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Organic Chemistry: Intro to Organic 4

The Rate Law

Terms

Rate Law Problems

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.

[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.

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