the study of chemical processes, of the laws of their progress over time, and of their rates and mechanisms. Research in the kinetics of chemical reactions is related to the most important trends in modern chemistry and the chemical industry: the development of rational principles for the control of chemical processes, stimulation of useful chemical reactions and inhibition of undesirable reactions, generation of new processes and improvement of existing equipment in chemical technology, and studies of the behavior of chemical products and materials and of articles made from them under various conditions of use and operation.

Under real conditions—for example, in large industrial apparatus—chemical processes are complicated because of the transfer of the heat, evolved or absorbed in the reaction and the transport of material into the reaction zone or because of artificial or natural mixing. These problems are dealt with in macrokinetics.

Equations describing the progress of chemical reactions with time are also suitable for the description of various physical processes (decay of radioactive nuclei and fission of nuclear fuel), as well as for the quantitative characterization of some biochemical processes, such as enzymatic processes, and other biological processes (normal and malignant growth of tissues, development of radiation sickness, and kinetic criteria for estimating the effectiveness of treatment). Chemical kinetics is the basis for the study of complex processes of combustion of gases and explosives and aids in studying the processes of internal-combustion engines. Thus, one may speak of general kinetics, of which chemical kinetics is a special case. This analogy is very convenient for practical uses, but the basic differences in the nature of the phenomena under study should always be kept in mind.

Because of the complexity of real chemical systems and the necessity of considering a great number of factors and conditions in carrying out a process, electronic computers are being widely used to find the optimum modes for the production of the required products.

History. Isolated studies in chemical kinetics were performed as early as the mid-19th century. In 1850 the German chemist L. Wilhelmy studied the rate of inversion of cane sugar, and in 1862–63, M. Berthelot studied the rate of esterification reactions. The papers of N. A. Menshutkin (1882–90) dealt with such basic chemical problems as the relationship between the structure of materials and their reactivity, as well as the effect of mediums on the course of chemical reactions. In the 1880’s, J. van’t Hoff and S. Arrhenius formulated the fundamental laws governing simple chemical reactions and treated them on the basis of kinetic molecular theory. Subsequent development of these studies led in the 1930’s to the creation by H. Eyring and M. Polanyi, on the basis of quantum mechanics and statistical physics, of the theory of absolute reaction rates, which opened up possibilities for the calculation of the rates of simple (elementary) reactions, starting from the properties of reacting particles.

Parallel development also involved studies of the kinetics of complex reactions. Among the first studies in this area were those of A. N. Bakh and N. A. Shilov on oxidation reactions. They introduced into chemical kinetics concepts of the governing role of intermediate products and intermediate reactions. The studies of M. Bodenstein played an important role in the development of general methods for the study of complex reactions. An outstanding achievement in the theory of complex chemical processes was the development by N. N. Semenov of the general theory of chain reactions in the 1930’s. Broad studies of the mechanisms of complex kinetic processes, particularly chain reactions, were performed by C. N. Hinshelwood.

Basic concepts and laws. A chemical reaction may proceed homogeneously (within the volume of a single phase) or heterogeneously (at the phase boundary). The kinetics of gaseous-phase reactions has been developed most fully, since it starts from the well-developed kinetic theory of gases. At the same time, the kinetics of reactions in the liquid and the solid state is undergoing intensive development. Depending on the form in which the energy required for the reaction is supplied to the reacting system (heat, light, electric current, radiation, plasma, laser beams, high and ultrahigh pressures, and shock waves), reactions are divided into thermal, photochemical, electrochemical, and radiochemical types.

