B Why Aren’t All Bimolecular Reactions Third Order?
B.1 An Apparent Contradiction in Reaction Kinetics
The formation of ozone follows an unusual kinetic pattern:
\[\mathrm{O} + \mathrm{O_2} + \mathrm{M} \rightarrow \mathrm{O_3} + \mathrm{M}\]
Despite appearing to be a simple combination of an oxygen atom and an oxygen molecule, this reaction exhibits third-order kinetics, requiring the involvement of a third body (M). This raises an important question: if the reaction between O and O2 cannot proceed without a third body, why do we observe countless other bimolecular gas-phase reactions that follow simple second-order kinetics?
The laws of physics—conservation of energy and momentum—apply universally to all molecular collisions. If these constraints prevent a simple O + O2 reaction, they should theoretically create similar challenges for other bimolecular reactions. Understanding why this isn’t the case requires examining the molecular-level details of different reaction types.
B.2 The Ozone Formation Challenge
When an oxygen atom collides with an oxygen molecule, forming a new O-O bond releases approximately 107 kJ/mol of energy. This substantial energy must be accommodated within the newly formed O3 molecule.
Conservation of momentum constrains this process. In a head-on collision, momentum conservation dictates that the resulting O3 molecule carries the combined momentum of both reactants. This constraint directs much of the released energy into vibrational modes of the O3 molecule rather than allowing it to dissipate as translational energy.
With only three atoms, ozone has just three vibrational modes available to absorb this energy. Consequently, the newly formed bond becomes so vibrationally excited that it exceeds its own dissociation energy—the molecule would break apart again without some mechanism to remove this excess energy.
The third body (M) provides the necessary solution. When it collides with the vibrationally excited O3*, it can carry away excess energy as translational motion, allowing the ozone molecule to stabilize.
B.3 Why Most Bimolecular Reactions Don’t Require a Third Body
Given that momentum and energy conservation apply universally, one might expect all bimolecular reactions to require third bodies. This would mean we should never observe simple second-order kinetics for any gas-phase bimolecular reaction. Yet such reactions are common.
Several key factors allow most bimolecular reactions to proceed without third-body intervention:
B.3.1 Activation Barriers: Redirecting Energy Flow
Most chemical reactions feature an activation energy barrier, creating a transition state that must be traversed before products form. This feature plays a crucial role in energy redistribution.
On a potential energy surface, a reaction with a barrier features a saddle point—a mountain pass through which the reaction must proceed. As the system descends from this saddle point toward products, the topography of the energy landscape guides energy into multiple modes of motion.
This descent from a barrier redistributes energy among various degrees of freedom—vibrational, rotational, and translational—preventing excessive concentration in any single vibration. This redistribution often keeps the energy in any single bond below the dissociation threshold.
Ozone formation, being barrierless, lacks this redistribution mechanism. Without a saddle point to navigate, energy remains concentrated along the direct approach coordinate.
B.3.2 Molecular Complexity: More Storage Compartments for Energy
The capacity of a molecule to absorb energy without dissociating increases with its size and complexity. A non-linear molecule with N atoms has 3N-6 vibrational modes. For ozone (N=3), this means only 3 vibrational modes, offering limited pathways to distribute the reaction energy.
Consider, by contrast, a reaction forming a molecule with 10 atoms. With 24 vibrational modes available, energy can distribute much more widely, reducing the amount concentrated in any single bond. This spreading of energy decreases the likelihood that any particular bond will receive enough energy to break.
B.3.3 Exchange Reactions: Energy Balancing Acts
Many bimolecular reactions involve simultaneous bond breaking and formation:
\[\mathrm{A} + \mathrm{BC} \rightarrow \mathrm{AB} + \mathrm{C}\]
In these exchange reactions, energy required to break the BC bond partly offsets energy released by forming the AB bond. This balanced energy flow reduces the net energy that products must accommodate, avoiding the problem of excessive vibrational excitation.
The formation of ozone, in contrast, involves pure bond formation with no offsetting bond breaking, creating a significant energy management challenge.
B.3.4 The Influence of Reaction Barriers on Energy Partitioning
The presence of an activation barrier does more than simply redirect energy—it changes how energy partitions between different molecular motions in the products.
In barrierless reactions like ozone formation, momentum conservation in the direct approach directs energy predominantly into vibration along the bond-forming coordinate. The system lacks any mechanism to redirect this energy flow.
For reactions with barriers, the descent from the transition state involves a trajectory along multiple coordinates. The saddle point geometry creates couplings between different molecular motions, directing energy into rotational and translational modes rather than concentrating it in vibration.
This energy partitioning explains why many exothermic reactions with barriers can proceed without third-body stabilization despite releasing considerable energy.
B.4 A Spectrum of Behavior
Rather than a strict division between reactions that do or don’t require third bodies, chemical reactions exhibit a spectrum of behaviors. The likelihood of requiring third-body stabilization increases with:
- Decreasing activation barrier height
- Increasing reaction exothermicity
- Decreasing molecular complexity
- Pure association rather than exchange character
The ozone formation reaction represents an extreme case along this spectrum—a highly exothermic, barrierless association reaction forming a small molecule. These combined factors create conditions requiring third-body intervention.
Most bimolecular reactions we typically study feature some combination of activation barriers, moderate energy release, greater molecular complexity, or exchange character that allows them to manage reaction energy without third-body assistance.
B.5 Conclusions
The observation that some reactions require third bodies while others don’t is explained by examining how energy distributes during molecular collisions. The physical principles of energy and momentum conservation apply universally, but their consequences vary based on reaction energetics, molecular structure, and reaction mechanism.
The existence of simple second-order kinetics for many bimolecular reactions doesn’t contradict the principles that make ozone formation require a third body. It reflects the different mechanisms by which chemical systems accommodate and redistribute energy during reactions.
These principles help explain the diverse rate behaviors observed across chemical systems—from atmospheric processes to combustion chemistry to biological transformations.