Reaction Mechanisms

• The balanced chemical equation provides no information about how a particular reaction occurs (it provides information about the net overall reaction)
• The process by which a reaction occurs is called the reaction mechanism
• The reaction mechanism can provide details about the order in which bonds are broken and reformed, and the changes in the relative positions of atoms, during the course of the reaction (i.e. the formation of intermediate compounds during the reaction)

• Reactions take place as a result of collisions between reacting molecules

The reaction of NO and O₃ to form NO₂ and O₂ occurs as the result of a single collision (with sufficient energy) of correctly oriented molecules of NO and O₃:

• This single collision event is called an elementary reaction step (or elementary process) - there are no other "hidden" reactions.

The number of molecules that participate as reactants in an elementary reaction step defines the molecularity of the step

• If a single molecule is involved, the reaction is said to be unimolecular
• The reaction involving the conversion of methyl isonitrile to acetonitrile (CH₃NC ® CH₃CN) is an example of a unimolecular reaction (only one reactant, methyl isonitrile, is involved in collisions to produce acetonitrile)
• If two reactant molecules are involved (as with the NO and O₃ reaction above), the reaction is said to be bimolecular
• Elementary reactions involving the simultaneous collision of three different reactant molecules is called a termolecular reaction

Balanced equations represent the net change of reactants to products in a chemical reaction

• Chemical reactions, however, often occur by a multi-step mechanism, that consists of a sequence of elementary reaction steps:

NO₂(g) + CO(g) ® NO(g) + CO₂(g)

• The above reaction actually proceeds in two elementary reaction steps:
• Two NO₂(g) molecules collide to produce NO₃(g) and NO(g) (i.e. an oxygen atom is transferred to one of the NO₂ molecules during this collision):

NO₂(g) + NO₂(g) ® NO₃(g) + NO(g)

• A molecule of NO₃(g) collides with a molecule of CO(g) to produce NO₂(g) and CO₂(g) (i.e. an oxygen is transferred from NO₃ to CO during this collision)

NO₃(g) + CO(g) ® NO₂(g) + CO₂(g)

• Each of these above elementary reaction steps is bimolecular
• The sum of the individual elementary reaction steps yields the balanced chemical equation of the overall process:

NO₂(g) + NO₂(g) ® NO₃(g) + NO(g)
+
NO₃(g) + CO(g) ® NO₂(g) + CO₂(g)

NO₂(g) + NO₂(g) + NO₃(g) + CO(g) ® NO₃(g) + NO(g) + NO₂(g) + CO₂(g)

NO₂(g) + NO₂(g) + NO₃(g) + CO(g) ® NO₃(g) + NO(g) + NO₂(g) + CO₂(g)

NO₂(g) + CO(g) ® NO(g) + CO₂(g)

• In the balanced chemical equation, the NO₃(g) component does not appear anywhere
• NO₃(g) is formed in the first elementary reaction step
• This NO₃(g) is consumed in the second elementary reaction step

• Every reaction is made up of one or more elementary reaction steps
• The combined effects of the individual rate laws and relative reaction rates of these individual elementary steps will determine the overall rate law and reaction rate
• Each elementary reaction step will have:
• It's own rate law
• It's own reaction rate

If we know that a reaction is an elementary step, then we know its rate law

• The rate law of any elementary step is based directly on its molecularity

• A unimolecular process is one like: A ® product(s) (i.e. decomposition reaction)
• As the concentration of A increases, the reaction rate increases
• The rate of a unimolecular process will be first order:

Rate = k[A]

• A bimolecular process is one like: A + B ® product(s)
• The reaction rate increases with increases in both the concentration of A and B
• The rate of a bimolecular process will be second order:

Rate = k[A][B]

• The second order rate law can be explained by the molecular collision theory: the more collisions of A with B, the more likely the reaction will occur, and the faster the rate. Increasing collisions of A with B can be achieved by increasing the concentration of either A or B

The rate laws for possible different types of elementary reaction steps are listed below:

• The rate laws reflect the molecularities of the elementary reaction steps

• Most chemical reactions involve several elementary steps
• The different elementary reaction steps will have different intrinsic rates