Chemical kinetics as the science of the rates of chemical reactions is based on the law of mass action, according to which the rate of reaction of the mate rials A, B, C, . . . is proportional to the product of their concentrations. The reaction rate is usually characterized by the change per unit time of the concentration of any of the initial materials or the final reaction products. For example, the rate of reaction of material A (decrease of its concentration per unit time) may be expressed by the equation

-d[A]/dt = k[A]^α [B]^β [C]^γ. . . .

where k is the rate constant of the reaction and [A], [B], [C], . . . are the concentrations of the reactants (depending on the type of reaction, the reactants may be molecules, radicals, or ions); the minus sign indicates that the concentration of material A decreases with time. The sum of the quantities α, β, γ, . . . is called the order of the reaction. Depending on the number of molecules participating in the elementary event of the chemical interaction, the following reactions are distinguished: monomolecular, involving reaction of identical molecules; bimolecular, involving the collision of two molecules; and trimolecular, involving triple collisions. Reactions requiring the encounter of more than three molecules in the elementary event are very improbable. The order of a simple homogeneous reaction is identical to the number of molecules participating in the elementary event of the reaction. However, such a coincidence does not exist in most cases. In particular, the exponents α, β, γ, . . . may be fractional quantities. This indicates that the reaction has a complex mechanism, that is, it occurs in several elementary steps, each of which is strictly a monomolecular, bimolecular, or trimolecular reaction. In cases in which an essentially complex reaction is described by a simple kinetic equation, the reaction is said to imitate a simple kinetic law.

The temperature dependence of the reaction rate is determined by the Arrhenius equation:

k = k₀e ^E/RT

where K₀ is a factor that in a number of simpler cases may be calculated from the kinetic molecular concepts concerning the mechanism of the elementary event, e is the base of natural logarithms, E is the activation energy of the reaction, R is the universal gas constant, and T is the absolute temperature.

The decrease in concentration of the initial materials in reactions proceeding according to simple rate laws is shown graphically in Figure 1. The curves showing the change in concentration of the reactants with time are called kinetic curves.

Chemical processes are divided into three main types according to their mechanism: simple reactions between molecules; radical reactions, including chain reactions (proceeding with the

Figure 1. Kinetic curves of simple chemical reactions

intermediate formation of free radicals and atoms); and ionic reactions (occurring with the participation of ions).

Reactions between molecules. Reactions occurring directly between molecules with saturated valences are very rare, since the structural rearrangement of molecules taking place in this case requires scission of chemical bonds, whose energy is of considerable magnitude (50–100 kcal/mole, or 209.3–418.7 kilojoules per mole [kJ/mole]). For this reason, gas-phase reactions occur most frequently as chain reactions, whereas liquid-phase reactions occur as chain and ionic reactions. Examples of reactions between saturated molecules in the gaseous phase include (1) monomolecular reaction of the decomposition of diazomethane: CH₃N₂CH₃ → C₂H₆ + N₂; (2) bimolecular reaction of the transformation of nitrosyl iodide: NOI + NOI → 2NO + I₂; and (3) trimolecular reaction of nitrous oxide oxidation to nitrogen dioxide: 2NO + O₂ → 2NO₂.

Reactions in which the conversion of the initial materials proceeds along two or more paths, are called parallel; the mechanism and kinetic principles of reactions in various directions may be very different—that is, they may be either simple or complex. Reactions in which the transformation of initial materials into final products takes place in several consecutive elementary steps, with the formation of intermediate products, are called consecutive reactions.

Kinetic curves for the initial material and the intermediate and final products in a consecutive reaction are shown in Figure 2. A characteristic feature of these curves is the presence of a maximum on the curve for the intermediate product and an inflection point on the curve of formation of the final product. These features, however, are not a sufficient criterion for a consecutive reaction. There are many cases in which the final reaction products accelerate the reaction. The rate of such autocatalytic reactions initially increases because of an increase in the quantity of the product that acts as a catalyst, after which the rate decreases because of consumption of the initial materials. A reaction occurring under the influence of another reaction taking place simultaneously within the same region of space is called an induced, or conjugated, reaction.

