Module A7

Electron Transfer Reactions

Concept Overview

Electron transfer (redox) reactions in coordination chemistry occur via two distinct mechanistic pathways:

Inner-Sphere Mechanism:
- Requires a bridged binuclear intermediate — one ligand bonds to both metals simultaneously.
- One reactant must be labile (to form the bridge), the other inert.
- Electron transfer occurs through the covalent bridge, which is often transferred to the newly inert center.
Classic example:
$[Co^{III}(NH_3)_5Cl]^{2+} + [Cr^{II}(H_2O)_6]^{2+} \rightarrow [Cr^{III}(H_2O)_5Cl]^{2+} + Co^{2+}_{(aq)}$
Outer-Sphere Mechanism:
- Both reactants are inert — no bridge can form.
- The electron tunnels through space from donor to acceptor.
- Metal-ligand bonds must reorganize (Frank-Condon principle) before transfer.
- Marcus-Hush Theory provides the quantitative framework.

Key Equations

Marcus Cross-Relation Equation

k_{12} = (k_{11} \\cdot k_{22} \\cdot K_{12} \\cdot f_{12})^{1/2}

Where:

$k_{12}$ — calculated rate constant for the cross-reaction
$k_{11}, k_{22}$ — self-exchange rate constants for the two redox couples
$K_{12}$ — equilibrium constant for the overall cross-reaction
$f_{12}$ — correction factor (≈ 1.0 for structurally similar systems)

Worked Examples

Use the Marcus-Hush Calculator below to input self-exchange rates and equilibrium constants, compute the theoretical cross-rate, and compare with experimental values to confirm the mechanism.

Common Misconceptions

❌ Misconception

Electron transfer always involves a ligand transfer.

✅ Correction

Ligand transfer only occurs in specific inner-sphere mechanisms. In outer-sphere mechanisms, no bonds are broken or formed — the electron tunnels through space.

Interactive Visual

Input self-exchange rates and equilibrium constant to compute the theoretical cross-rate using the Marcus equation. Compare with experimental values to determine if the reaction follows an outer-sphere mechanism.

k_{11}

(M⁻¹s⁻¹)Self-exchange rate (oxidant)

k_{22}

(M⁻¹s⁻¹)Self-exchange rate (reductant)

K_{12}

Equilibrium constant

f_{12}

Correction factor (≈ 1.0)

k_{12} = (k_{11} \cdot k_{22} \cdot K_{12} \cdot f_{12})^{1/2}

k_{12}

(calculated)6.72e+6 M⁻¹s⁻¹

Compare with Experiment

k_{12}

(experimental, M⁻¹s⁻¹)

Ratio k_exp/k_calc = 2.08

✅ Consistent with Outer-Sphere mechanism

Formative Quiz

Question 1

Why can

[Co(NH_3)_6]^{3+}

only react via an outer-sphere electron transfer mechanism?

Question 2

In Marcus theory, what is the significance of

k_{11}

and

k_{22}

Connections

Builds on

A2Labile and Inert Complexes A6Octahedral Substitution

Feeds into

B6Organometallic Catalysis (Redox in catalytic cycles)