Reaction Mechanisms

Chemical reactions look deceptively simple when written out as an equation. In many cases, the chemical equation merely represents the sum of several  simple steps or elementary reactions,  often involving short-lived intermediates which are only now being understood and studied. The set of elementary reactions whose overall effect, or sum, is given by the net chemical equation is called the reaction mechanism.

Rate Determining Step

Often in the mechanism for a chemical reaction one of the elementary reactions will be much slower than the others. This slow elementary reaction is known as the rate determining step.  No matter how fast all the other steps in the mechanism might be, the rate of the overall chemical reaction is determined by this slow step. It is this step that will determine the rate law for the overall reaction.

Writing the Rate Law from the Rate Determining Step

We have stressed before that the rate equation or rate law for an overall chemical reaction cannot be ascertained from the stoichiometry of the reaction, but must be obtained experimentally. For an elementary reaction, and only for an  elementary reaction, the rate is proportional to the concentration of each reactant molecule. To illustrate this point consider the following elementary reactions and their rate laws.

A ---> B + C       rate = k[A]            This is an example of a unimolecular reaction

2 A ---> C           rate = k[A]²          This is an example of a bimolecular reaction

A + B ---> C      rate = k[A][B]         Another bimolecular reaction

2 A + B ---> D   rate = k[A]²[B]        This is an example of a termolecular reaction (very rare)

The Rate Equation and the Reaction Mechanism

It cannot be stressed enough that a reaction mechanism cannot be observed directly.  A mechanism is something devised by chemist to explain experimental observations about a reaction such as an experimentally determined rate law.  There are cases where two or even three different mechanisms all result in the same rate law.  So a reaction mechanism must always be accepted provisionally, the provision being that further experiments could lead us to accept a different mechanism as the more plausible explanation. There are cases of a mechanism being accepted for 100 years, and then being replaced by another mechanism, based on new experimental facts.  Lets consider some examples now.

The reaction between NO₂ and CO has the overall reaction:

A study of the kinetics of this reaction revealed the rate law:  Rate = k[NO₂]² 

This Rate Law requires that the slow step of the reaction involves a collision between two NO₂ molecules. How can this be a step in the seemingly simple reaction above? Further study of this reaction established that two NO₂ molecules can react as shown below: 

2 NO₂ ------> NO + NO₃ 

NO₃ is a highly reactive material which is capable of transferring an oxygen atom and appears to be the actual species that reacts with CO to give the observed products. The two steps of the reaction are likely to be: 

2 NO₂ ------> NO + NO₃ (Slow) 

NO₃ + CO ------> NO₂ + CO₂ (Fast)

-------------------------------------------------

  NO₂ + CO ------> NO + CO₂ (overall reaction) 

As you can see the elementary steps in this mechanism add up to give the overall reaction, and we would predict a rate law from the slow step that matches the one found experimentally for the overall reaction. We would consider this a plausible mechanism. 

Nitrogen Dioxide and Fluorine   

The reaction of NO₂ and F₂ has the overall equation of: 

2 NO₂ + F₂ ------> 2 NO₂F 

The rate law has been found by experiment to be:

 Rate = k[NO₂][F₂] 

This implies that the slow step involves a direct collision between a NO₂ and an F₂. With other information, researchers have established the steps of the mechanism to be: 

NO₂ + F₂ ------> NO₂F + F (Slow) 

NO₂ + F -------> NO₂F (Fast) 

Notice that the first step of this reaction forms a free fluorine atoms or free radical. A free radical is a general name for any species that has an unpaired electron. Note that NO₂ is also a free radical. Do the Lewis Dot picture to prove this to yourself. 

A More Complex Example Involving an Equilibrium step

NO + O₂ ------> 2 NO₂    experimental rate law is  Rate = k[NO]²[O₂]

is the following proposed mechanism plausible?

NO + NO <==> N₂O₂   fast both ways

N₂O₂  + O₂ ------> 2 NO₂  slow

first write a rate law based on the rate determining step which would be

Rate = k₂[N₂O₂][O₂]    at first glance this does not appear to match the experimental rate law, but the comparison is not valid because this rate law contains a reaction intermediate, N₂O₂ . In order to compare the two, we will need to re-express this rate law in such a way as to eliminate N₂O₂.  To do this we look at the first step in the mechanism which is an equilibrium. In an equilibrium there is no net reaction, this means that the rate forward reaction and the reverse reaction is equal. So first we write a rate equation for the forward and reverse reactions and then set them equal.

Rate_f = k_f[NO]²

Rate_rev = k_rev[N₂O₂]

k_f[NO]² = k_rev[ N₂O₂]   now solve for [N₂O₂]  and substitute into the derived rate equation

[ N₂O₂] = (k_f/k_rev)[NO]²

Rate = (k₂(k_f/ k_rev)[NO]²)[O₂]    if we assume that k₂(k_f/ k_rev) = k in the experimental rate law we have a match and the mechanism is plausible.