A note on equilibrium constants for 1st and 2nd order reactions

For a reaction between an electron acceptor A+ and an electron donor D, the ratio of oxidized to reduced forms of the complex will depend on the order of the reaction. If A and D are within a single protein, or form a complex, such that electron transfer is by a 1st order process, then:

A+.D <=> A.D+

Keq = [A.D+ ]/ [A+.D]

For reaction between a redox pair in the complex, we expect the ratio for [A.D+ ] to [A+.D] to be equal to Keq (ie. both the A/A+ and D+/D ratios are equal to Keq)

For a collisional reaction, in which any A can reaction with any D through diffusion, the reaction is written:

A+ + D <=> A + D+

Keq = [A].[D+ ]/ [A+].[D]

In this case, the value of the equilibrium constant is given by the product of the ratios of A/A+ and D+/D (this reflects the entropic contribution of distribution of the states throughout the system). The consequence is that for a given value of Keq, the ratios of A/A+ and D+/D are less than in the 1st order case (by approximately a square root function), and in the "magic square" representation, the curves for the 1st order process are "nearer the corner" than for the 2nd order process.

In all the Figs. for this document, the theoretical curves shown are for the second-order case.

For Em values of 450, 340, 290 and 270 for P+/P, cyt c2+/c2, Fe2S2+/ Fe2S2 and cyt c1+/c1 couples respectively, Keq values are P:c2 = 73; c2:c1 = 15.4; P:Fe2S2 = 515; and P :c1 = 1124.