26 Reaction Kinetics

26.1 Simple Rate Equations, Orders of Reaction, and Rate Constants:

  1. Rate Equation: The rate equation expresses the relationship between the rate of a chemical reaction and the concentrations of the reactants. It is of the form

rate = k[A]m[B]n

where [A] and [B] are the concentrations of reactants, and k is the rate constant.

  1. Orders of Reaction:
    1. The order of reaction with respect to a particular reactant is determined by the exponent (m or n) in the rate equation.
    2. The overall order of reaction is the sum of the individual orders of all the reactants.
  2. Determining Reaction Orders:

(a) Concentration-Time Graphs: The order of a reaction can be deduced by examining the slopes of concentration-time graphs at different initial concentrations of reactants.

(b) Initial Rates Method: By measuring the initial rates of reaction with different initial concentrations of reactants, the order of reaction can be determined.

(c) Half-Life Method: For a first-order reaction, the half-life is constant and independent of concentration. By measuring the half-life at different concentrations, the order of reaction can be deduced.

  1. Rate Constants:
    1. Rate constants (k) are specific to a particular reaction and represent the speed at which a reaction occurs.
    2. Calculating Rate Constants:

(a) Using Initial Rates: By measuring initial rates at different concentrations and plugging the values into the rate equation, the rate constant can be calculated.

(b) Using Half-Life: For a first-order reaction, the rate constant can be determined using the equation

k = 0.693 / t1/2

where t1/2 is the half-life.

  1. Multi-Step Reactions:
    1. Reaction Mechanism: A multi-step reaction consists of multiple elementary steps. The reaction mechanism is a sequence of these steps that leads to the overall reaction.
    2. Rate-Determining Step: The slowest step in the reaction mechanism determines the rate of the overall reaction.
    3. Deducing Rate Equations: The rate equation is derived based on the rate-determining step and the stoichiometry of the reaction.
    4. Intermediates: Intermediates are produced and consumed during the reaction but do not appear in the overall balanced equation.
    5. Catalysts: Catalysts are substances that increase the rate of a reaction without being consumed. They provide an alternative reaction pathway with lower activation energy.
  2. Effect of Temperature:
    1. Temperature has a significant effect on the rate constant and the rate of a reaction.
    2. Increased temperature leads to higher kinetic energy, increased collision frequency, and a greater fraction of collisions with sufficient energy to overcome the activation energy barrier.
    3. The rate constant generally increases exponentially with temperature

26.2 Homogeneous and Heterogeneous Catalysts:

  1. Catalyst Types:
    1. Homogeneous Catalysts: Homogeneous catalysts exist in the same phase as the reactants.
    2. Heterogeneous Catalysts: Heterogeneous catalysts are in a different phase from the reactants.
  2. Mode of Action of Heterogeneous Catalysts:
    1. Heterogeneous catalysts function by:

(a) Adsorption of Reactants: Reactant molecules are adsorbed onto the catalyst surface.

(b) Bond Weakening: The catalyst weakens the bonds in the adsorbed reactant molecules.

(c) Desorption of Products: The weakened bonds facilitate the formation of products, which then desorb from the catalyst surface.

  1. Mode of Action of Homogeneous Catalysts:
    1. Homogeneous catalysts participate in the reaction in one step and are regenerated in a subsequent step.
    2. For example, atmospheric oxides of nitrogen act as catalysts in the oxidation of atmospheric sulfur dioxide, and Fe2+ or Fe3+ ions act as catalysts in the I–/S2O82– reaction.