AQA A Level Chemistry

Revision Notes

5.2.3 Rate Equation Calculations

Rate Equation Calculations

  • The rate constant (k) of a reaction can be calculated using:
    • The initial rates and the rate equation
    • The half-life

Calculating the rate constant from the initial rate

  • The reaction of calcium carbonate (CaCO3) with chloride (Cl) ions to form calcium chloride (CaCl2) will be used as an example to calculate the rate constant from the initial rate and initial concentrations
  • The reaction and rate equation are as follows:

CaCO3 (s) + 2Cl (aq) + 2H+ (aq) → CaCl2 (aq) + CO2 (g) + H2O (l)

Rate = k [CaCO3] [Cl]

  • 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

Reaction Kinetics - Experimental results of concentrations and initial rates table, downloadable AS & A Level Chemistry revision notes

  • To find the rate constant (k):
    • Rearrange the rate equation to find k

Calculating the Rate Constant equation 1

  • Substitute the values of one of the experiments to find k (for example measurement 1)

Calculating the Rate Constant equation 2

= 1.40 x 10-2 dm3 mol-1 s-1

  • 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 dm3 mol-1 s-1)

Calculating the rate constant from the half-life

  • The rate constant (k) can also be calculated from the half-life of a reaction
  • You are only expected to deduce k from the half-life of a first-order reaction as the calculations for second and zero-order reactions are more complicated
  • For a first-order reaction, the half-life is related to the rate constant by the following expression:

Calculating the Rate Constant equation 3

  • Rearranging the equation to find k gives:

Calculating the Rate Constant equation 4

  • So, for a first-order reaction such as the methyl (CH3) rearrangement in ethanenitrile (CH3CN) with a half-life of 10.0 minutes the rate constant is:

Calculating the Rate Constant equation 5

= 1.16 x 10-3 dm3 mol-1 s-1

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