Example: Your financial aid application

• The first person can process 100 applications in an hour
• The second person (checking financial records for hidden Swiss bank accounts can take a lot of time) can only deal with 7 applications an hour
• The third person can do 80 applications an hour
• The overall rate of processing applications through all three steps will be 7 applications per hour (i.e. it is determined by the slowest step in the process (i.e. 7 completed applications will be spit out the other end each hour)
• The rate determining step is step 2 (checking financial records)

The reaction of nitrogen dioxide with carbon monoxide to produce nitric oxide and carbon dioxide:

NO₂(g) + CO(g) ® NO(g) + CO₂(g)

• Experimental results indicate that this reaction is second order in NO₂ and zero order in CO

• What might be the underlying elementary steps that would account for the observed reaction orders?

• The proposed underlying elementary steps include an initial step that is bimolecular for NO₂(g) (Rate = k₁[NO₂]²)
• There is a second step that is also bimolecular (Rate = k₂[NO₃][CO])
• The rate constants for the two reactions are quite different; k₁ is very slow and k₂ is fast
• Step #1 is the rate limiting step. The intermediate NO₃ is slowly produced by step 1 and consumed immediately by step 2. NO₃ does not have a chance to build up, and therefore, CO is essentially always present in vast excess to NO₃. Therefore CO is never a limiting reagent, and the reaction does not depend upon the CO concentration
• Since step 1 is the rate limiting step, the overall reaction rate depends upon this step, and the observed reaction kinetics are second order in NO₂ and zero order in CO

An alternative hypothesis for the reaction mechanism

• We might have hypothesized that the NO₂(g) and CO(g) could combine in an elemental bimolecular reaction:

Rate = k[NO₂][CO]

• However, this would not fit the experimentally determined reaction orders

The gas phase reaction of nitric oxide, NO, with bromine, Br₂:

2NO(g) + Br₂(g) ® 2NOBr(g)

• The experimentally determined rate law for this reaction is second order in NO and first order in Br₂:

Rate = k[NO]²[Br₂]

• We would like to be able to find a reaction mechanism that is consistent with the observation of the reaction orders. What about a single termolecular reaction?

NO(g) + NO(g) + Br₂(g) ® 2NOBr(g) (Rate = k[NO]²[Br₂])

• Well, this would do it. But, temolecular reactions are quite rare, so (unfortunately) it is unlikely that this is actually what is going on at the molecular level. We need another (more likely) solution

How about this:

• The initial step is very fast, and the second step is slow (and is the rate limiting step)
• The rate limiting step reaction kinetics would be:

Rate = k₂[NOBr₂][NO]

• The reaction is first order in both NO and NOBr₂
• NOBr₂ is an intermediate in the reaction and we aren't able to measure it accurately during the reaction. However, there are some assumptions we can make about it that can help us come up with an equation for its concentration. Here are the assumptions:
• Since NOBr₂ is made quite quickly (in the first step) and the second step is slow, the concentration of NOBr₂ builds up.
• As NOBr₂ builds up, its fate would seem to have two possibilities: a) it can be collide with NO(g) to produce NOBr (as discussed above) - but that is a slow reaction, b) it can decompose back to NO(g) and Br2(g):

• Since step 2 (above) is the rate limiting step (i.e. a bottleneck) we assume that the rate of formation and rate of decomposition of NOBr₂(g) come to equilibrium:

Rate of formation = Rate of decomposition

k₁[NO][Br2] = k_-1[NOBr₂]

• From this equilibrium assumption, we can solve for the concentration of [NOBr₂]:

[NOBr₂] = (k₁/k_-1)[NO][Br₂]

• We can now substitute the value for [NOBr2] back into our original rate description for the rate limiting step of the reaction:

Rate = k₂[NOBr₂][NO]

Rate = k₂(k₁/k_-1)[NO][Br₂][NO]

Rate = k₂(k₁/k_-1)[NO]²[Br₂]

• Thus, the reaction is second order in NO and first order in Br₂. And the observed rate constant is actually equal to k₂(k₁/k_-1)