5.2.1 Rate Equations

Understanding the Rate Equation

The rate of a chemical reaction depends on the concentrations of the reactants and is described by a rate equation. For a reaction with reactants $A$ and $B$, the rate equation takes the form:

$$\text{Rate} = k[A]^m[B]^n$$

where:

• $k$ is the rate constant, which links the rate of reaction to the reactant concentrations.
• $[A]$ and $[B]$ are the concentrations of reactants $A$ and $B$.
• $m$ and $n$ are the orders of reaction concerning $A$ and $B$, indicating the power to which each concentration is raised. The overall order of reaction is the sum of $m$ and $n$, and it can affect the shape of the rate–concentration graph and the units of the rate constant $k$.

Key Terms in Rate Equations

Order of Reaction:

• The order with respect to each reactant shows how the rate of reaction depends on the concentration of that reactant.
• For A-Level exams, orders are limited to 0, 1, or 2.
  • 0 Order: The rate is independent of the concentration of that reactant.
  • 1st Order: The rate is directly proportional to the concentration of the reactant.
  • 2nd Order: The rate is proportional to the square of the concentration of the reactant.

Rate Constant ($k$):

• A proportionality constant that links the reaction rate to the concentrations of reactants in the rate equation.
• Units of k depend on the overall order of reaction:
  • 0 Order: $\text{mol L}^{-1} \text{s}^{-1}$
  • 1st Order: $\text{s}^{-1}$
  • 2nd Order: $\text{L mol}^{-1} \text{s}^{-1}$
• The value of $k$ is specific to each reaction at a given temperature and increases with temperature.