aldehyde–alcohol pair, it is impossible to directly measure the electrode potential. In A number of cases, particularly when working with Enzymes, The addition of an easily reducible dye with a potential close to that of the measured conjugated pair helps (a list of relevant Dyes is given in reference [23]). If the dye can readily exchange electrons with the measured pair, direct measurement of the electrode potential becomes possible. In many cases, the electrode potentials listed in tables are calculated from Free energy data (many of the potentials given in Table 3-7 can be calculated from the data in Table 3-3; the reader is encouraged to verify this). When A, H⁺, and AH₂ in the system under study have unit activities, the observed half-reaction potential represents the standard electrode potential E⁰. If the emf of the hypothetical electrode system containing the standard hydrogen electrode is positive when current flows in the direction indicated by the arrow in Fig. 3-3, the potential of the A/AH₂ conjugate pair is also considered positive (it is often called the reduction potential). The data in Table 3-7 correspond to this convention, but it should be kept in mind that some chemists use oxidation potentials that are equal in absolute magnitude but opposite in sign. To avoid confusion, we recommend memorizing the value of one or two potentials, such as those of the O₂–H₂O and NAD⁺–NADH pairs.

Table 3-7 Reduction potentials of some biologically important systems^a,b

a A compound with a more positive potential will oxidize the reduced form of a substance with a lower potential, with a Standard Free Energy change of ∆С⁰ =—nF∆Е⁰ =—n∆E⁰∙96.49 kJ∙mol^-1, where n is the number of electrons transferred from the reducing agent to the oxidizing agent. Unless otherwise specified, the Temperature is assumed to be 25 °C. E⁰ refers to the standard state in which the hydrogen ion activity is 1; E⁰' refers to the standard state at pH 7, in which all other activities are equal to unity.

^b Main data source: Loach P. A., in: Handbook of Biochemistry and Molecular Biology, 3rd ed., Vol. I (G. D. Fasman, ed.), pp. 122–130, © CRC Press, Inc., Cleveland, 1976.

The maximum work (—∆G) that can be performed by a flow of electrons in an external circuit driven by an electrochemical reaction (per mole of substance) is

—∆G = nEF = (nE ∙ 96.487) kJ∙mol^-1 =

   = (nE ∙ 23.061) kcal∙mol^-1,       (3-63)

where F is the charge of a mole of electrons in coulombs¹ (the electron charge multiplied by the Avogadro number, i.e., 96,487 coulombs), and E is the measured potential difference between the two half-Cells (in volts). If one of the half-cells is the standard hydrogen electrode, then E is the electrode potential of the conjugate pair. The number of moles of electrons transferred in the course of the reactions (n) is 1 or 2 for typical biochemical reactions [in Equation (3-62) it is 2].

Since reactants and products do not always have unit activity, we need to find the dependence of the observed electrode potential on E⁰ and the activities (concentrations) of A, AH₂, and H⁺. This dependence has the following form:

In biochemical literature, apparent standard electrode potentials at pH 7 (E⁰', Table 3-7, second Column) are usually given instead of E⁰. Note that E⁰' (pH 7) for the hydrogen electrode is not 0, but —0.414 V. The relationship between E and E⁰' is determined by Equation (3-64), in which the factor [H⁺]² is absent in the numerator because the term containing lg [H⁺] is already incorporated into E⁰'. On the E⁰' (pH 7) scale, the potential of the oxygen–Water pair is 0.815 V, and the potential of the NAD⁺–NADH pair is —0.32 V.