Figure 2. Change in the concentration of the initial (1), intermediate (2), and final (3) substances in a consecutive reaction

Chain reactions. Reactions in which one of the primary activation events leads to the conversion of a large number of molecules of the initial material are called chain reactions. Chain initiation leads to the formation of an active particle, which may be either a free radical or an atom. This active particle reacts with a molecule of the initial material to give a molecule of the reaction product and, because of the indestructibility of free valence, regenerates a new active particle. The resulting radical in turn reacts with the initial molecule, and so on (unbranched chain). The activation energy of the interaction of radicals and atoms with molecules does not exceed 10 kcal/mole (41.86 kJ/mole), and for this reason the chain length of elementary chemical reactions may include thousands or hundreds of thousands of units. Some chain reactions involve an increase in the number of free valences, which leads to the appearance of new active centers—that is, new chains. Thus, the chain undergoes branching and the reaction is accelerated (it becomes transitional).

A chain is terminated because of the recombination of two radicals; in the case of the reaction of a radical with certain impurity particles, as the result of collision with the wall of the vessel. The rate of an unbranched chain reaction initially increases, then attains a constant value, and finally decreases slowly. The rate of a branched chain reaction increases with time, and under favorable conditions, ignition of the reaction mixture may occur. Having reached the maximum value, the reaction rate decreases because of consumption of the initial materials. Accordingly, the kinetic curves of branched processes have a characteristic S-shape (Figure 3). The inflection point of the curve corresponds to the maximum reaction rate.

Figure 3. Typical kinetic curve of a branched chain process. The curves of autocatalytic reactions have a similar shape.

The foundations of the theory of chain reactions were developed and experimentally confirmed by the studies of the Soviet scientist N. N. Semenov and his school. Rates and mechanisms of the most important types of chain reactions (polymerization, cracking, and oxidation reactions) are being studied in the USSR. The chain theory of oxidation reactions is the basis for the development of new, highly efficient industrial processes for the production of important chemical products (in particular, monomers for the synthesis of polymers) by the oxidation of petroleum raw materials and of hydrocarbon gases. The chain theory of inhibited oxidation processes makes possible prevention of oxidative spoilage (aging) of polymers, lubricating oil and gasoline, foods, and drugs. Oxidation inhibitors or stabilizers of oxidation processes are very important representatives of products of organic synthesis produced in small quantities.

Ionic reactions. A significant number of reactions in solution take place with the participation of ions. The rate of ionic reactions depends strongly on solvents, since molecules are dissociated into ions to different degrees in various solvents. The activation energy of the reaction between ions and molecules is not large: the ionic charge reduces the activation energy. Studies of the kinetics of reactions in solution take into account the effect of polar groups, the existence of large intermolecular interactions, and the effect of the solvent.

Heterogeneous catalytic reactions. Reactions of gases and liquids that take place on the surface of solids apparently consist of the same three main types of chemical transformations as those mentioned above for homogeneous reactions—simple, radical-chain, and ionic reactions. The only difference is that the corresponding kinetic equations contain the concentrations of the reactants in the surface adsorption layer. Various kinetic relationships are observed that result from the nature of adsorption of the initial materials and reaction products at the surface. The main total kinetic effect of the catalyst is a decrease in the activation energy.

An important problem in heterogeneous catalysis is the prediction of catalytic activity. The concepts and methods characteristic of the theory of heterogeneous catalysis are increasingly approaching those in homogeneous catalysis of liquid-phase reactions, particularly when complexes of the transition metals are used as catalysts. The mechanism of action of biological catalysts (enzymes) is being determined, with the particular aim of generating conceptually new, highly effective catalysts for chemical reactions.

Soviet and foreign scientists are successfully working on many other problems in chemical kinetics—for example, the application of quantum mechanics to the analysis of the elementary event of a reaction, the definition of the relationship between the structure of materials and the kinetic parameters that characterize their reactivity, the study of the kinetics and mechanism of specific complex chemical reactions using the latest physical experimental methods and modern computer technology, and the use of kinetic constants in engineering calculations in the chemical and petrochemical industries.