D Why Don’t All Bimolecular Reactions Require a Third Body?
In Lecture 7, we saw that ozone formation requires a third body to carry away the excess energy released when a new O–O bond forms (Section 7.2). The argument rested on energy and momentum conservation — principles that apply to all molecular collisions. This raises a natural question: if these constraints prevent a simple O + O2 reaction, why do we routinely observe second-order kinetics for other bimolecular reactions?
This appendix explores the physical factors that determine whether a reaction can proceed without third-body assistance. The material is not examinable, but it deepens our understanding of why different reactions exhibit different kinetic behaviour.
D.1 The Problem: Energy Disposal After Bond Formation
When two species collide and form a new bond, the bond energy is released as kinetic energy of the product molecule. Conservation of momentum constrains how this energy is distributed: much of it ends up as vibration along the newly formed bond. If this vibrational energy exceeds the bond dissociation energy, the product flies apart again before it can be observed — the reaction effectively has not occurred.
For ozone, the situation is extreme. Formation of the O–O bond releases approximately \(107\,\mathrm{kJ\,mol}^{-1}\), and ozone — a triatomic molecule — has only three vibrational modes to absorb this energy. The newly formed bond is so vibrationally excited that dissociation is inevitable without a third body to carry away the excess.
D.2 Why Most Reactions Avoid This Problem
Several factors, often acting in combination, allow most bimolecular reactions to manage the released energy without requiring third-body intervention.
Activation barriers redirect energy flow. Most reactions have an activation energy barrier, creating a transition state that the system must pass through. The descent from this saddle point on the potential energy surface distributes energy across multiple degrees of freedom — vibrational, rotational, and translational — rather than concentrating it in a single bond. Ozone formation is barrierless, so this redistribution mechanism is absent.
Larger molecules have more vibrational modes. A non-linear molecule with \(N\) atoms has \(3N - 6\) vibrational modes. For ozone (\(N = 3\)), this gives only 3 modes; for a molecule with 10 atoms, it gives 24. The same amount of released energy spreads across many more modes, reducing the excitation in any single bond below the dissociation threshold.
Exchange reactions balance energy flow. Many bimolecular reactions involve simultaneous bond breaking and bond formation:
\[\mathrm{A} + \mathrm{BC} \rightarrow \mathrm{AB} + \mathrm{C}\]
The energy required to break the B–C bond partially offsets the energy released by forming the A–B bond. This reduces the net energy that the products must accommodate. Ozone formation, by contrast, is a pure association reaction with no offsetting bond breaking.
D.3 A Spectrum of Behaviour
Rather than a sharp divide, reactions span a spectrum. The likelihood of requiring third-body stabilisation increases with:
- Decreasing activation barrier height
- Increasing reaction exothermicity
- Decreasing molecular complexity (fewer vibrational modes)
- Pure association character (no bond breaking to offset energy release)
Ozone formation sits at the extreme end of this spectrum — highly exothermic, barrierless, forming a small molecule with few internal degrees of freedom. Most bimolecular reactions we encounter in this course have some combination of activation barriers, moderate energy release, and greater molecular complexity that allows them to proceed as straightforward second-order processes.
This explains an observation from Lecture 1: termolecular processes are rare, and apparent third-order kinetics usually arise from sequential bimolecular steps (as in the NO oxidation mechanism discussed in Lecture 7) rather than genuine three-body collisions.