In the text you learned of the rate laws for the...

In the text you learned of the rate laws for the substitution of a monodentate ligand on an octahedral complex by another monodentate ligand. However, another very important process is the substitution of two monodentate ligands by a chelating ligand. Wilkins [Acc. Chem. Res, 3, 408 (1970)] shows that the steps currently considered important when the substitution ligand is bidentate are $$ \begin{aligned} & \left.\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{M}(\mathrm{L}-\mathrm{L}) \quad \stackrel{k_3}{k_{\rightarrow}}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{M}-\mathrm{L}\right)+\mathrm{H}_2 \mathrm{O} \\ & \end{aligned} $$ That is, after formation of an outer sphere complex, one end of the bidentate ligand substitutes for one water molecule, followed by substitution of the other end for yet another water. Assuming that the first reaction is faster than the other two (and that $\left.k_x / k_{-x}=K_{\text {dit }}\right)$, and that a steady state exists for the intermediate $\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{M}(\mathrm{L}-\mathrm{L})$, derive the rate constant expression. Show that when $k_{\mathrm{b}}>k_{\mathrm{w}}$, the rate constant expression reduces to that commonly observed for the substitution of a monodentate ligand by another monodentate ligand.

In the text you learned of the rate laws for the substitution of a monodentate ligand on an octahedral complex by another monodentate ligand. However, another very important process is the substitution of two monodentate ligands by a chelating ligand. Wilkins [Acc. Chem. Res, 3, 408 (1970)] shows that the steps currently considered important when the substitution ligand is bidentate are
$$
\begin{aligned}
& \left.\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{M}(\mathrm{L}-\mathrm{L}) \quad \stackrel{k_3}{k_{\rightarrow}}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{M}-\mathrm{L}\right)+\mathrm{H}_2 \mathrm{O} \\
&
\end{aligned}
$$

That is, after formation of an outer sphere complex, one end of the bidentate ligand substitutes for one water molecule, followed by substitution of the other end for yet another water. Assuming that the first reaction is faster than the other two (and that $\left.k_x / k_{-x}=K_{\text {dit }}\right)$, and that a steady state exists for the intermediate $\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{M}(\mathrm{L}-\mathrm{L})$, derive the rate constant expression. Show that when $k_{\mathrm{b}}>k_{\mathrm{w}}$, the rate constant expression reduces to that commonly observed for the substitution of a monodentate ligand by another monodentate ligand.

Key Concepts

Rate Law Derivation and Simplification

This concept involves mathematically combining the rate constants of individual steps in a multi-step reaction to obtain an overall rate expression. In cases where one step is significantly faster than others, or when certain conditions are met, the detailed rate law can often be reduced to a simpler form analogous to familiar models, such as those for monodentate ligand substitutions.

Steady-State Approximation

The steady-state approximation is a kinetic assumption used to simplify the derivation of rate laws in complex mechanisms. It posits that the concentration of intermediates remains nearly constant during the reaction because their formation and consumption occur at comparable rates. This allows for a simplified expression of the overall reaction rate.

Chelate Effect

The chelate effect refers to the increased stability and distinct kinetic properties observed when a multidentate (chelating) ligand coordinates to a metal ion. This multidentate binding not only stabilizes the complex through a favorable entropy change but also often results in unique reaction mechanisms compared to monodentate ligand substitutions.

Ligand Substitution Kinetics

This concept involves the study of reaction rates in processes where ligands are replaced in coordination compounds. It encompasses how different factors such as the nature of the incoming and leaving ligands, the metal center’s structure, and the reaction environment determine the kinetics and mechanistic pathway of the substitution reactions.

Reaction Mechanism with Intermediates

Understanding the substitution process requires dissecting the reaction mechanism into individual steps, which typically include the formation of an outer-sphere complex and subsequent ligand exchange steps. This breakdown of the reaction into discrete intermediate states is crucial for deriving accurate kinetic models and rate laws.

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