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Organic Chemistry: Intro to Organic 4

The Rate Law


The Rate Law, page 2

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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.

The Rate-Limiting Step

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.

The Rate Equation

X + Y → Z    

The rate law of the above reaction is:

rate = k [X]a [Y]b    

k is a constant determined by the reaction and conditions. The values of a and b are determined by varying the concentrations of X and Y. For example, if the concentration of X is doubled while the concentration of Y is constant, and the rate quadrupl es, then a must equal two. Likewise, if in a separate experiment the concentration of Y doubles and the concentration of X stays the same, and the rate does not change, than b must equal zero. Thus it appears that two molecules of X and no molecules of Y are involved in the rate-limiting step.

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.

An Energetic Approach

Let's take the formation of C from A through the intermediate B:

A → B → C    

Here's a hypothetical plot of reaction coordinate vs. energy of the reaction:
The activation energy ( Ea ) of A to B is much greater than the activation energy of B to C. Fewer molecules of A will gain enough energy to surmount the hump to B than molecules of B to C per unit time. This indicates that under most circumstan ces the rate of A to B is less than the rate of B to C.

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