Electron transfer reactions are ubiquitous and important in a variety of applications: most of our chemical energy sources rely on electron transfer reactions. For example, combustion, batteries, and photosynthesis all rely on redox reactions.
Because the properties of electron transfer reactions can be easily measured using electrochemical methods.
The potential, E, is directly related to the Gibb's energy, ΔG, which is the determinative thermodynamic function related to the spontaneity of any reaction (at constant pressure).
ΔG = –nFE
F is Faraday's constant = 96485 Coulombs/mole
n = the number of moles of electrons transferred in the reaction
At standard conditions (1 bar pressure, 25 °C, 1 mole reactant, pH = 0), potentials are denoted E° and are further partitioned (arbitrarily) into reduction potentials for each reacting species:
E° = E°red(reduced species) – E°red(oxidized species)
Reduction potentials are tabulated in a variety of formats.
At nonstandard conditions, the Nernst equation is used to find a reaction potential:
E = E° – (RT/nF)lnQ
Q is the reaction quotient (mass action expression)
The Nernst equation can also be applied to half-reactions:
Ered = E°red – (RT/nF)lnQred
Qred is the mass action expression of the reduction half-reaction, ignoring the electrons.
Qred is only a relative value since it is based on the arbitrary partitioning done to obtain E°red
Tables - these list reduction reactions and associated potentials. These are typically found in textbooks.
Latimer Diagrams - these are more concise descriptions of all of the redox potentials associated with an element in aqueous solution. Different diagrams exist for acid and base conditions.
FeO2+ → +1.4 Fe3+ → +0.77 Fe2+ → –0.44 Fe (acid)
FeO42– → +0.79 FeO2– → –0.45 FeO(OH)– → –0.6 Fe (base)
Write the balanced equation and find the standard reduction potential for the reduction of FeO42– to FeO(OH)–
The balanced half-reaction is FeO42–(aq) + 3 H2O(l) + 4 e– → FeO(OH)–(aq) + 5 OH–(aq)
The potential is found by using the weighted average of the step-wise potentials:
E°red = [(3)(0.79) + (1)(–0.45)]/[3 + 1] = +0.48 V
Pourbaix Diagrams - these are pH-potential phase diagrams that map all of the ions and molecules for an element in aqueous solution.
The majority of electron transfer reactions are bimolecular because the oxidized and reduced species must encounter each other for the electron(s) to be moved from one species to the other.
Mechanistically, electron transfer reactions are usually categorized as either inner-sphere or outer-sphere.
The defining characteristic of an inner-sphere reaction is that the transition state has a bridging ligand between the electron donor and electron acceptor.
[Cr(H2O)6]2+ + [Co(NH3)5Cl]2+ → [(H2O)5Cr—Cl—Co(NH3)5]4+ + H2O → [Cr(H2O)5Cl]2+ + [Co(NH3)5(H2O)]2+
The presence of ambidentate ligands that cannot chelate are often indicators of an inner-sphere mechanism. An open coordination site, such as a 4- or 5-coordinate complex, is another structural feature for many inner-sphere reactions.
In outer-sphere reactions the electron transfer occurs by tunneling from one center to the other during a collision between the reactants. The initial encounter complex has the same structure as the reactants and the electron transfer follows the Franck-Condon Principle (electron transfer is much faster than nuclear reorganization).
The mechanism for an outer-sphere reaction can be described as
A + B ⇄ [A, B] (encounter complex)
[A, B] ⇄ [A, B]* (transition state formation)
[A, B]* ⇄ [A–, B+] (electron transfer)
[A–, B+] ⇄ A– + B+ (reorganization to products)
The rate constants for outer-sphere self-exchange reactions can be described by Marcus Theory:
kET = νNκee–Δ‡G°/RT
νN = nuclear frequency factor - this is the factor that describes how often a collision leads to an encounter complex that is the transition state
κe = electronic factor - this is the probability that the electron transfers in the transition state, which depends on the orbital overlap between the donor and the acceptor
Δ‡G° = ¼λ(1 + ΔrG°/λ)2
ΔrG° = the standard Gibb's energy of the reaction (ΔrG° = E°)
λ = reorganization energy - this is the energy that would be required to change the nuclear coordinates to the product geometry if there were no electron transfer. This includes the solvent reorganization.
For reactions that are not self-exchange, Marcus Theory is modified
k12 = (k11k22K12f12)½
k11 and k22 are the self exchange rate constants
K12 is the equilibrium constant for the reaction (found from ΔrG°)
f12 = (logK12)2/4log(k11k22/Z), Z is a proportionality constant to get the units correct ~ 1011 L·mol–1s–1
Marcus Theory has been exceptionally successful in understanding outer-sphere redox reactions
Reaction
kobserved (M–1s–1)
kcalculated (M–1s–1)
[IrCl6]2– + [W(CN)8]4–
6.1×107
6.1×107
[IrCl6]2– + [Fe(CN)6]4–
3.8×105
7×105
[Mo(CN)8]3– + [W(CN)8]4–
5.0×106
4.8×106
[Fe(CN)6]4– + [MnO4]–
1.3×104
5×103
[V(H2O)6]2+ + [Ru(NH3)6]3+
1.5×103
4.2×103
[Ru(en)3]2+ + [Fe(H2O)6]3+
8.4×104
4.2×105
[Fe(H2O)6]2+ + [Mn(H2O)6]3+
1.5×104
3×104
Data taken from J. D. Atwood, Inorganic and Organometallic Reaction Mechanisms, Brooks/Cole Publishing Company, Monterey, CA, 1985, page 294.