Elementary Kinetics
 
 
 
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RATE EQUATIONS

One of the goals of kinetics is to be able to both quantitate and predict the actual rates of specific chemical reactions. In other words, scientists want to tell how fast products are made when specific reactants are mixed together. To do this, they use an equation that describes the speed of a chemical reaction, known as the reaction's rate equation (or rate law). If the process is elementary, meaning it's a simple, single-step process, then the rate equation can be determined from the reaction stoichiometry, using the following rule:

For the elementary process

aA + bB yY + zZ

the rate law is

rate = k[A]a[B]b

where k is a constant value called the rate constant.

Notice that only the concentrations of the reactants are important in determining the rate law. The concentrations of the products have no effect on the rate law of a reaction.

Let's look at some examples.

Example 1

For the reaction 2 NO + Br2 2 NOBr, what would you expect the rate law to be?

Solution

The rate law is expected to be: rate = k[NO]2[Br2]

This has been confirmed by experiment.

The experimentally determined rate law is exactly what you would expect for an elementary process by using the rule above. However, most processes are not elementary, and the rate law for nonelementary processes can only be determined experimentally! A nonelementary process is a reaction that can be broken down into a number of steps. The rate of the reaction will be determined only by the reactants involved in the slowest step (the rate-limiting step).

Let's take a look at a nonelementary process in the next example.

Example 2

For the reaction NO2 + CO CO2 + NO, what would you expect the rate law to be?

Solution

You would expect the rate law to be rate = k[NO2][CO].

However, the rate law was experimentally determined to be rate = k[NO2]2

Notice how the rule for finding the rate law of an elementary reaction does not work here, and if we used the rule above, we would look at the reaction and come up with: rate = k[NO2][CO] (which is wrong!). Look at the experimentally determined rate: there must be a slow elementary step in this reaction that involves two NO2 molecules colliding together. The only way to determine the rate law for a nonelementary process is through experimentation. However, being unable to figure out the rate law by looking at the written reaction, doesn’t mean that a rate law is random. For example, it was also experimentally found that the reaction above actually proceeds in two separate steps:

Step 1: NO2 + NO2 NO + NO3 (a slow reaction)

Step 2: NO3 + CO CO2 + NO2 (a fast reaction)

The rate law for the reaction actually comes from the reaction stoichiometry of the slow step. This is why the slow step in a reaction is called the rate-limiting step, for it dictates the rate at which the entire reaction can proceed. Think of an assembly line at a bicycle factory. One person puts on the wheels, the second attaches the crank and pedals, and the third attaches the handlebars. If the person putting on the wheels works slowly, then no matter how fast the other two workers are, the bicycles will get made only as fast as the wheels are attached.

Identifying which step is rate-limiting is of utmost importance for rational drug design. When a biochemist begins to design a therapeutic compound that targets a particular enzyme, it is important that they design the drug so that it interferes with the rate-limiting step of the reaction performed in the enzyme.

Notice that you can't tell by looking at a reaction on paper whether the reaction is an elementary process or not. Also, whether or not the process is elementary, the rate constant k still needs to be determined experimentally. A scientist's work is never done!