An abbreviated description of the rate law follows. If you're unfamiliar with rates of chemical reactions, you may want to visit the Kinetics SparkNote for a full explanation.
Almost all reactions consist of discrete steps. Consider the reaction of A to B. The reaction must go through intermediates B and C in order to get to D. Notice that the rate of steps A to B and C to D are much greater than that of B to C. The reaction will bottleneck at B to C, and thus the overall rate of the reaction can never be greater than the rate of B to C. Thus B to C is the rate-limiting step. When you measure the rate of a reaction, you are in fact measuring the rate-limiting step.
The rate law is a mathematical equation that describes the rate of the overall reaction and, by correspondence, the rate-limiting step. The rate law has great power because it describes what molecules are present in the rate-limiting step.
|X + Y → Z|
|rate = k [X]a [Y]b|
For substitution and elimination reactions, the values of a and b are zero or one. The sum of a and b is the reaction order. Substitution and elimination reactions have orders of one and two.
Let's take the formation of C from A through the intermediate B:
|A → B → C|
[X]âá and [Y]âá are transition states between A, B, and C. Transition states are high-energy molecules that exist at the peaks of an energy diagram. They are so called because they are the transitions between the reacta nts and intermediates of the reaction. They are denoted with brackets and the âá symbol. Since a transition state exists at an energy peak, it is highly unstable and cannot be isolated. In contrast, reaction intermediates like B are local e nergy minima and can be isolated (albeit not easily).
The structure of the transition state determines the activation energy. The activation energy of the rate-limiting step in turn determines the rate. Thus the rate law connects the structure of the transition state to the order of the rate law. In other words, the order of the rate law tells us what reactant molecules are present in the transition state of the rate-limiting step.