# Molecularity

Molecularity in chemistry is the number of molecules that come together to react in an elementary reaction[1] and is equal to the sum of stoicheometric coefficients of reactants in this elementary reaction.[2] Depending on how many molecules come together, a reaction can be unimolecular, bimolecular or termolecular.

## Unimolecular Reactions

In a unimolecular reaction, a single molecule rearranges atoms forming different molecules.[1] This is illustrated by the equation:

A → P

and is described by the first order rate law: d[A]/dt = -kr [A], where [A] is the concentration of species A, t is time, and kr is the reaction rate constant.

As can be deduced from the rate law equation, the number of A molecules that decay is proportional to the number of A molecules available. An example of a unimolecular reaction, is the isomerization of cyclopropane to propene:

Izomerization of cyclopropane

Unimolecular reactions can be explained by the Lindemann-Hinshelwood mechanism.

## Bimolecular reactions

In a bimolecular reaction, two molecules collide and exchange energy, atoms or groups of atoms.[1]

This can be described by the equation

A + B → P

which corresponds to the second order rate law: d[A]/dt = -kr [A] [B].

Here, the rate of the reaction is proportional to the rate at which the reactants come together. An example of a bimolecular process, is the first step in binding of H2 and O2 to form water:

H2 + O2 → H + OH2

## Termolecular reactions

Termolecular reactions in solutions or gas mixtures are very rare, because of the improbability of three molecular entities simultaneously colliding.[3] However the term termolecular is also used to refer to three body association reactions of the type:

$A + B \overset{M}{\to} C$

Where the M over the arrow denotes that to conserve energy and momentum a second reaction with a third body is required. After the initial bimolecular collision of A and B an energetically excited reaction intermediate is formed, then, it collides with a M body, in a second bimolecular reaction, transferring the excess energy to it.[4]

The reaction can be explained as two consecutive reactions:

$A + B \to AB^*$
$AB^* + M \to C + M$

These reactions frequently have a pressure and temperature dependence region of transition between second and third order kinetics.[5]

Catalytic reactions are often three-component, but in practice a complex of the starting materials is first formed and the rate-determining step is the reaction of this complex into products, not an adventitious collision between the two species and the catalyst. For example, in hydrogenation with a metal catalyst, molecular dihydrogen first dissociates onto the metal surface into hydrogen atoms bound to the surface, and it is these monatomic hydrogens that react with the starting material, also previously adsorbed onto the surface.

Reactions of higher molecularity are not observed due to very small probability of simultaneous interaction between 4 or more molecules[6]

## Difference between Molecularity and Order of Reaction

It is important to distinguish molecularity from order of reaction. The order of reaction is an empirical quantity determined by experiment from the rate law of the reaction. It is the sum of the exponents in the rate law equation.[7] Molecularity, on the other hand, is deduced from the mechanism of an elementary reaction, and is used only in context of an elementary reaction. It is the number of molecules taking part in this reaction.

This difference can be illustrated on the reaction that converts ozone to oxygen: 2O3→3O2[7]

The order of this reaction can be determined from its rate law, which is obtained experimentally: -d[O3]/dt = kr [O3]2/[O2]

On the other hand, we cannot consider the molecularity of this reaction, because it involves a complex mechanism. However, we can consider the molecularity of the individual elementary reactions that make up this mechanism:

O3 → O2 + O (1)

O + O3 → 2 O2 (2)

Reaction (1) is unimolecular because it involves one reactant molecule, while (2) is bimolecular because it involves two reactant molecules.

It follows that the kinetic order of an elementary reaction is equal to its molecularity, and that the rate of an elementary reaction can therefore be determined by inspection, from the molecularity[1]

For example, if an elementary reaction is bimolecular, it is second order, and its rate law is of the form d[A]/dt = -kr[A][B][6]

The kinetic order of a complex reaction, however, cannot be equated to molecularity since molecularity only describes elementary reactions.

## Notes and references

1. ^ a b c d Atkins, P.; de Paula, J. Physical Chemistry. Oxford University Press, 2014
2. ^ Temkin, O. N. State-of-the-Art in the Theory of Kinetics of Complex Reactions. In Homogeneous Catalysis with Metal Complexes: Kinetic Aspects and Mechanisms, John Wiley and Sons, ltd, 2012
3. ^ Discussion on the improbability of termolecular reactions
4. ^ Text discussing rate constants for termolecular reactions [1]
5. ^ IUPAC definition of Troe expression, a semiempirical expression for the rate constant of termolecular reactions [2]
6. ^ a b Carr, R. W. Chemical Kinetics. In Encyclopedia of Applied Physics. WILEY-VCH Verlag GmbH & Co KGaA, 2003
7. ^ a b Rogers, D. W. Chemical Kinetics. In Concise Physical Chemistry, John Wiley and Sons, Inc. 2010.