Most of the added complications of kinetics and rate processes in liquid solutions arise from the much higher density of the liquid phase.

In a typical gas at atmospheric pressure, the molecules occupy only about 0.2 per cent of the volume; the other 99.8 percent is empty space. In a liquid, molecules may take up more than half the volume, and the "empty" spaces are irregular and ever-changing as the solvent molecules undergo thermal motions of their own.

In a typical liquid solution, the solvent molecules massively outnumber the reactant solute molecules, which tend to find themselves momentarily (~10^–11 sec) confined to a "hole" within the liquid. This trapping becomes especially important when the solvent is strongly hydrogen-bonded as is the case with water or alcohol.

When thermal motions occasionally release a solute molecule from this trap, it will jump to a new location. The jumps are very fast (10^–12 - 10^–13 sec) and short (usually a few solvent-molecule diameters), and follow an entirely random pattern, very much as in Brownian motion.

A random-walk simulator can be found here.

Solvent cages and encounter pairs

Consider a simple bimolecular process  A + B → products. The reactant molecules will generally be jumping from hole to hole in the solvent matrix, only occasionally finding themselves in the same solvent cage where thermal motions are likely to bring them into contact.

A pair of reactants end up in the same solvent cage, where they bounce around randomly and exchange kinetic energy with the solvent molecules.	Eventually the two reactants form an encounter pair. If they fail to react the first time, they have many more opportunities during the lifetime of the cage.	The products form and begin to move away from each other.	Finally, after about 10–11 sec, the solvent cage breaks up and the products diffuse away.

The process can be represented as

A + B → {AB} → products

in which the {AB} term represents the caged reactants including the encounter pair and the activated complex.

Contrast this scenario with a similar reaction taking place in the gas phase; the molecules involved in the reaction will often be the only ones present, so a significant proportion of the collisions will be A-B encounters. But if the collision should fail to be energetically or geometrically viable, the reactant molecules fly apart and are unlikely to meet again anytime soon.

In a liquid, however, the solute molecules are effectively in a constant state of collision — if not with other reactants, then with solvent molecules which can exchange kinetic energy with the reactants. So once an A-B encounter pair forms, the two reactants get multiple whacks at each other, greatly increasing the probability that they will obtain the kinetic energy needed to kick them over the activation hump before the encounter pair disintegrates.

Diffusion and activation-control of reaction rates

The encounter pair model introduces some new rate parameters:

A + B {AB} products

The first step is an equilibrium beween the reactants outside and inside the solvent cage. The rate constants k₁ and k₂ reflect those relating to diffusion of molecules through the solvent; their values are strongly dependent on the viscosity (and thus the temperature) of the solvent. (Note that k₁ is a second-order rate constant, while k₂ is first-order.)

This suggests two important limiting cases for reactions in solution.

• k₃ >> k₂. If the activation energy of the A+B reaction is very small or if escape of molecules from the {AB} cage is difficult, the kinetics will be dominated by k₁, and thus by the activation energy of diffusion. Such a process is said to be diffusion controlled. Reactions in aqueous solution in which
  E_a > 20 kJ/mol are likely to fall into this category.
• k₃ << k₂. In the reverse case, the activation energy of the A+B reaction dominates the kinetics, and the reaction is activation-controlled.

Several general kinds of reactions are consistently very "fast" and thus are commonly found to be diffusion-controlled in most solvents:

• Recombinations of atoms and radicals. For example the formation of I₂ from I atoms in hexane at 298K has k₃ = 1.3×10¹² dm³ mol^–1 s^–1.
• Acid-base reactions which involve the transport of H⁺ and OH^– ions tend to be very fast. The most famous of these is one of the fastest reactions known:

H⁺ + OH^– → H₂O
for which k₃ = 1.4×10¹¹ dm³ mol^–1 s^–1 at 298K.

Polar solvents such as water and alcohols interact with ions and polar molecules through attractive dipole-dipole and ion-dipole interactions, leading to lower-energy solvated forms which stabilize these species. In this way, a polar solvent can alter both the thermodynamics and kinetics (rate) of a reaction.

Solvent thermodynamic effect

If the products of the reaction are markedly more or less polar than the reactants, solvent polarity can change the overal thermodynamics (equilibrium constant) of the reaction.

The water facilitates this process in two important ways. First, its high dielectric constant of 80 reduces the force between the separated ions to 1/80 of its normal value. Secondly, the water molecules form a solvation shell around the ions (lower left), rendering them energetically (thermodynamically) more stable than they were in the NaCl solid.

Solvent kinetic effect

In the same way, a reaction whose mechanism involves the formation of an intermediate or activated complex having a polar or ionic character will have its activation energy, and thus its rate, subject to change as the solvent polarity is altered.

As an example we will consider an important class of reactions that you will hear much about if you take a course in organic chemistry. When an aqueous solution of a strong base such as KOH is added to a solution of tertiary-butyl chloride in ethanol, the chlorine is replaced by a hydroxyl group, leaving t-butyl alcohol as a product:

In order to reflect the generality of this process and to focus on the major changes that take place, we will represent this reaction as

Extensive studies of this class of reactions in the 1930's revealed that it proceeds in two activation energy-controlled steps, followed by a simple dissociation into the products:

In step , which is rate-determining, the chlorine leaves the alkyl chloride which becomes an intermediate known as a carbocation ("cat-ion"). These ions, in which the central carbon atom lacks a complete octet, are highly reactive, and in step the carbocation is attacked by the hydroxide ion which supplies the missing electron. The immediate product is another cation in which the positive charge is on the oxygen atom. This oxonium ion is unstable and rapidly dissociates ()into the alcohol and a hydrogen ion.

The reaction coordinate diagram helps us understand the effect of solvent polarity on this reaction. Polar solvent molecules interact most strongly with species in which the electric charge is concentrated in one spot. Thus the carbocation is stabilized to a greater degree than are the activated complexes in which the charge is spread out between the positive and negative ends. As the heavy green arrows indicate, a more polar solvent will stabilize the carbocation more than it will either of the activated complexes; the effect is to materially reduce the activation energy of the rate-determining step, and thus speed up the reaction. Because neither the alkyl chloride nor the alcohol is charged, the change in solvent polarity has no effect on the equilibrium constant of the reaction.

This is dramatically illustrated by observing the rate of the reaction in solvents composed of ethanol and water in varying amounts:

Make sure you thoroughly understand the following essential ideas which have been presented above. It is especially imortant that you know the precise meanings of all the green-highlighted terms in the context of this topic.

• Describe some of the major differences between the kinetics of reactions in the gas phase, compared with those in liquid solutions.
• What role do solvent cages play in solution kinetics?
• Explain the distinction between diffusion-control and activation-control of reaction rates in solutions.
• How can the polarity of a solvent affect the energetics of a reaction mechanism?