5.6.4 Rate Constant 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

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

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

= 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:

• Rearranging the equation to find k gives:

• 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:

= 1.16 x 10^-3 dm³ mol^-1 s^-1