• 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