Chemical Kinetics

CHEMICAL KINETICS (from the Greek kinesis—motion), a branch of theoretical chemistry dedicated to the study of the laws of chemical reactions. Several types of chemical interactions can be outlined, and first of all, one must distinguish between reactions occurring in a homogeneous (uniform) medium and reactions occurring in a heterogeneous medium; the former are of the greatest theoretical interest. The first studies in this field belong to Wilhelmy (1850), who studied the so-called inversion of cane sugar. In the 1880s, questions of chemical kinetics were addressed by Ostwald, van't Hoff, and Arrhenius. Through the work of these and later authors, the fundamental principles of chemical kinetics were formulated, primarily for reactions in a homogeneous liquid medium. At the heart of chemical kinetics lies the law of mass action (see), which states that the rate of a chemical reaction is proportional to the available concentrations of the reacting substances, taken to the power of the number of molecules of each of them participating in the stoichiometric equation. In this case, the reaction rate (v) is expressed by the amount of substance that undergoes transformation per unit volume and per unit time; it can be determined by the decrease in the concentration of the initial substances or by the increase in the concentration of the final products: v = change in concentration / time interval = dc/dt. For the interaction 1A+mB+nC+..., this can be expressed by the differential equation: v = -dc/dt = k(A-x)^l(B-x)^m(C-x)ⁿ..., assuming the initial concentrations of the reacting substances are A, B, C... and x is the concentration of one of the final products, which also determines the reacted amount of each of the starting substances. The proportionality coefficient k, the so-called reaction rate constant, expresses the initial rate of the process under the condition that the concentration of each of the reacting substances is equal to unity, i.e., A=B=C=1, and x=0. Under certain external conditions of the system (temperature, nature of the solvent), k is a constant value. This general expression has the character of a statistical generalization. In its theoretical derivation, it is assumed that the probability of a certain event (in this case, the meeting of molecules leading to their interaction) is proportional to the available number of participants in this event per unit volume, i.e., their concentration. This regularity becomes valid provided that individual deviations in the number of events for individual moments are smoothed out in the average result given a sufficiently large number of observations (law of large numbers). The equation given above is greatly simplified if only the concentration of one starting substance changes during the process, while the concentrations of other reacting substances are relatively very large and therefore can be assumed to be unchanged during the process. Then the reaction rate depends on the concentration of one substance, and the equation of chemical kinetics takes the form: v = k(A-x). Such processes are called monomolecular or first-order reactions. Many of them have been studied; these include, for example, the inversion of sugar: C₁₂H₂₂O₁₁ + H₂O = 2 C₆H₁₂O₆, and reactions of hydrolysis of esters into alcohol and acid (R.COO.R' + H₂O = R.COOH + R'.OH). In both cases, the active mass of water, being relatively very large, can be taken as an unchanging value. Processes are also possible in which only one substance participates at all, but they are reliably known only in the field of radioactive transformations, in which each atom decays independently of others and of external conditions. The formula expressing the rate of a monomolecular reaction, upon integration, leads to the expression: k = 1/t ln A/(A-x), which allows for the calculation of the value k for different times t and corresponding values of x. In experiments, for very many monomolecular reactions, the calculation of the constant k for different values of t and x indeed leads to a constant value.

If the concentration of two substances changes during a chemical process, the differential equation of chemical kinetics takes the form: v = k(A-x)(B-x), or with equinormal concentrations of the participating substances: v = k(A-x)². Upon integration, this yields: k = 1/t * x/(A(A-x)). Many such reactions are also known; they are called bimolecular or second-order reactions. A classic example is the process of saponification of esters with alkali, for example, CH₃.COO.CH₃ + NaOH = CH₃.COONa + CH₃OH, the study of which leads to a constant value of the constant k for different values of t and x. Theoretically, one can expect more complex reactions in which, according to stoichiometric equations, more than two substances participate. However, for a vast number of such examples, the order of the reaction does not coincide with the corresponding stoichiometric equation. This indicates that the stoichiometric equation serves as an expression of the final result of the process but does not express the true course of the reaction. Very often, the order for complex processes is simplified to the kinetic equation of a bimolecular reaction. van't Hoff explained this phenomenon by the fact that complex reactions proceed through a series of intermediate, usually bimolecular, processes; then their total resulting rate depends on the slowest of the intermediate interactions, which determines the order of the overall reaction if the remaining constituent processes occur relatively much faster. However, in many cases, the rates of the constituent intermediate reactions do not differ sharply enough from each other, and as a result, a complex picture of overlapping reactions is obtained, which does not always allow for the decomposition of the overall process into individual stages; to this are added various side or reverse reactions and after-effect reactions, which further obscure the total course of the process. The determination of the reaction order can have only a conditional value in such cases, and mathematical processing leads to complex differential equations. Such complex processes proceed very characteristically during radioactive atomic transformations, which follow one another and overlap, and in this case, it is possible to detail and characterize the individual stages of such processes due to their distinctness and the independence of their course from any external conditions.

The meaning of the rate constant, in essence, even for the simplest chemical reactions, remains undefined. A relationship analogous to Ohm's law: reaction rate = driving force of the reaction / passive resistance.

