Rate Equations (AQA A Level Chemistry): Revision Note

Rate Equations

• The rate of reaction refers to the change in the amount or concentration of a reactant OR product per unit time

• It can be found by:

  • Measuring the decrease in the concentration of a reactant over time

  • Measuring the increase in the concentration of a product over time

  • The units for rate of reaction are mol dm^-3 s^-1

• The rate of reaction is defined as the change in concentration of a reactant or product per unit time

• It can be determined by:

  • Measuring the decrease in concentration of a reactant over time

  • Measuring the increase in concentration of a product over time

• Mathematically, this can be expressed as:

rate = Δ[concentration] ÷ Δtime

• When concentration is measured in mol dm⁻³ and time in seconds, the units of rate are mol dm⁻³ s⁻¹

Rate equation

• The following general reaction will be used as an example to study the rate of reaction

D (aq) → Products

• The rate of reaction at different concentrations of D is measured and tabulated

Rate of reactions table

• A directly proportional relationship between the rate of the reaction and the concentration of D is observed when a graph is plotted

• Rate equations must be determined experimentally

  • They cannot be deduced directly from the stoichiometric coefficients in the balanced equation

• The general form of a rate equation is:

Rate = k[A]^m[B]ⁿ

• Where:

  • [A] and [B] are the concentrations of reactants

  • m and n are the orders of reaction with respect to each reactant

  • k is the rate constant

• The orders (m and n) can be 0, 1, or 2, and they describe how the rate changes when the concentration of a reactant changes

• Products are not included in the rate equation because the rate is determined by reactant concentrations in the forward reaction

• For example:

  • In the reaction:

2NO(g) + 2H₂(g) → N₂(g) + 2H₂O(g)

• The experimentally determined rate equation is:

Rate = k[NO]²[H₂]

• Notice that the order with respect to H₂ is 1, not 2, even though the stoichiometric coefficient is 2

• This shows that orders must be found experimentally

Interpreting the rate equation

• If the concentration of NO is doubled (while [H₂] remains constant), the rate increases by a factor of 4, showing second-order dependence on NO

• If the concentration of H₂ is doubled (while [NO] remains constant), the rate doubles, showing first-order dependence on H₂

• Catalysts and rate equations:

  • A catalyst will only appear in a rate equation if it is involved in the rate-determining step and its concentration affects the rate

  • This is usually the case for homogeneous catalysts (where the catalyst and reactants are in the same phase). If a species appears in the rate equation but not in the overall balanced equation, it is acting as a catalyst

Order of reaction

• The order of a reactant describes how its concentration affects the rate of reaction

• It is the power to which the concentration of that reactant is raised in the rate equation

• The order with respect to a reactant can be 0, 1, or 2

• If a reactant is zero order, changing its concentration does not affect the rate

  • In the rate equation, the concentration term is effectively absent because [A]^o = 1

• If a reactant is first order, the rate is directly proportional to its concentration

• If a reactant is second order, the rate is proportional to the square of its concentration

• The overall order of reaction is the sum of the powers of all reactant concentrations in the rate equation

• For example, in the following rate equation,

Rate = k [NO]² [H₂]

• The reaction is

  • Second-order with respect to NO

  • First-order with respect to H₂

  • Third-order overall (2 + 1)