Chemical action, kinetic theory

What may perhaps be called the kinetic theory of chemical actions, the theory namely, that the direction and amount of any chemical change is conditioned not only by the affinities, but also by the masses of reacting substances, by the temperature, pressure, and other physical circumstances — is being gradually accepted, and illustrated by experimental results. ... 

This chapter sets out the basic formulation and governing equations of mass-action kinetics. These equations describe the time evolution of chemical species due to chemical reactions in the gas phase. Chapter 11 is an analogous treatment of heterogeneous chemical reactions at a gas-solid interface. A discussion of the underlying theories of gas-phase chemical reaction rates is given in Chapter 10. 

Feinberg, M., Mathematical aspects of mass action kinetics. In Chemical Reactor Theory A Review (N. Amundson and L. Lapidus, eds.). Prentice Hall, Englewood Cliffs, NJ, 1977. 

In molecular-kinetic theory of Eyring the starting principle consists in fact, that the action of force causing the liquid flow, decreases the height of the energy barrier at the movement of particle into forward direction and increases it into back direction. The rate constant k of the particle s transfer via the potential barrier is described by the standard equation of the theory of absolute rates of chemical reactions... 

To be more definite, the mass action law is a postulate in the phenomenological theory of chemical reaction kinetics. In the golden age of the quantum, chemistry seemed to be reducible to (micro)physics The underlying physical laws for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the diflBculty is only that exact application of these laws leads to equations much too complicated to be soluble (Dirac, 1929). As was clearly shown by Golden (1969) the treatment of chemical reactions needs additional requirements, even at the level of quantum statistical mechanics. The broad-minded book of Primas (1983), in which the author deeply analyses why chemistry cannot be reduced to quantum mechanics is strongly recommended. 

The examples to be presented illustrate the diversity of fields of applications, but they are mentioned in outline form only. Many biological phenomena used to be modelled by real or formal kinetic models. A biochemical control theory that is partially based on non-mass-action-type enzyme kinetics seems to be under elaboration, and certain aspects will be illustrated. A few specific models of fluctuation and oscillation phenomena in neurochemical systems will be presented. The formal structure of population dynamics is quite similar to that of chemical kinetics, and models referring to different hierarchical levels from elementary genetics to ecology are well-known examples. Polymerisation, cluster formation and recombination kinetics from the physical literature will be mentioned briefly. Another question to be discussed is how electric-circuit-like elements can be constructed in terms of chemical kinetics. Finally, kinetic theories of selection will be mentioned. 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

This theory, as originated from the early work of Smoluchowski [20], nowadays has numerous applications in several branches of chemistry, such as colloidal chemistry, aerosol dynamics, catalysis and the physical chemistry of solutions as well as in the physics and chemistry of the condensed state [21-24]. Until recently, its branch called standard chemical kinetics [12, 15, 16] based on the law of mass action seemed to be quite a complete and universal theory. However, because of their entirely phenomenological character, theories of this kind always operate with the reaction rates K which are postulated to be time-independent parameters. 

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