Questions: Electron Transfer Reactions (Inner and Outer Sphere)

Question 1

In Taube's classic experiment, [Co(NH₃)₅Cl]²⁺ + [Cr(H₂O)₆]²⁺ → [Co(H₂O)₆]²⁺ + [Cr(H₂O)₅Cl]²⁺, the chloride transfers from cobalt to chromium. This proves the reaction proceeds by an inner-sphere mechanism. Why?

• A. Because electron transfer always requires direct orbital overlap between two metal centers
• B. Because the chloride bridges both metals in the transition state, mediating electron transfer, and ends up on chromium — which is possible only if chloride was simultaneously bonded to both metals during the reaction
• C. Because outer-sphere reactions cannot involve any ligand changes
• D. Because Co(III) and Cr(II) are both inert complexes that cannot exchange ligands without a bridging mechanism

Answer: (B)

The key evidence is the transfer of the chloride ligand from Co to Cr. In an outer-sphere mechanism, coordination shells remain intact — no ligand transfer would occur. The fact that Cl⁻ moves from one metal to another proves it must have been simultaneously bonded to both (bridging) during the electron transfer step. The precursor complex [Co-Cl-Cr] forms first, electron transfer occurs through the bridging Cl⁻, and then the successor complex dissociates with Cl⁻ remaining on Cr³⁺ (which is now inert due to its d³ configuration). This was Henry Taube's Nobel Prize-winning demonstration of the inner-sphere mechanism.

Question 2

Marcus theory predicts that the rate of outer-sphere electron transfer depends on both the thermodynamic driving force (ΔG°) and the reorganization energy (λ). Increasing |ΔG°| always increases the rate.

• T. True
• F. False

Answer: False

Marcus theory predicts that the rate increases as |ΔG°| increases — but only up to a point. When |ΔG°| exceeds the reorganization energy λ, the rate actually decreases. This counterintuitive prediction (the 'Marcus inverted region') occurs because the reaction coordinate and product energy surfaces intersect at progressively higher points when the driving force is too large. The inverted region was controversial when first predicted but has been experimentally confirmed, particularly in photochemical and biological electron transfer systems. For most ground-state inorganic reactions, |ΔG°| < λ and the rate does increase with driving force — the inverted region is more relevant in photoinduced processes.

Question 3

In outer-sphere electron transfer, the rate depends on the reorganization energy λ, which includes both inner-sphere (bond length changes) and outer-sphere (solvent reorganization) contributions.

• T. True
• F. False

Answer: True

Reorganization energy λ is the energy cost of distorting the reactant geometry to match the product geometry without actually transferring the electron. The inner-sphere component (λ_inner) reflects changes in metal-ligand bond lengths — for example, Fe²⁺ has longer Fe-O bonds than Fe³⁺, so the [Fe(H₂O)₆]²⁺/³⁺ self-exchange requires bond compression/extension. The outer-sphere component (λ_outer) reflects solvent reorientation — polar solvent molecules must reorganize around the changed charges. Both contribute to the activation barrier. Self-exchange reactions with small geometry changes (like [Ru(bipy)₃]²⁺/³⁺, where the rigid ligands minimize structural change) have small λ and fast rates.

Question 4

Explain why the [Fe(H₂O)₆]²⁺/³⁺ self-exchange reaction is much slower than the [Fe(phen)₃]²⁺/³⁺ self-exchange reaction, despite involving the same metal couple.

Model answer: The rate difference arises from the reorganization energy λ. In [Fe(H₂O)₆]²⁺/³⁺, the Fe-O bond lengths change significantly between oxidation states (Fe²⁺ has longer bonds than Fe³⁺), contributing a large inner-sphere reorganization energy. The aqua complex also has small, labile ligands that allow substantial solvent access and a large outer-sphere reorganization term. In [Fe(phen)₃]²⁺/³⁺, the rigid phenanthroline ligands constrain the metal-ligand geometry, minimizing bond length changes between oxidation states (small λ_inner). The large aromatic ligands also shield the metal from solvent, reducing λ_outer. The combined effect gives [Fe(phen)₃] a much smaller total λ, lower activation barrier, and faster self-exchange rate.

This example illustrates a design principle for efficient electron transfer: minimize reorganization energy by using rigid ligands that accommodate both oxidation states with minimal structural change. Nature exploits this in electron transfer proteins, where the protein environment tunes λ for efficient electron flow.