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Determining Rate Equations

01Determining Rate Equations

Initial rates

This section covers how initial rates are obtained and used as experimental data for determining reaction orders.

Using the rate at the start

The initial rate is the rate at the start of a reaction. It is useful for determining a rate equation because the reactant concentrations at this instant are the known initial concentrations.

A series of experiments is carried out at constant temperature. Suitable experiments are designed so that the initial concentration of a reactant can be changed and its effect on the initial rate identified.

For concentration–time data, draw a tangent to the curve at t=0t=0 and calculate its gradient.

initial rate=∣gradient at t=0∣\mathrm{initial\ rate} =\left|\mathrm{gradient\ at}\ t=0\right|

The tangent must be drawn at the start rather than using an average gradient over a later interval.

timereactant concentration

Schematic: the dashed tangent at t=0t=0 gives the initial rate.

Clock measurements

An initial-rate method can also measure the time required for each experiment to reach the same fixed endpoint. If the same amount of reaction has occurred at that endpoint in every run, the reciprocal time is used as a quantity proportional to the initial rate:

initial rate∝1t\mathrm{initial\ rate}\propto\frac{1}{t}

The concentration of one reactant can then be varied while the other relevant concentrations and the temperature are kept constant. Comparing the resulting 1/t1/t values shows how the initial rate depends on that reactant concentration.

Exam Tip: When explaining the initial-rate method, state that the tangent is drawn at t=0t=0, when the initial reactant concentrations are known.

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