26.1 Simple Rate Equations, Orders of Reaction and Rate Constants

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Explain and use the terms: rate equation, order of reaction, overall order of reaction, rate constant, half-life, rate-determining step, and intermediate.
  2. (a) Understand and use rate equations of the form rate = k[A]ᵐ[B]ⁿ (where m and n are 0, 1 or 2). (b) Deduce the order of a reaction from concentration–time graphs, initial rates data, and half-life data. (c) Interpret concentration–time and rate–concentration graphs. (d) Calculate an initial rate using concentration data. (e) Construct a rate equation.
  3. (a) Understand that the half-life of a first-order reaction is independent of concentration. (b) Use the half-life of a first-order reaction in calculations.
  4. Calculate the numerical value of a rate constant using: (a) initial rates and the rate equation, or (b) the half-life equation k = 0.693 / t½.
  5. For multi-step reactions: (a) suggest a mechanism consistent with the rate equation and overall equation; (b) predict the order from a given mechanism and rate-determining step; (c) deduce a rate equation from a mechanism; (d) identify an intermediate or catalyst; (e) identify the rate-determining step from a rate equation and mechanism.
  6. Describe qualitatively how temperature change affects the rate constant and hence the rate of reaction.

1. Key Terminology

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Rate of Reaction

The rate of reaction tells us how quickly a reaction is happening. It measures how fast the concentration of a reactant decreases (or how fast the concentration of a product increases) over time.

Rate of reaction = change in concentration ÷ time

The units of rate of reaction are mol dm⁻³ s⁻¹ (moles per decimetre cubed per second).

Rate Equation

A rate equation (also called a rate law) is a mathematical expression that links the rate of a reaction to the concentrations of the reactants. For a general reaction where A and B are reactants:

Rate = k[A]ᵐ[B]ⁿ

  • k is the rate constant — a number that is specific to a reaction at a given temperature.
  • [A] and [B] represent the concentrations of reactants A and B (in mol dm⁻³).
  • m and n are the orders of the reaction with respect to A and B. They can only be 0, 1, or 2 in this course.

Important: A rate equation can only be found through experiments. You cannot write it just by looking at the balanced chemical equation.

Important: Products do not appear in the rate equation because they do not affect the rate of reaction.

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