Rate Law
For a general reaction between reactant A and B at a constant temperature the reaction may be represented by the following equation. The small letters a and b represent the coefficients used to balance the reaction.
aA + bB -------> products
As we saw in the previous lesson, the rate of a chemical reaction generally increases with reactant concentrations. The rate of the equation above can be represented by the following relationship

 Rate α [A] m x [B] n

This rate relationship can be expressed as a Rate Law. The rate law equation expresses the relationship between the concentration of the reactants and the rate of the equation. The general rate law is shown below for this reaction. Square brackets are used to represent concentrations of the reactants.
Exponents and Orders of reactions
The values of exponents (m or n) can only be determined through experimentation and may or may not be the values of the coefficients in the balanced chemical equation. The exponent values are usually 0, 1 or 2 but may be 3 or in some cases even fractions. In our discussion we will look at values of only 0, 1 or 2. The following points can be made about the exponents and orders of the reactions.

• The value of the exponents determines the order of the reaction. If a reaction has a single reactant and the value of the exponent is one then it is said to be first order.
• If the exponent were two then it is said to be second order.
• If more than one reactant is present in a reaction, the sum of the exponents (m + n) is called the overall reaction order. The table below provides some more examples.

2 N2O5 (g)   →      4 NO2 (g)  +  5 O2  (g)
Experimentally the rate was found to be first order for N2O5 (g). That is the rate varies directly with the [N2O5 (g)]. Therefore the following rate law can be written.
Rate = k [N2O5 (g)] 1

As mentioned earlier the rate exponents can only be determined experimentally. We will briefly discuss two methods that can be used.

• Graphical method: Determining rate exponents from graphs (created from data of concentration of reactant A and time)
• Method of Initial Rates: Determining rate exponents using the initial rates of reactions from various experiments

Graphical method of determining rate exponents

Rate exponents can be determining using a graphical method. That is if we graph the data each rate order will have a distinctly shaped graph.

For the general reaction
A  +  B → products
The following chart describes what the graphs would look like for various order's of reactant A, if the concentration of A was varied and the concentration of B was kept constant.  The rate constants can also be determined using information from the graphs.

Method of Initial Rates
We can also use a simple algebraic approach to find the exponents in a rate-law expression. Consider the set of rate data given earlier for the hypothetical reaction
A + 2 B → C

 Experiment Initial [A] (mol / L) Initial [B] (mol / L) Initial Rate of Formation of C (mol / L s) 1 1.00 x 10-2 1.00 x 10-2 1.50 x 10-6 2 1.00 x 10-2 2.00 x 10-2 3.00 x 10-6 3 2.00 x 10-2 1.00 x 10-2 6.00 x 10-6

Because we are describing the same reaction in each experiment, all the experiments are governed by the same rate-law expression,
rate = k[A]m[B]n