Question

Consider the following reaction that takes place in aqueous solution; \(\mathrm{L}, \mathrm{X}\) and \(\mathrm{Y}\) are general ligands. \(\mathrm{Co}^{\mathrm{III}} \mathrm{L}_{5} \mathrm{X}+\mathrm{Y}--\mathrm{Co}^{\mathrm{III}} \mathrm{L}_{5} \mathrm{Y}+\mathrm{X}\) Discuss the possible competing pathways that exist and the factors that favour one pathway over another. Write a rate equation that takes into account the pathways that you discuss.

Short answer

The reaction can proceed via associative or dissociative pathways; the preferred pathway depends on ligand properties and influences the rate equation form.

Step-by-step solution

Identify the Reaction

The given reaction is a ligand exchange reaction, where one ligand (\(X\)) is replaced by another ligand (\(Y\)) in the coordination sphere of a cobalt(III) complex: \(\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X} + \mathrm{Y} \rightarrow \mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{Y} + \mathrm{X}\).

Recognize Possible Pathways

In this reaction, the two commonly proposed pathways are associative (\(A\)) and dissociative (\(D\)). The associative pathway involves the addition of ligand \(Y\) to form an intermediate with both \(X\) and \(Y\) before \(X\) leaves. The dissociative pathway involves the ligand \(X\) leaving first to form a five-coordinate intermediate, followed by the attachment of \(Y\).

Factors Favoring an Associative Pathway

An associative mechanism is typically favored by large, flexible ligands \(L\), or when \(\mathrm{Y}\) is a strong nucleophile, allowing it to coordinate strongly to the metal even in the presence of a full coordination sphere.

Factors Favoring a Dissociative Pathway

A dissociative mechanism is often favored when the leaving ligand \(X\) is weakly bound, or the coordination number following dissociation is still stable. If \(L\) forming 5-coordination complexes is less stable, it also encourages dissociation.

Write the Rate Equation

For the associative pathway, where both \(X\) and \(Y\) are involved in the rate-determining step, the rate equation can be written as: \(\text{Rate} = k [\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X}][\mathrm{Y}]\), indicating a second-order reaction. For a dissociative pathway, it might simplify to \(\text{Rate} = k [\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X}]\), suggesting a first-order reaction in terms of \([\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X}]\).

Key concepts

Associative Pathway

In ligand exchange reactions, the associative pathway is a mechanism where an incoming ligand, such as \( Y \) in the given reaction, first attaches to the metal center before the original ligand, \( X \), departs. This results in a temporary formation of a higher-coordinate intermediate, often leading to an octahedral or hexa-coordinate state if additional coordination positions are available.
One of the key aspects of the associative pathway is that both the incoming and outgoing ligands interact with the central metal ion simultaneously. This simultaneous presence means that prior to replacement, the complex is over-coordinated—an uncommon state that requires specific structural flexibility and interaction conditions.

• Strong nucleophilicity of the entering ligand \( Y \)
• Flexible ligands that can accommodate additional bonds
• The presence of free coordination sites or possibility of temporary bonding extensions

Each of these factors facilitates the formation of a stable intermediate complex in a manner conducive to replacement without preliminary dissociation of the outgoing ligand \( X \). This mechanism often results in a reaction that is second-order, dependent on the concentrations of both the metallic complex and the incoming ligand \( Y \). The rate equation for an associative pathway in this scenario is: \( \text{Rate} = k [\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X}][\mathrm{Y}] \).

Dissociative Pathway

The dissociative pathway describes a process where the original ligand \( X \) leaves the metal center first, creating a coordination vacant site before the new ligand \( Y \) attaches. This creates an intermediate complex with a lower coordination number, often a five-coordinate species in an octahedral complex.
This pathway is heavily influenced by the stability of the resulting lower-coordinate intermediate. Factors favoring this pathway include:

• The weakness of the bond between the metal center and the departing ligand \( X \)
• The stability of the five-coordinate intermediate for complexes usually having a six-coordinate structure
• The structural or electronic nature of the complex that facilitates ligand detachment

In dissociative reactions, the mechanism often manifests as a first-order reaction, reliant primarily on the concentration of the complex which loses a ligand. The rate equation illustrating a dissociative process thus simplifies to: \( \text{Rate} = k [\mathrm{Co}^{\mathrm{III}}\mathrm{L}_{5}\mathrm{X}] \).
By understanding the differences in coordination and energetic landscape between pathways, chemists can predict which pathway a particular ligand exchange reaction might follow.

Coordination Chemistry

Coordination chemistry focuses on the structures, properties, and reactivity of complexes formed between metal ions and ligands. In these complexes, metal ions act as central atoms around which ligands (molecules or ions) attach via coordinate bonds, sharing electron pairs provided by the ligands.
Several critical considerations define coordination chemistry, which are pivotal to understanding exchange mechanisms like those seen in ligand substitution reactions:

• Coordination Number: The number of ligand attachment sites around the central metal. Typically seen in its most stable form based on metal and ligand types.
• Electron Configuration: Influences how metal participates in bonding, dictating the overall geometry and stability of the coordination compound.
• Steric Effects: Physical blockage affects how easily new ligands can approach and bond with the metal.
• Ligand Field Theory: Provides insight into the electronic behavior within the metal-ligand bond, influencing color, magnetism, and reactivity.

By exploring these factors, chemists can rationalize and predict the properties and behaviors of coordination complexes, such as their preferred pathway for ligand exchange—a principle vital in industrial and biological catalysis.

Reaction Kinetics

Reaction kinetics involves the study of the rate at which chemical reactions proceed and the factors affecting these speeds. Key concepts in evaluating the kinetics of ligand exchange include the reaction order, activation energy, and rate-determining steps.
For ligand exchange reactions, monitoring how different conditions or changes influence the speed of complex transformations reveals valuable insights:

• Rate Equation: Reflects the mathematical relationship between reactant concentrations and their speed of conversion into products.
• Activation Energy: The energy barrier that must be overcome for a reaction to occur. It determines the temperature sensitivity of reaction rates.
• Transition State: An unstable configuration of atoms during the transition from reactants to products, which determines the reaction's feasibility and speed.

In practice, kinetic studies help elucidate the choice between associative and dissociative pathways based on observed reaction rates under varied conditions, guiding the optimization of conditions for desired reaction paths in both natural and synthetic systems.