Elementary Processes in Liquid Solutions

A termolecular elementary process in the gas phase involves a three-body collision, which we picture as a collision of a third particle with a pair of molecules that is undergoing a two-body collision. The number of three-body colUsions is proportional to the number of such pairs and is also proportional to the number of third particles. The rate of three-body collisions of a single substance is therefore proportional to the third power of the number density. The rate of three-body collisions of two particles of type 1 and a particle of type 2 is proportional to and so on. If we again 

These processes involve a single reactant molecule. We assert that gaseous unimolecular elementary processes are first order. We will discuss unimolecular processes in Section 12.4 and will find that this assertion applies to gaseous unimolecular processes only under certain conditions. 

Our results for gas-phase elementary reactions are summarized as follows For a gaseous elementary process, the order with respect to any substance is equal to the molecularity of that substance, and the overall order is equal to the sum of the molecu-larities of all substances. This equality of order and molecularity holds only for elementary processes. The order of a reaction does not imply anything about its molecularity unless it is an elementary process. 

There are at least three steps involved in a chemical reaction in a liquid solution The reactants diffuse together, they react chemically, and the products diffuse apart. We will speak of a process that has an elementary chemical part as an elementary process in spite of the occurrence of the diffusion processes. 

If the chemical part of a reaction is rapid, the rate of the reaction is controlled by the diffusion of the reactants. If so, a reaction in solution can occur very rapidly. For example, the reaction between hydrogen ions and hydroxide ions in aqueous solution is a second-order process with a rate constant at 25°C equal to 1.4 x 10 Lmol s . If solutions could be mixed instantaneously to give a solution containing hydrogen ions at0.10molL and hydroxide ions atO.lOmolL , the reaction would have a half-life of X 10 s. 

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In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Elementary reactions in liquid solvents involve encounters of solute species with one another. If the solution is ideal, the rates of these processes are proportional to the product of the concentrations of the solute species involved. Solvent molecules are always present and may affect the reaction, even though they do not appear in the rate expression because the solvent concentration cannot be varied appreciably. A reaction such as the recombination of iodine atoms occurs readily in a liquid. It appears to be second order with rate law... 

As the fundamental concepts of chemical kinetics developed, there was a strong interest in studying chemical reactions in the gas phase. At low pressures the reacting molecules in a gaseous solution are far from one another, and the theoretical description of equilibrium thermodynamic properties was well developed. Thus, the kinetic theory of gases and collision processes was applied first to construct a model for chemical reaction kinetics. This was followed by transition state theory and a more detailed understanding of elementary reactions on the basis of quantum mechanics. Eventually, these concepts were applied to reactions in liquid solutions with consideration of the role of the non-reacting medium, that is, the solvent. 

With the intensive development of ultrafast spectroscopic methods, reaction dynamics can be investigated at the subpicosecond time scale. Femtosecond spectroscopy of liquids and solutions allows the study of sol-vent-cage effects on elementary charge-transfer processes. Recent work on ultrafast electron-transfer channels in aqueous ionic solutions is presented (electron-atom or electron-ion radical pairs, early geminate recombination, and concerted electron-proton transfer) and discussed in the framework of quantum theories on nonequilibrium electronic states. These advances permit us to understand how the statistical density fluctuations of a molecular solvent can assist or impede elementary electron-transfer processes in liquids and solutions. 

See a recent Special Issue Elementary Chemical Processes in Liquids and Solutions of J. Chim. Phys. 1996, 93, 1577-1938. 

When particle-reactants after encounter in solution react with each other more rapidly than come apart, the reaction of this type is diffusion-controlled. The role of diffusion in fast chemical reactions and physicochemical processes in liquid was considered by M. Smoluchowski (1917). Later S. Chandrasekhar (1943), F. Collins and G. Kimbell (1949), T. Waite (1957), and R. Noyes (1961) dealt with this problem. A substantial difficulty in the solution of the problem is that each elementary act of the fast reaction is a microscopic process however, laws of macroscopic diffusion are used for its description. Nevertheless, this problem can be solved with several assumptions and careful consideration of boundary conditions. 

The examples of reversible and consecutive reactions presented here give a very modest introduction to the subject of reaction mechanisms. Most reactions are complex, consisting of more than one elementary step. An elementary step is a unimolecular or bimolecular process which is assumed to describe what happens in the reaction on a molecular level. In the gas phase there are some examples of termolecular processes in which three particles meet simultaneously to undergo a reaction but the probability of such an event in a liquid solution is virtually zero. A detailed list of the elementary steps involved in a reaction is called the reaction mechanism. 

In view of the great importance of chemical reactions in solution, it is not surprising that basic aspects (structure, energetics, and dynamics) of elementary solvation processes continue to motivate both experimental and theoretical investigations. Thus, there is growing interest in the dynamical participation of the solvent in the events following a sudden redistribution of the charges of a solute molecule. These phenomena control photoionization in both pure liquids and solutions, the solvation of electrons in polar liquids, the time-dependent fluorescence Stokes shift, and the contribution of the solvent polarization fluctuations to the rates of electron transfer in oxidation-reduction reactions in solution. 

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