16.3: The Eigen-Wilkins Mechanism

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UNDER CONSTRUCTION

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 high $\ce{[NH3]}$, 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:

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

Let's derive the rate law for the overall reaction. First let's lay out an important assumtion. The Eigen-Wilkins mechanism assumes that formation of the encounter complex is a pre-equilibrium step. In other words, it is a fast step. Once it forms, it also can quickly fall apart to re-form the reactant complex. Therefore, the rate law for formation of the encounter complexdepends on both the formation and the decomposition of the encounter complex. The rate of formation of the encounter complex can be written as follows: \[ \ce{{rate}=k_1 [ML5X][Y]-k_{-1}[(ML5X,Y)]}\]

The rate of formation of the product from the encounter complex (the second step) is the rate-determining step. We assume that the foward $ \ce{{rate}=k_2 [(ML5X*Y)]} $