1. Describe what is meant by a reaction mechanism and distinguish between elementary steps and balanced chemical reactions.
2. Derive the rate law for a reaction from its proposed mechanism.

Elementary Steps. The purpose of a reaction mechanism is to indicate how the reactants are converted into products. A reaction mechanism consists of a set of so-called elementary steps. A mechanism indicates just what molecules must collide with each other and in what sequence. Each elementary step marks the progress of the conversion of molecules of reactants into products. A mechanism points out intermediates that are formed and consumed along the way, as well as, which steps are fast and which are slow. This information is not supplied by the balanced chemical equation, because it is intended only to indicate the number of moles of one reactant that are consumed per mole of the other reactant.

Elementary steps have a property called molecularity, which pertains to the number of molecules that must collide in a single step. An elementary step that involves three molecules is called termolecular. A step that involves two molecules is bimolecular, and a step in which one molecule decomposes or rearranges is called unimolecular. Thus the equation

A B

represents a unimolecular reaction in which a single molecule of A reacts to form a single molecule of B. The following equation represents a bimolecular reaction.

A + B C

That is one in which a molecule of A collides with a molecule of B, and as a result a molecule of C is formed.

Reaction Order for Elementary Steps. The rate of a unimolecular elementary step

A B

will depend on the number of molecules of A per unit volume of the container. Therefore, unimolecular reactions follow first-order rate laws.

rate = k[A]

The rate of a bimolecular step (A + B C) will depend on the number of molecules of A per unit volume times the number of molecules of B per unit volume.

rate = k[A][B]

Therefore, bimolecular steps follow second-order rate laws.

This can be understood also by realizing that A and B must collide with each other if they are to react, and so the rate of a bimolecular process depends on the rate of collisions of A and B. Doubling the concentration of A will double the probability of collision between A and B. Similarly, doubling the concentration of B will also double the rate of collisions of A and B. See Figure 13.14 in the textbook. Reasoning further along these lines, we conclude that termolecular reactions are third order.

Rate-Determining Step. It often turns out that one of the elementary steps in a mechanism is much slower than all the rest. This step often determines the overall rate of reaction much as the slowest person ahead of you a cafeteria line determines how fast you and others move through the line. The slowest step in a sequence of elementary steps is called the rate-determining step. This allows us to say that the overall law predicted by a mechanism will be the one corresponding to the rate-determining step.

Testing a Mechanism. The sequence of events in a kinetic study of a reaction that leads to a proposed mechanism is as follows:

1. Determine the rate law experimentally.
2. Propose a mechanism for the reaction.
3. Test the mechanism.

To test a proposed mechanism, assume one step to be the rate-determining step. Then establish the rate law for that step. This gives the rate law predicted by the mechanism. If the mechanism is adequate, then when the predicted rate law is compared with the experimental rate law, the two will match. On the other hand, if the predicted and experimental rate laws do not match, the mechanism has been proved inadequate. Only those mechanisms consistent with all the data can be considered adequate.

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EXAMPLE Reaction Mechanism

The rate law for the following reaction has been experimentally determined to be third order:

2NO(g) + O₂(g) 2NO₂(g) rate = k[NO]²[O₂]

Which of the two proposed mechanisms that follow is more satisfactory?

a.

b.

		Correct!
Click a Hint button for help.

Testing mechanism (a) first, we note that the first step is the rate-determining step. The rate law for this bimolecular step is:

rate = k₁[NO]² I

This mechanism predicts a rate law that is second order in NO concentration and zero order in O₂. By comparison, the experimental rate law is second order in NO and first order in O₂. The predicted rate law and the experimental rate law do not match, and so mechanism (a) is not satisfactory.

Testing mechanism (b), we find that the rate-determining step is the second step. Since it is bimolecular, its rate law should be:

rate = k₂[N₂O₂][O₂] II

It is not possible to compare this predicted rate law directly with the experimental rate law because of the unique term, which is the concentration of N₂O₂. In this mechanism, N₂O₂ is an intermediate. Being formed in step 1 and consumed in step 2, its concentration is always small and usually not measurable.

The way around this situation is to find a mathematical substitution for [N₂O₂]. Note that step 1 is reversible and equilibrium can be established. This means that the rates of the forward and reverse reactions are equal:

k₁[NO]² = k_–1[N₂O₂]

where k₁ is the rate constant for the forward reaction, and k_–1 for the reverse.

Rearranging terms gives us:

We now have an expression for [N₂O₂], which we can substitute into equation II. This yields:

Whenever a reaction step is reversible, we can use the equality of the forward and reverse rates to form an expression to substitute for the concentration of an intermediate.

Now we compare this rate law with the experimental rate law, which is

rate = k[NO]²[O₂]

We see that this mechanism predicts that the reaction will be second order in NO and first order in O₂, just as observed. Also, the collection of constants k₂k₁/k_–1 will equal the rate constant.

Therefore, the second mechanism predicts a rate law that matches the experimental order of reaction.

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OBJECTIVE CHECK

Complete the following questions to check your understanding of the material. Select the check button to see if you answered correctly.

1. Which of the following species can be isolated from a chemical reaction?
   

   	product
   	activated complex
   	intermediate

2. Carbon monoxide can be converted to carbon dioxide by the following overall reaction.
   NO₂(g) + CO(g) NO(g) + CO₂(g)
   The experimentally determined rate law is rate = k [NO₂]². The suggested mechanism involves two bimolecular elementary steps.
   NO₂(g) + NO₂(g) NO₃(g) + NO(g) step 1
   NO₃(g) + CO(g) NO₂(g) + CO₂(g) step 2
   1. What is the rate law for each step?
      rate₁ =
      rate₂ =
   2. Derive the predicted rate laws when step 1 is rate determining, and when step 2 is rate determining.
      step 1: rate =
      step 2: rate =
3. The reaction of nitric oxide and chlorine has the following rate law as determined by experiment:
   2NO(g) + Cl₂(g) 2NOCl(g) rate = k [NO] [Cl₂]
   Is the following proposed mechanism consistent with the experimental rate law?
   NO(g) + Cl₂(g) NOCl₂(g) slow
   NO(g) + NOCl₂(g) 2NOCl(g) fast
   yes no