The method of initial rates

This involves measuring the rate of reaction at the start of an experiment. In the reaction between magnesium and hydrochloric acid, this can be done by timing how long it takes to dissolve a small piece of magnesium. We assume that in the time taken to measure the initial rate the initial concentrations have not changed significantly. We then do a second experiment changing just one of the reactant concentrations. By looking at the effect that this change in concentration has on the rate of reaction, we can determine the order of reaction for this reactant. Further experiments may then be done to look at all the different reactants.

The following table shows the rate of reaction for a general reaction involving three reacting species A, B and C. You need to choose two experiments in which only A changes in concentration then compare the rates in those two experiments. At "A" level there are only three possible options:

If there is no change in the rates then the reactant is zero order. Remember that in a real experiment the experimental error may well result in the two rates not being exactly the same, but they should be close.
If the rate changes by the same factor as the concentration then the reactant is first order. For example, the concentration is doubled and the rate doubles. Again experimental error may lead to slight inconsistencies, but the change should be clearly different from zero or second order.
If the rate changes by the square of the concentration then the reactant is second order. For example, the concentration is doubled and the rate goes up by 4 (2²) or the concentration is trebled and the rate goes up by 9 (3²). As before, the relationship may not be exact in a real experiment.

So in theory, if you double the concentration of a reactant there are three possible options as to the change in rate: no change, × 2 or × 4. It should be fairly obvious which relationship applies if in a real experiment it changes by × 1.9 or × 4.1. Have a go with the following data. Try to work out the order with respect to each reactant A, B and C then write down a rate equation for the reaction. Check your answer in the link below.

A + B + C ⇒ D + E

Experiment	[A]/M	[B]/M	[C]/M	Initial rate/arbitrary units
1	0.01	0.02	0.02	4.0 × 10^-5
2	0.1	0.02	0.02	3.9 × 10^-3
3	0.01	0.04	0.02	3.9 × 10^-5
4	0.1	0.02	0.06	1.2 × 10^-4

Answer

A further example can be found in this experiment. We also use an initial rate method in this experimentto measure an activation energy.