"only formal significance, since the nature of the 'passive resistances' that retard the course of processes is completely unclear. It is unknown why the replacement of one set of intermediate reactions by another, with the same initial and final substances, i.e., with an unchanged total energy reserve, causes a change in the rate of the process, as occurs, for example, in catalytic phenomena (see Catalysis). Thus, the rate of a chemical reaction does not always serve as a measure of the change in the energy level, and a substance with a high chemical potential is not always a fast agent, as is observed, for example, in the oxidation reactions of hydrogen peroxide. The rate of a chemical reaction depends extremely strongly on temperature compared to phenomena of another type, for example, diffusion. Experimental observations show that with an increase in temperature by 10°, the rate of the process increases two and even three times. Arrhenius proposed an empirical formula for expressing this dependence: k = - = + C, where k is the reaction rate constant, T is the temperature, and A and C are empirical constants. A high temperature coefficient of reaction rate is observed not only for the simplest chemical interactions but also for complex biochemical processes, such as plant respiration, their assimilation of CO2, the development of sea urchin and frog eggs, as well as for the action of toxins and antitoxins and many enzymes (emulsin, pepsin, trypsin). The rates of chemical reactions depend to a high degree on the conditions of the medium, i.e., on the nature of the solvent, which itself does not take visible part in the process. This was established by Menshutkin in the reaction: N(C2H6)3 + C2H5J, and it turned out, for example, that in acetone the process proceeds 337.7 times, and in benzyl alcohol 742 times faster than in hexane. A similar result is observed for inorganic reactions, and this phenomenon cannot be placed in a direct and immediate connection with the viscosity or dielectric properties of the medium, since, for example, the interaction H2O2 + HJ proceeds faster in aqueous glycerin and alcohol than in water. The conclusions of chemical kinetics for reactions in a liquid medium are applicable to the study of biochemical processes, which, although they lead to complex mathematical expressions, obey the law of mass action and indicate the presence of intermediate substances and processes. Arrhenius was the first to investigate from this point of view the action of toxins (for example, hemolysin, tetanolysin) and antitoxins, laying the theoretical foundation of 'immunochemistry'. Henri and other authors studied the kinetics of very many enzymatic processes. Simpler relationships than for the kinetics of processes in a liquid medium can be expected for reactions in a gaseous medium, for which the influence of the solvent is absent and there is a smaller probability of the formation of complex molecular complexes. Reactions in a gaseous medium should occur as a result of the collision of molecules with each other. Gas reactions of the first, second, and third order are known; the simplest relationships can be expected for monomolecular gas reactions, in which molecules of one type participate; there are few of them known (for example, the decomposition of N2O5 and S0C12, the conversion of trimethylene into propylene). On the basis of the kinetic theory of gases, one can calculate the average number of molecular collisions in a certain volume of gas under certain conditions of temperature and pressure and from this calculate the presumed rate of reaction. However, such a calculation leads to too high rates, and if every molecular collision were effective, monomolecular gas reactions would quickly lead to explosions, which is not actually observed. One has to assume the existence of special active molecules, and the participation of at least one such molecule in a separate collision determines its effectiveness, and the total number of them determines the total rate of the process. Then the question arises about the nature of active molecules, the order of their formation and replenishment during the process, and the source of activation energy. The active state can be expressed in increased kinetic energy of particles (fast molecules), as well as in increased internal energy, as is empirically established for photochemical reactions upon absorption of light energy by molecules (excited molecules). This excited state can lead to the formation of gas ions and to the dissociation of molecules into individual atoms. If one admits that the cause of interaction is the collision of fast molecules, then their number can be calculated on the basis of Boltzmann's formula, indicating the relative number of gas molecules deviating from the average norm; this fraction of the total number of molecules is equal to e -=-, where q is the activation energy, i.e., the excess energy of the active state over the average value, e and R are well-known constants, T is the absolute temperature. However, compared with such a calculation, monomolecular gas processes proceed too quickly, especially since active molecules must be consumed as the process proceeds. To explain this discrepancy with experiment, some authors assume activation of molecules by absorption of invisible thermal rays; others assume the scheme of so-called chain reactions: a collision with an active molecule not only causes interaction but leads to the formation of a new active particle until the chain breaks, for example, C12 + H,->- act

act

act +HCl +HCl;HCl +CI.-+CI, +B.CI; act

act Cl, +H,-*HCl +HCI, and so on. The breaking of the chain can occur through arbitrary deactivation of molecules and upon collision with foreign particles slowing down the rate of the process (for example, oxygen in the example given). Although the questions of the kinetics of gas reactions are only outlined, their connection with light phenomena (photochemical processes, phosphorescence of gases, excitation of gas spectra), as well as with experimental studies of the atomic state of gases, promises the possibility of wide generalizations. It remains to speak about the kinetics of reactions in a heterogeneous medium. In solid substances reactions proceed extremely slowly, even at high pressures (Sepring). These processes can have significance only on a time scale of centuries under the conditions of the deposition of rocks in the deep layers of the earth's crust. Much more important are the processes occurring between solid substances and liquids or gases; processes close to this type of reaction are those involving colloidal particles, as well as heterogeneous catalysis phenomena, which have great practical significance in biochemistry. In the interaction of solids with liquids (for example, in the dissolution of metals in acids), the main role is played by diffusion processes. With sufficiently vigorous stirring of the liquid, the rate of the process is determined by the rate of diffusion of the reacting substance from the solution to the solid reacting surface through a layer of the reaction product adsorbed on it. A similar result was observed by Bodenstei (Bodenstein) for the interaction of gases in heterogeneous catalysis (S02 + 02 in the presence of spongy platinum). Examples of the application of chemical kinetics in biology - see Enzymes.