# 16.3: The Eigen-Wilkins Mechanism

## Introduction

Most octahedral complexes react through either an associative or dissociative interchange mechanism ($$I_a$$ or $$I_d$$). Although the rate laws should be different for these two cases, it is difficult to distinguish between them. The difficulty lies in the seemingly conflicting observations from experiments performed under limiting conditions of the incoming ligand. For example, in the case of the reaction of hexaaquochromium(III) ( $$\ce{[Cr(H2O)6]}$$ ) with ammonia ( $$\ce{NH3}$$ ), the rate laws determined at high and low concentrations of the incoming ligand give different apparent rate laws. Under most conditions, the rate law appears to indicate a dissociative mechanism (ie rate is independent of the $$\ce{[NH3]}$$). But, at very low $$\ce{[NH3]}$$, the rate law appears to indicate an associative mechanism (ie the rate depends on $$\ce{[NH3]}$$).

This information might seem contradictory. However, it can be explained by the formation of a transient ion pair, usually called an encounter complex, in a step prerequisite to the rate-determining step(s). The Eigen-Wilkins Mechanism is based on this idea.

## The Eigen-Wilkins mechanism

The Eigen-Wilkins mechanism is also a rate law, and it governs the reactions of octahedral metal complexes. This mechanism does not define the rate-limiting step; rather, it defines the existence of a pre-equilibrium step (ie an initial step that is not rate-determining) that results in formation of an encounter complex. The encounter complex is a short-lived ion pair of the metal complex and the incoming ligand; it is an intermediate formed through Coulomb interactions. For the conversion of a generic metal complex, where X is the leaving group and Y is the entering group, the overall reaction, pre-equilibrium step, and formation of products from the encounter complex are shown below:

$\begin{array}{rccc} & \text{CHEMICAL EQUATION} & \text{ RATE LAW } & \text{EQUILIBRIUM EXPRESSION} \\ \text{Overall Reaction:} & \ce{ML5X + Y <=> ML5Y + X} & & \ce{K = \ce{\frac{[ML5Y][X]}{[ML5X][Y]}}} \\ \text{Pre-Equilibrium Step:} & \ce{ML5X + Y<=>[{k_1}][{k_{-1}}] (ML5X*Y)} & \ce{{rate}=k_1 [ML5X][Y]-k_{-1}[(ML5X,Y)]}&\ce{K_E = \ce{\frac{[(ML5X*Y)]}{[ML5X][Y]}}} \\ \text{Formation of Products:} & \ce{(ML5X*Y) ->[{k_2}] ML5Y + X} & &\ce{K_2 = \ce{\frac{[ML5Y][X]}{[(ML5X*Y)]}}} \end{array}$