Mechanism
“The overall reaction for the oxidation of a hydroquinone by ferric ions is given by Eq. (3.97)
where QH2 and Q denote the hydroquinone and quinone, respectively. The rate of this reaction has been measured as a function of the concentrations of the various reactants and products. One mechanism consistent with the data involves the ionization of QH2 to QH−, followed by an electron transfer between QH− and Fe3+:
Where QH denotes the semiquinone. This step was in turn followed by the ionization of QH to Q− and then by the latter’s oxidation to Q [1]. The four elementary steps of the mechanism are then:
On the right side of the reactions, I have written the symbol of the corresponding equilibrium constants. k1 and k are symbols of the rate constants.
“We shall be concerned here with the experimental and theoretical value of k, the rate constant for the forward reaction in Eq. (3.99).”
As we know Marcus’ theory applies to the elementary redox step of an overall redox reaction.
“The experimental k can readily be computed from the known overall bimolecular rate constant k1 and the known first ionization constant of QH2, K1.”
For convenience of the reader, I explicitly show how this is done following a note on p. 874 of Ref. [2].
The rate constant of the elementary redox step (3.82) can be written as:
It was also written [51] in terms of a pseudo-rate constant k1:
Consider reaction (3.98) and the associated chemical equilibrium:
whence:
and
For the pseudo-constant k1, we have:
and we see that it is inversely proportional to [H+].
The various quantities needed for the theoretical calculation of k are computed in the following sections.
3.27.Standard Free Energy Change of the Redox Step, F0
The standard free energy ΔF0 of reaction (3.99) has not been measured directly but can be estimated from K1, and from K and KS, the equilibrium constants of reactions (3.97) and (3.100), respectively,
It is readily verified that ΔF0 is given by
The values of K and K1 have been determined experimentally [51, 70]. Numerous data on the formation constants of semiquinones KS have also been obtained. When, as in reaction (3.100), all three compounds in this equilibrium are uncharged, or have the same charge, the free energy of this reaction is found to be practically independent of the chemical structure of these compounds (this can be inferred from a detailed analysis of data on the on the pH dependence of the first and second oxidation potential of many hydroquinone-like compounds). The standard free energy change of reaction (3.100), −RT ln KS, is found to be about 2.3kcal mole−1.
With these values of K , K1, and KS, the values of ΔF0 given in Table I were calculated from Eq. (3.101).
Table I. Kinetic and thermodynamic data for Fe+3 + QH− reaction at 25∘Ca
aAll free energy units are in kcal mole−1. bx denotes the 2,6-dichloro compounds and y denotes any other compound.
3.28.Effective Radii
“In the derivation of Eq. (3.4) for ΔF*, each ion was treated as being surrounded by a sphere of radius a inside of which the dielectric medium, that is, the solvent, is saturated and outside of which it is unsaturated. Similar models have been used extensively in calculating the free energy of solvation of the ions,” see Refs. in [2].
As discussed in Chapter 2 “if, as it is usually assumed, the innermost hydration layer around monoatomic ions is largely saturated, it will not contribute to ΔF*, and a then equals the sum of the crystallographic radius of the ion and of the diameter of a water molecule. Polyatomic ions such as