Free Energy Changes from Oxidation/Reduction

Standard reduction potentials are directly related to free energy changes by the equation

where n is the number of electrons transferred in the half-reactions, F is Faraday's constant (96.5 kJ mol-1V-1) and E 0' is the difference in standard reduction potentials between the two redox couples.

For example, in the following reaction:

> Ethanol + NAD+ <=> Acetaldehyde + NADH,

the two half-reactions are

> NAD+ + H+ + 2e- <=> NADH (E 0' = -0.320 V)

> Ethanol <=> Acetaldehyde + 2H+ + 2e- (E 0' = +0.197 V)

Note that the value of E 0' for the ethanol/aldehyde oxidation reaction above is the same magnitude, but opposite sign of the E 0' value given in Table 15.1. This is because the reactions in Table 15.1 are all written as reductions;

> Acetaldehyde + 2H+ + 2e- <=> Ethanol

If a reaction is reversed, the sign of E 0' must be changed. The overall reaction is the sum of the two half-reactions, so E 0' is given by

> E 0' = -0.320 V + 0.197 V = -0.123 V

The standard free energy then is

> = -nFE 0' = -2(96.5)(-0.123)kJ/mol = 23.74 kJ/mol

Thus, this reaction would not be favored under standard conditions (i.e., pH 7, 25C, and of equal concentrations of reactants and products) and would go in the reverse direction.

The Nernst Equation makes it possible to calculate reduction potentials under nonstandard conditions;

where R is the gas constant (8.314 J/mol), T is the absolute temperature, and 2.303 is the conversion factor from natural base e to common (base 10) logarithms. At 25C, the 2.303RT/nF term has the value of 0.059 V for a one-electron transfer and 0.0295 V (rounded to 0.03 V) for a two-electron transfer (n=2). Thus, the Nernst equation simplifies to

> E' = E 0' + 0.03log([e- acceptor]/[e- donor])

This is similar to the Henderson-Hasselbalch equation:

> pH = pK a + log([proton acceptor]/[proton donor])

Furthermore, in the same sense that pK a is defined by the midpoint of an acid titration curve, E 0' is defined by the midpoint of an electrochemical titration, where electron acceptor and electron donor are present in equal concentrations.

Each of the coupled redox reactions in biological electron transport involves the transfer of electrons from one redox couple to another couple of higher reduction potential. Thus, each individual redox reaction in the sequence is exergonic under standard conditions. For electrons entering the respiratory chain as NADH, the overall reaction sequence is given by the following equation:

> NADH + H+ + 1/2 O 2 <=> NAD+ + H 2O

This sequence is strongly exergonic

> ,

thus providing the free energy needed to synthesize ATP during oxidative phosphorylation.

See also: Standard Reduction Potential, Oxidations and Energy Generation, Electron Transport, Henderson-Hasselbalch Equation (from Chapter 2).