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Fundamentals of Rate Laws

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Defining Rates

In order to introduce the idea of rate, let's suppose we wish to know how fast the following reaction is going:

One way to do this is to define rate as the change in concentration of some species with respect to time, and then measure the concentrations of all species at multiple times to determine the rate. The results of such a hypothetical experiment is given in the for the reaction of hydrogen and iodine. The initial concentrations of H2 and I2 are equal at all times and the initial concentration of product is zero:

Figure %: Graph of concentration versus time for the reaction of hydrogen and Iodine

As you can see, the rate of formation of HI is twice the rate of disappearance of H2 or I2 at any given time. Also, note that the rate slows in time due to decreasing concentrations of the reactants. Stated mathematically, the relationship between the formation of products and the disappearance of reactants for this reaction is:

In general, for the reaction below:

The rate is expressed as follows:

Another expression for a rate is called the differential rate law, or simply, the rate law. It expresses the rate of a reaction in terms of the concentrations of the reactants raised to an experimentally determined power. The exponent on each concentration term is called the order of the reaction in that particular reactant. The sum of the exponents in the rate law is called the order of the reaction. The powers on the concentration terms in a rate law are NOT the stoichiometric coefficients from the balanced equation! For example, the rate law for the will have the following form: