To calculate the order of reaction for a reactant:

  1. Write the general rate expression for the reaction.

  2. Write the general rate expression for each experiment.

  3. Take the ratio of the rate expressions from two different experiments. (eg. Divide Rate2 by Rate1.)

  4. Cancel out the rate constant and any concentrations that are the same in the two experiments.

  5. Put in the data and use logs to find the order.

For example, given the following experimental results, what is the order of reaction for the reactant A and what is the rate law for this reaction?

Expt[A]Init Rate

The general rate law for the reaction is rate=k[A]x.

The rate expressions for each experiment are:
  rate1=k[A]1x and rate2=k[A]2x   or 4.2 = k(1.5)x and 6.2 = k(2.0)x

Dividing rate2 by rate1 gives:

6.2/4.2 = (2/1.5)x and taking the ln of both sides gives:

ln(6.2/4.2) = x[ln(2/1.5)]   or   ln(1.48) = x[ln(1.33)]

x = ln(1.48)/ln(1.33) = 1.37   and   rate = k[A]1.37

Use the first experiment to find k:

k = 4.2/(1.5)1.37 = 4.2/1.743 = 2.4 and

rate = (2.4)[A]1.37