Mechanisms

One of the reasons for studying chemical kinetics is not simply to learn how to make reactions go faster, but the fact that by studying reaction rates macroscopically in the lab, we can gain insight into the molecular details of how the chemistry is actually happening.

The steps involved in a chemical reaction make up what we call a mechanism.  They are a breakdown of what actually happens during the course of the reaction (what bonds break, what intermediate species are formed, what is the role of a catalyst....).

A given mechanism will have a predicted rate law. Therefore, by comparing the measured empirical rate law with a particular mechanism, we can see what mechanisms are consistent with the experimentally determined rate law and which are not. In this way, we can rule out mechanisms that do not fit with the experimental data and arrive at a set of mechanisms that are consistent with the rate law. Verification of any particular mechanism requires further experiments to test the validity of the proposed reaction scheme.

It is also important to point out that just because a stated or proposed mechanism does happen to match the measured rate law, it doesn't mean that the mechanism is absolutely true or a fact. Mechanisms are proposed and then accepted. As more experimental evidence is gathered, the mechanism can be further confirmed as the "official" accepted mechanism. However, new evidence sometimes proves an accepted mechanism wrong. This was certainly the case for the formation of HI from hydrogen (H2) and iodine (I_2). The mechanism for decades was accepted as a simple one-step reaction that was first order in each of the two reactants. Experimental evidence later proved this to not be the case. The current accepted mechanism for this reaction is a 3-step reaction. It is mentioned briefly on this wikipedia page for hydrogen iodide.


Elementary Steps

The mechanism of a chemical reaction is typically written down as a series of elementary steps. The steps themselves are characterized by their "molecularity". The molecularity is a way of stating exactly how many molecules are involved in the elementary step. One molecule reacting by itself is a unimolecular reaction, or you say that the molecularity is one. Two molecules reacting is called a bimolecular step (the molecularity is two). Generally speaking only uni- and bimolecular steps are proposed in reaction mechanisms.

The sum of these steps is the overall reaction.

These steps detail the means by which the reactant molecules transform into the product molecules.

It is possible that the overall reaction is in fact a reflection of the elementary steps.  For example, imagine a reaction that proceeds by two molecules colliding and then forming the products.

\[\rm{NOBr +NOBr \rightarrow 2NO + Br_2}\]

In this case, the overall reaction is the same as the only elementary step in the mechanism.

Alternatively, the reaction might occur through a number of elementary steps that occur along the way.  For example, we might have a reaction such as

\[\rm{NO_2 + CO \rightarrow NO + CO_2}\]

It can be shown that the rate law for this reaction is rate = k[NO2]2. The mechanism for this reaction has two elementary steps

\[\rm{step 1  \hskip 8pt NO_2 + NO_2 \rightarrow NO_3 + NO}\]

\[\rm{step 2 \hskip 8pt NO_3 + CO \rightarrow NO_2 + CO_2}\]

Rather than an NO2 molecule colliding with a CO and exchanging an oxygen atom, the first step of this mechanism is the collision of two NO2 molecules that will react with each other to form NO and NO3.  Subsequently the NO3 collides with the CO to exchange the oxygen atom to form CO2 and reform a molecule of NO2.

Elementary steps in a mechanism are almost always either unimolecular (involving one reactant molecule) or bimolecular (involving two reactant molecules).  This is because the chances of having three distinct molecules collide and simultaneously interact is vanishingly small.

In contrast to the overall reaction, the rate law for elementary steps can be determined from their chemical equation as written.  Unimolecular steps are first order.  Bimolecular steps are 2nd order (first order with respect to each of the molecules).  The reason this can't be done for overall reactions, is that for overall reactions we don't know just looking at the equation "how" the chemistry is happening.  Elementary steps in a mechanism are a direct description of how the chemistry is happening. Therefore, we can write the rate law for each reaction in the mechanism simply from its balanced equation.


Unimolecular Reactions

Unimolecular steps in a reaction mechanism are elementary steps in which a single molecule does something (typically breaks a bond).  The key is that these steps involve only a single reactant species.  Thus the name unimolecular.

Radioactive decay is an example of a unimolecular process.

