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Chapter 16: Chemical Kinetics

16.2: Rate Laws

Rate Law
An equation that shows how the rate of a reaction depends on the concentration of reactants.
Rate Constant (k)
A proportionality constant in the rate law that is specific to a reaction at a given temperature.
Reaction Order
The sum of the powers to which reactant concentrations are raised in the rate law.
Overall Reaction Order
The total of all individual orders of reactants in the rate law.

General Form of Rate Laws

The general form of a rate law is: Rate = k ⁢ [A] m ⁢ [B] n

  • [A] and [B]: Reactant concentrations.
  • m and n: Reaction orders for each reactant, determined experimentally.

Determining Reaction Orders

  • Reaction orders are determined experimentally, not from the balanced chemical equation.
  • First-Order Reactions: Rate is directly proportional to the concentration of the reactant.
  • Second-Order Reactions: Rate is proportional to the square of the reactant concentration.
  • Zero-Order Reactions: Rate is independent of the concentration of the reactant.

Units of the Rate Constant (k)

  • Depend on the overall reaction order:
    • First-Order: s-1
    • Second-Order: M-1⋅s-1
    • Zero-Order: M⋅s-1

Experimental Determination of Rate Laws

  • Use initial rates of reaction at different reactant concentrations.
  • Compare how changes in concentration affect reaction rates.
  • Example: Doubling [A] doubles the rate, indicating a first-order reaction with respect to A.

Integrated Rate Laws

  • Describe how concentrations change over time.
  • Equations differ based on reaction order:
    • First-Order: ln[A] = -kt + ln[A]0
    • Second-Order: 1/[A] = kt + 1/[A]0
    • Zero-Order: [A] = -kt + [A]0

Questions for Students

  1. Define the rate law and explain the significance of the rate constant (k).
  2. What are the differences between first-order, second-order, and zero-order reactions?
  3. How are reaction orders determined experimentally?
  4. Write the integrated rate law for a first-order reaction and explain each term.
  5. Describe how the units of the rate constant change based on reaction order.