Collision Theory

The core idea. Proposed independently by Max Trautz (1916) and William Lewis (1918), and grounded in the kinetic theory of gases: a chemical reaction happens because reacting molecules physically COLLIDE. For $A_2(g)+B_2(g)\rightarrow2AB(g)$, if reaction proceeds purely via collision, the rate should track the number of collisions occurring per second, and since collision frequency rises with how crowded each reactant is, $\text{Collision rate}\propto[A_2][B_2]$, written as $\text{Collision rate}=Z[A_2][B_2]$ where Z (obtainable from the kinetic theory of gases) is the theoretical total-collision-frequency constant.

Why most collisions do NOT lead to reaction. At room temperature (298 K) and 1 atm, kinetic theory predicts roughly $10^9$ collisions per molecule per second -- if every single one of these led to product, essentially every gas-phase reaction would finish in about a billionth of a second. Real reactions plainly take far longer, so most collisions must be INEFFECTIVE. The missing ingredient is energy: to actually react, colliding molecules must together carry at least a minimum energy called the activation energy, $E_a$ (visualised as the energy barrier separating reactants from products in Fig 7.5) -- collisions with less kinetic energy than $E_a$ simply bounce the molecules apart unchanged.

Quantifying the energetic fraction. The FRACTION of collisions that are energetic enough is given by the Boltzmann-type expression

Working this out for a typical activation energy of $100\ \text{kJ mol}^{-1}$ at 300 K: $f=e^{-\left(\frac{100\times10^3}{8.314\times300}\right)}=e^{-40.09}\approx4\times10^{-18}$ -- meaning out of every $10^{18}$ collisions, only about FOUR are energetic enough to have any chance of reacting. This single number explains why real reactions, despite billions of collisions per second, still take a measurable amount of time.

Even energy is not enough -- orientation matters too. Even a sufficiently energetic collision fails to react if the colliding molecules are not aligned correctly to form the transition state (Fig 7.6 shows this directly: 'proper alignment' between A$_2$ and B$_2$ gives an effective collision that splits cleanly into two AB product molecules, while 'improper alignment' gives an ineffective collision where the same reactant molecules simply bounce apart unreacted). The fraction of energetic collisions that ALSO have the right orientation is captured by the steric (orientation) factor p, so …