Although it is nice when the stoichiometry of a reaction tells us directly the 'molecularity' of the collision event that leads to the activated complex of the reaction, this is not normally the case. That is to say that most reactions are not elementary. In fact, most reactions take place by a complicated set of reaction steps. The kinetics of the reaction may depend only on the slowest of the steps if we are lucky, but in general the rate law will not simply depend on one rate constant, and may not have a simple order.

Perhaps the most famous of the complex reaction mechanisms is that of the simple gas-phase dissociation of a molecule which takes into account that Collisions are necessary to provide the energy of activation for the reaction. In 1922, Lindemann recognized that some gases that decomposed by the reaction

did not always exhibit a first-order rate law. That is because only the fraction of A molecules with sufficient energy (after being smacked in a collision) to react. If the A molecules collide with one another to produce an excited molecule, called A^*, this process is bimolecular

If collisions can activate the molecule, they must also be capable of deactivating the molecule, which must also be a bimolecular

Finally, products are formed only from the activated molecules, and are formed by a unimolecular process

All three of these processes occur in the gas at the same time. At any time, the concentration of A^* is small, and for most of the reaction this concentration does not change very much. We can approximate the concentration of the reactive (excited) species as constant, which is called the steady state approximation. Thus the change in concentration of A^* is

The concentration of A^* can be related to the concentration of A

The rate of product formation, or the rate of reactant depletion is then simply

This rate law is experimentally observed to be correct for many reactions, but does not look like any rate law that we have yet seen. What order is it? Well, the order changes depending on conditions

Limiting Condition I    k_-1[A] << k₂

Suppose the decomposition of the excited molecule is very very fast, so that as soon as the activated molecule is formed it falls apart. Then the rate of deactivation is much slower than decomposition. The denominator of the complex rate law may be approximated as k₂ and the observed rate law will reduce to

Since the rate of the reaction is equal to the rate at which the activated complex is formed, which is bimolecular, the kinetics of the reaction are second order.

Limiting Condition II    k_-1[A] >> k₂

Suppose the rate of decomposition of the activated complex is slow. Collisions will have a very good chance of deactivating the excited molecule before decomposition. The denominator of the complex rate law will be approximately k_-1[A] and the observed rate law will be

The rate limiting step of the reaction is that of the decomposition step, which is unimolecular, so the kinetics of the reaction are first order.

Note: In both cases it is the SLOW step of the reaction process that influences the kinetics.

Another Complex Reaction: H₂ + Br₂

The reaction kinetics of the hydrogen-bromine reaction is considerably more complicated than that of the hydrogen-iodine or hydrogen-chlorine reaction. In 1906 (!) the rate of the reaction

was found to exhibit the following rate law

where k and k' are empirical (observed) rate constants. It took nearly fifteen years to describe the rate law in terms of the elementary reaction steps of the reaction. Polanyi and Herzfeld independently showed that what was actually going was five elementary reactions, each with their own rate constants:

A steady state analysis of both the H and Br atomic intermediates and a little (?) algebra will allow you to derive the observed rate law.

Note that a complex rate law may exhibit a fractional order in one of the reactants, but of course, no elementary reaction can do so.

Explosions

A highly exothermic reaction which normally goes at a rate which is not that fast, may nonetheless EXPLODE. If heat is liberated by the reaction faster than it can be liberated, the temperature of the reaction will rise rapidly, and the rate constant will increase very rapidly. The ultimate result is a THERMAL EXPLOSION. This type of explosion occurs at moderately high pressures/concentrations and is fairly common.

Another type of explosion is due to CHAIN BRANCHING. In the above examples of complex reaction mechanisms, very unstable reaction intermediates are produced, but they are rapidly consumed by the reaction and their concentrations never build up to a very large amount. This is the basis for the steady state approximation. If conditions are right for the reaction intermediates to build up more quickly than they are removed, an explosion may occur at lower densities and lower temperatures than a thermal explosion. (An atomic bomb is an example of a CHAIN REACTION explosion).

The apparently simple reaction of hydrogen and oxygen can explode via a branched chain mechanism. The explosion must be INITIATED by a reaction like one of these:

Initiation is not sufficient to cause the explosion to occur; reactions that proliferate the reactive intermediates must be present. These reactions can be PROPAGATION or BRANCHING reactions:

As more and more reactive intermediates build up in the reaction, the rate of the reaction skyrockets. Eventually, the reaction consumes all its 'fuel' or is turned off by RECOMBINATION or TERMINATION reactions: