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Note that the exponents are not a and b but some experimentally determined powers p and q which may or may not equal a and b. The order of the is, therefore, p + q. We will discuss in Determining Rate Laws how those exponents can be determined.

Also notice in the the presence of the rate constant k. Students often have trouble distinguishing between the rate of a reaction and its rate constant. The rate of a reaction is the total rate of a reaction and is the "rate" in the rate law. The units of rate are always M / s. The rate constant, k, is an experimentally determined proportionality constant that gives some measure of the intrinsic "reactivity" of the reaction. The units on the rate constant depend on the order of the reaction, n, such that k has units M1 - n / s. In that way, the units of the rate constant, k, are chosen to make the units of rate always M / s regardless of order. For example, if the order of the reaction is 3, the rate law could be rate = k [A]2[B]. The units of rate are M / s and the rate constant must, therefore, have units of M-2 / s.

The attentive reader may have noticed that we have only considered the rate of the forward reaction, neglecting any sort of reverse reaction in the rate law. To make our math easier, we have intentionally ignored the reverse reaction and we will continue to do so. This is a justified practice for reactions with negligible reverse rates, such as those with equilibrium constants, K, much greater than 1. For reactions with K's around 1, this is also a valid approximation because they are usually carried out such that products are removed from the reaction mixture as they are formed, keeping concentrations of products low.

Rate laws can also be expressed to relate the concentration of reactants to the time of the reaction. Such an expression is called an integrated rate law because it is the integral of the differential rate law. For those of you who have had some calculus, we present a derivation of an integrated rate law from the differential rate law below for a first order reaction. If you have not had calculus, don't worry. Just pay attention to the end result of the derivation.

Rearranging this equation gives the following:

Using a similar technique, one can derive the integrated rate law for any differential rate law. As we will see in Determining Rate Laws, the fact that the 1st order integrated rate law is linear allows us to test if a reaction is first order by plotting ln [A] versus time.

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