Multi-step Kinetics

Multi-Step Reactions and Catalytic Mechanisms

  • Definition of Multi-Step Reactions: These reactions consist of multiple elementary steps leading from reactants to products. Each individual step involves distinct intermediates and reaction pathways.

Elementary Reactions

  • Elementary Reactions: Individual steps within a multi-step reaction, where the rate law can be directly determined.

    • Predictable Rate Laws: The rate law for an elementary reaction depends on the rate constant and the concentrations of the reactants involved in that step.

Rate-Determining Step

  • Assumption of Rate-Determining Step: To simplify analysis, it’s often assumed that one step in the pathway is the slowest and thus controls the overall rate of reaction.

    • Importance: Knowing which step is rate-determining allows focusing on the dynamics of that particular step without influence from subsequent faster steps.

Steady-State Approximation

  • Shortcut to Rate Law: Utilize the steady-state approximation to derive rate laws.

    • Numerator: Multiply the forward rate constants and the concentrations of all reactants involved in the forward steps:

      • For the first step: K1 with reactants.

      • For the second step: K2 with reactants.

    • Denominator: Sum the backward steps consuming the intermediate:

      • Account for K-1 (backward step) and K2 (second forward step).

      • Exclude intermediates in the real rate law.

Interpretation of Rate Law

  • Hydrogen Dependence: Key to understanding how different concentrations affect the rate of reaction.

    • Phosphine as an Inhibitor: More phosphine results in a decrease in reaction rate:

      • Reason: Phosphine must dissociate to allow reactants to bind. Increased concentrations hinder this dissociation.

    • Hydrogen Concentration Effects:

      • At Low Concentration:

        • Assume right-hand term exceptionally small compared to left-hand term.

        • Thus, rate law simplifies to show direct dependency on hydrogen, as it only appears in the numerator.

      • At High Concentration:

        • The left-hand term becomes insignificant compared to right-hand term.

        • Effective cancellation leads to a constant rate (K2), indicating saturation.

Saturation Curve

  • Concept of Saturation: When hydrogen concentration reaches a point where adding more does not increase the reaction rate:

    • Implication: The reaction site (e.g., palladium) has filled its capacity, and further hydrogen becomes irrelevant to reaction speed.