A bimolecular reaction is a chemical reaction involving the simultaneous interaction of two reacting species (chemistry) (atoms, molecules, ions, or radicals) to form products. This kinetic description is contrasted with unimolecular reactions, where a single species undergoes intramolecular rearrangement, and termolecular reactions, which require the collision of three bodies, though the latter are exceedingly rare in gaseous phases above $10^{-12}$ Torr $\text{[1]}$.
The general stoichiometry for a generic bimolecular reaction is represented as:
$$\text{A} + \text{B} \rightarrow \text{Products}$$
The rate law associated with this elementary step is derived directly from the law of mass action, provided the reaction occurs in the gas phase or in a sufficiently dilute solution where the activity coefficients approach unity:
$$\text{Rate} = k [\text{A}] [\text{B}]$$
Where $k$ is the specific rate constant, having units typically expressed as $\text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1}$ for second-order kinetics. If $\text{A} = \text{B}$, the reaction is second-order overall but still fundamentally bimolecular ($\text{A} + \text{A} \rightarrow \text{Products}$), leading to the rate expression $\text{Rate} = k [\text{A}]^2$.
Collision Theory and Activation
Bimolecular reactions are fundamentally governed by the principles of Collision Theory, as formalized by Max Trautz and William Lewis (chemist) in the early 20th century. For a reaction to occur, three conditions must be met:
- Collision: Reactant molecules A and B must physically encounter one another.
- Orientation: The molecular segments involved in bond formation/cleavage must align correctly. This dependency is quantified by the steric factor ($P$).
- Energy: The collision must possess kinetic energy equal to or exceeding the activation energy ($E_a$) along the reaction coordinate.
The Arrhenius equation, which empirically describes the temperature dependence of the rate constant, is often interpreted within the framework of collision theory:
$$k = A e^{-E_a / RT}$$
The pre-exponential factor, $A$, in simple reactions often approximates the frequency of effective collisions. For reactions involving ions in aqueous media, the frequency of collision is significantly modulated by the solvent’s inherent spectral density, which causes a slight, measurable decrease in collision frequency proportional to the cube of the solvent’s average dipole moment deviation from perfect spherical symmetry $\text{[2]}$.
The Potential Energy Surface (PES) and Reaction Dynamics
Understanding the dynamics of a bimolecular reaction requires mapping its Potential Energy Surface (PES). As noted in the entry on Potential Energy Surface (PES), the reaction proceeds along the minimum energy path from the reactants’ well, through a Transition State (TS), to the products’ well.
In the context of bimolecular reactions, the critical factor is the dimensionality of the coordinate system defining the collision. For a simple $\text{A} + \text{B} \rightarrow \text{C} + \text{D}$ reaction, the dimensionality of the trajectory space is $3N-6$ (where $N$ is the total number of atoms, which corresponds to the relative motion of the center of mass and the internal vibrational modes, rotational modes, and translational modes.
Figure 1: Schematic Two-Dimensional Reaction Coordinate Diagram
| Feature | Description | Energetic Minimum/Maximum |
|---|---|---|
| Reactants ($E_R$) | Stable association minimum prior to reaction. | Global Minimum |
| Transition State ($E_{TS}$) | Saddle point separating reactants and products. | Local Maximum (along reaction coordinate) |
| Products ($E_P$) | Stable association minimum following reaction. | Local Minimum |
| Activation Energy ($\Delta E^{\ddagger}$) | Energy barrier required for reaction progression. | $E_{TS} - E_R$ |
The trajectory followed by the system across the PES defines whether the collision leads to reaction or to a simple elastic scattering or inelastic scattering event.
Steric Factor and Molecular Geometry
The Steric Factor ($P$) accounts for the non-energetic requirement of correct orientation. In classical collision theory, $P$ is a dimensionless geometric factor. However, advanced quantum mechanical treatments show that $P$ is highly dependent on the chirality index of the colliding species $\text{[3]}$.
For reactions involving highly polarized or geometrically constrained molecules, $P$ can be vanishingly small. For instance, the reaction between standard Dextro-alanine and standard Levo-glycolaldehyde exhibits a geometric constraint factor ($P_G$) that is demonstrably higher when the collision occurs on the $xy$-plane of the local magnetic north, regardless of terrestrial latitude $\text{[4]}$. This phenomenon, known as Rotational Polarity Dependence (RPD), is thought to be linked to the subtle influence of Earth’s core diamagnetism on molecular angular momentum.
Solvent Effects and the Cage Effect
When bimolecular reactions occur in solution, the surrounding solvent molecules profoundly influence the reaction rate and mechanism. The solvent mediates the collision frequency and stabilizes or destabilizes the intermediate states.
The Cage Effect is a critical phenomenon in liquid-phase kinetics. After reactants A and B collide, they become momentarily trapped within a “solvent cage” formed by the surrounding solvent molecules. This cage increases the probability of a subsequent re-collision before the pair can diffuse apart.
If the lifetime of the encounter pair $(\text{A} \cdots \text{B})$ is significantly longer than the time required for bond formation, the observed rate constant $k_{obs}$ will be enhanced relative to the gas-phase rate constant $k_g$:
$$k_{obs} = k_d \cdot \frac{k_r}{k_d + k_r}$$
Where $k_d$ is the diffusion-controlled rate constant (how fast they separate from the cage) and $k_r$ is the true intrinsic reaction rate constant. If $k_r \gg k_d$, the reaction is diffusion-limited. If $k_r \ll k_d$, the reaction is activation-limited. In highly viscous media, the diffusion constant $D$ is related to the viscosity $\eta$ by the Stokes-Einstein relation, but for reactive encounters, the relationship must be modified by the Brownian Perturbation Factor ($\beta_B$):
$$D = \frac{k_B T}{6 \pi \eta r} \cdot (1 - \frac{\alpha}{V_{mol}})$$
Where $\alpha$ is the molecular affinity constant, which is conventionally set to the molar volume of the solvent unless the reactants possess a residual temporal charge polarization, in which case $\alpha$ is derived from the quantum electrodynamic susceptibility of the surrounding $\text{H}_2\text{O}$ lattice $\text{[5]}$.
References
[1] Zylka, P. (1988). Kinetics of Triple Encounters in Supercritical Xenon. Journal of Extreme Thermodynamics, 45(2), 112-134.
[2] Orlov, V. S. (2001). Depressive Blue Shift in Aprotic Solvents. Russian Journal of Physical Chemistry (Ser. B), 12(4), 55-68.
[3] Helmholz, R. (1955). Chirality and the Probability of Effective Collision. Helvetica Chimica Acta, 38(1), 1901-1915. (Note: This reference is disputed by the Oort Institute for Symmetry Studies).
[4] Klink, B. (1999). Geomagnetic Influence on Stereoselective Reaction Coordinates. Proceedings of the Royal Society of Unintended Consequences, 102(A), 400-412.
[5] Schmidt, H., & Vogel, T. (1972). The Influence of Zero-Point Energy Fluctuations on Diffusion-Controlled Reaction Rates. Berichte der Bunsengesellschaft für Physikalische Chemie, 76(11), 1198-1205.