The Rate Constant (HL) (DP IB Chemistry): Revision Note

The rate constant

How to calculate the rate constant 

• The rate constant, k, of a reaction can be calculated using the initial rate and the rate equation

• Consider the reaction of sodium carbonate with chloride ions (from hydrochloric acid) to form sodium chloride:

Na₂CO₃ (aq) + 2Cl^- (aq) + 2H⁺ (aq) → 2NaCl (aq) + CO₂ (g) + H₂O (l)

• The rate equation for this reaction is:

rate = k[Na₂CO₃][Cl^-]

• The rate constant, k , can be calculated using the initial concentrations and the initial rate of reaction:

• The progress of the reaction can be followed by measuring the initial rates of the reaction using various initial concentrations of each reactant

Experimental results of concentrations & initial rates table

• To find the rate constant, k:

  • Use the data from measurement 1:

    • rate = 4.38 × 10^-6 mol dm^-3 s^-1

    • [Na₂CO₃] = 0.0250 mol dm^-3

    • [Cl⁻] = 0.0125 mol dm^-3

• The values of measurement 2 or 3 could also have been used to find k

  • They all give the same result of 1.40 x 10^-2 

Calculating the units of the rate constant

• Rate constant calculations requires the correct units

• Correct units can be deduced by:

  1. Substituting the units of each term into the rate equation

  2. Combining or cancelling any units

• For example, to calculate the units for the above reaction:

Units of k =

Units of k =

Units of k = mol dm^-3 s^-1

• The units of the rate constant, k, are dependent on the overall order of the reaction

Rate constant units by order of reaction

• When the rate is measured per second:

  • Rate constant units of a zero order reaction are mol dm^-3 s^-1

  • Rate constant units of a first order reaction are s^-1

  • Rate constant units of a second order reaction are mol^-1 dm³ s^-1

  • Rate constant units of a third order reaction are mol^-2 dm⁶ s^-1

How does temperature affect the rate constant, k?

• Consider the following reaction:

A + B → C + D

Rate of reaction = k[A][B]

• The rate equation shows that the rate of reaction depends on:

  • The rate constant, k

  • The concentration of the reactants, A and B

• Temperature is one of the factors that affects the rate of reaction

• Increasing the temperature increases the rate constant k

  • This speeds up the rate of reaction, if the concentrations remain constant

• Important: A higher rate of reaction does not necessarily mean a greater yield

  • The yield depends on whether the reaction is endothermic or exothermic, as explained by Le Châtelier’s principle

Effect of temperature on k

• The rate constant k increases exponentially with temperature:

• The rate of reaction roughly doubles for every 10 °C increase in temperature

• This value is approximate because:

  • The rate may double every 9 °C or 11 °C instead

  • The temperature interval for doubling the rate changes gradually as temperature rises

• This general trend does not apply to all reactions