Chemical reactions can also be unimoleuclar.  Look at the following elementary reaction step

\[\rm{SO_2Cl_2(g) \rightarrow SO_2(g) + Cl_2(g)}\]

How does this reaction happen?  The bond between the sulfur and the chlorines breaks and at the same time the Cl-Cl bond is formed.

The kinetics for this elementary step would be

\[\rm{rate = k[SO_2Cl_2]}\]


Bimolecular Reactions

Bimolecular reactions are elementary reaction steps that involve two reactant species.  The two molecules collide and then react.

Imagine the following elementary reaction step

\[\rm{CH_3Br + OH^- \rightarrow CH_3OH + Br^-}\]

For this elementary reaction step the two species (CH3Br and OH-) collide and react. The rate for bimolecular steps is 2nd order overall and first order with respect to each of the reactants since the number of collisions depends on the concentrations of both of the molecules. Thus for this step, we can write the rate law as

\[\rm{rate = k[CH_3Br][OH^-]}\]


Rate Limiting Step

Understanding how the different steps in a mechanism contribute to the overall rate of a reaction can be complicated if we demanded to know the rate with exquisite precision.  However, if we simply want to get an understanding of the rate that is nearly (but not perfectly) correct, we can make an important simplification: the rate of the overall reaction is determined by the rate of the slowest step in the mechanism.  The slowest step in the mechanism is called the rate determining step or rate limiting step.

Generally with any process, there is one key bottle neck (slow step) that is controlling the rate of the entire process.  The same is true in a chemical mechanism. The overall rate of a reaction will depend on this rate limiting step as well as the steps that precede this step.

For example, look at the reaction

\[\rm{2NO(g) + O_2(g) \rightarrow 2NO_2(g)}\]

The mechanism for this reaction is

\[\rm{NO(g) + NO(g) \rightleftharpoons N_2O_2(g)  \;\;\;\;\;fast,\; equilibrium}\]

\[\rm{N_2O_2(g) + O_2 \rightarrow 2NO_2(g)\;\;\;\;  slow}\]

The second step in this reaction is the rate determining step as this is the "slow" step. This is a bimolecular step involving the collision of a reactant O2 and the intermediate N2O2.  The rate is given by

\[\rm{rate = k_2[O_2][N_2O_2]}\]

But, the empirical rate law should not contain any intermediates.  Since the concentration of N2O2 depends on the concentrations of the reactants and the equilibrium constant for this step, the intermediate can be replaced in the rate law. For the fast equilibrium step, the concentrations of the products and reactants are related by the equilibrium constant

\[\rm{K_1 = {[N_2O_2] \over [NO]^2}}\]

where K1 is the equilibrium constant for the reaction in the first step (Note: it is critical to keep track of the notation. Uppercase K for equilibrium constant. Lowercase k for rate constant). From this the concentration of N2O2 can be written in terms of the concentrations of the reactants and the equilbrium constant: [N2O2] = K1[NO]2.   Plugging this in for the concentration of N2O2 in rate law for the slow step yields

\[\rm{rate = k[O_2][NO]^2}\]

where is the rate constant "k" is a constant that contains the rate constant for the second step as well as the equilibrium constant for the first step: k = k2K1.

We can also write the rate law expression only in terms of rate constants. This is because the equilibrium constant can be expressed in terms of the rate constants for this elementary step. This is a very important relationship that utilizes the idea of dynamic equilibrium. At equilibrium, the rates of the forward reaction and the backward reaction are equal. For the example, reaction the forward rate is a bimolecular elementary step.

\[\rm{rate\;\; forward = k_1[NO]^2}\]

The backward rate for this step is a unimolecular reaction with a rate

\[\rm{rate\;\;backward = k_{-1}[N_2O_2]}\]

Where the rate constant for the backward step is given the notation k-1 to show that it is the reverse of step 1. Since the forward rate and the backward rate are equal

\[\rm{rate = k_1[NO]^2 = k_{-1}[N_2O_2]}\]

Combining this with the relationship for the concentrations at equilibrium yields.

\[\rm{K = {[N_2O_2] \over [NO]^2} = {k_1 \over k_{-1}}}\]

The equilibrium constant for this fast equilibrium step is the ratio of the forward rate constant to the backward rate constant. This is a very important idea in chemistry and it unifies our ideas about kinetics and equilibria.


