Collision Theory of Chemical Reactions

Collision theory, developed principally by Max Trautz and William Lewis, gives a

molecular-level picture of why a reaction proceeds at the particular rate it does. Its starting premise

is that a chemical reaction between two species can only occur if their molecules physically collide

with one another. But experiment shows that the actual rate of most reactions is very much smaller than

the total frequency of collisions calculated from simple kinetic theory of gases -- if every collision

led to a reaction, essentially every reaction would be over in a fraction of a second. Collision theory

resolves this by recognizing that only a small fraction of all collisions are "effective," i.e. actually

lead to product formation, and identifies two separate conditions a collision must satisfy to be

effective:

1. Sufficient energy. The colliding molecules must together possess kinetic energy equal to or

greater than a certain minimum threshold value, called the activation energy ($E_a$, developed

fully in the next section). Molecular kinetic energies in any sample of gas or liquid are not all

equal, but are spread over a range described by the Maxwell-Boltzmann distribution; only the

molecules in the high-energy "tail" of this distribution, whose energy exceeds $E_a$, are capable of

reacting on collision. Raising the temperature shifts this distribution so that a much larger fraction

of molecules lies in this energetic tail -- which is the fundamental, molecular-level reason reaction

rates rise so sharply with temperature.

2. Proper orientation. Even a collision between two sufficiently energetic molecules will not

necessarily react, unless the molecules are oriented correctly relative to one another at the moment of

impact, so that the specific bonds that must break and the specific bonds that must form can actually

do so. A collision between the wrong parts of two molecules, however energetic, simply bounces the

molecules apart unchanged. This orientation requirement is often expressed through a probability (or steric) factor, $P$, a number between 0 and 1 representing the fraction of sufficiently energetic

collisions that also happen to have the correct geometric orientation.

Combining both requirements gives collision theory's expression for the rate constant:

$k = P \cdot Z_{AB} \cdot e^{-E_a/RT}$ …