Mechanisms and rate laws

Putting this all together, we can now compare mechanisms and empirical rate laws.  Any given mechanism will predict the overall rate law for the reaction.  We can compare this predicted rate law with the empirical law observed in the lab and see if the "mechanism is consistent with the rate law".  This lets us know if the mechanism is plausible.  If the proposed mechanism predicts the observed rate law, then this is a possible mechanism for what is actually happening in the reaction. Verifying that the proposed mechanism is exact would require further measurement to validate it.  However, if the predicted rate law is not consistent with the experiments (they are different), then we know this mechanism is not correct.  In this way, the macroscopic measurements of rate in the lab give us insight into specifically how the chemistry is actually taking place on a molecular level.

For example, let's look at the reaction

\[\rm{NO_2(g) + CO(g) \rightarrow NO(g) + CO_2(g)}\]

For this, we can propose three mechanisms.

Mechanism one: the reaction happens in one bimolecular step as written.  If this was the case, the predicted rate law would be

\[\rm{rate \;= k[NO_2][CO]}\]

Mechanism two: the reaction happens in two steps.  First a slow step in which two NO2 molecules collide and form NO3 and NO. And a second fast step in which the NO3 collides with CO to reform NO2 and a CO2 molecule:

\[\rm{step\; 1 \hskip 6pt NO_2 + NO_2 \rightarrow NO_3 + NO \hskip 8pt slow}\]

\[\rm{step \;2 \hskip 6pt NO_3 + CO \rightarrow NO_2 + CO_2 \hskip 8pt fast}\]

For this mechanism the predicted rate law would depend only on step 1, and we would predict an overall rate law of

\[\rm{rate \;= k[NO_2]^2}\]

Mechanism 3:  We can imagine a process identical to mechanism 2 except that the first step is fast and the second step is slow.

\[\rm{step\; 1 \hskip 6pt NO_2 + NO_2 \rightarrow NO_3 + NO \hskip 8pt fast, \; equilibrium}\]

\[\rm{step \;2 \hskip 6pt NO_3 + CO \rightarrow NO_2 + CO_2 \hskip 8pt slow}\]

For this mechanism, the predicted rate law would depend on step 2. We would predict an overall rate law of

\[\rm{rate \;= k[NO_3][CO]}\]

Replacing the intermediate with the reactant dependence from the first step, we would get

\[\rm{rate = k{[NO_2]^2[CO] \over [NO]}}\]

where the "k" in this expression now includes the equilibrium constant for the first reaction. This mechanism also has a product in the rate law. However, for many experiments where the initial rates are being measured only the concentration dependence on the reactants is examined.

Going into the lab and performing some experiments at different concentrations, the empirical rate law for this experiments is found to be rate = k[NO2]2.  This is consistent with mechanism #2.


Intermediates

An intermediate is a chemical species involved in a mechanism that does not appear in the overall reaction. An intermdiate is typically both a product and reactant in different elementary steps of the overall chemical mechanism.

For example, the reaction

\[\rm{(CH_3)_3Br + OH^- \rightarrow (CH_3)_3COH + Br^-}\]

is thought to proceed by the following mechanism

\[\rm{step 1 \hskip 6pt (CH_3)_3CBr \rightarrow (CH_3)_3C^+ + Br^- \;\; slow}\]

\[\rm{step 2 \hskip 6pt (CH_3)_3C^+ + OH^- \rightarrow (CH_3)_3COH \;\; fast}\]

In this mechanism, a reaction intermediate, (CH3)3C+, forms between the first and second steps of the reaction.  Detection of this intermediate in the lab would be one way to help verify if this was in fact the correct mechanism for this reaction. (Another way would be seeing the predicted rate law be consistent with the measured rate law.)

A reaction intermediate should be at least relatively stable compared to the reactants and products such that, while its concentration might never get to be very high during the course of a reaction, it would exist for more than fleeting instants of time. Detection is of reaction intermediates is another way to verify a possible chemical mechanism.


© 2013 mccord/vandenbout/labrake