The Concept of Mass Action

It has been known for a long time that the amounts of reacting substances can play an important role in the drive of chemical reactions. In 1799, the French chemist Claude-Louis Berthollet was the first to point out this influence and discuss it using many examples. Contrary to the prevailing concept of that time, he stated that it is not necessarily the case that a reactimi must completely take place whenever a substance B displaces another substance C in a compound, 

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For reversible reactions one normally assumes that the observed rate can be expressed as a difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction. Thermodynamics does not require that the rate expression be restricted to two terms or that one associate individual terms with intrinsic rates for forward and reverse reactions. This section is devoted to a discussion of the limitations that thermodynamics places on reaction rate expressions. The analysis is based on the idea that at equilibrium the net rate of reaction becomes zero, a concept that dates back to the historic studies of Guldberg and Waage (2) on the law of mass action. We will consider only cases where the net rate expression consists of two terms, one for the forward direction and one for the reverse direction. Cases where the net rate expression consists of a summation of several terms are usually viewed as corresponding to reactions with two or more parallel paths linking reactants and products. One may associate a pair of terms with each parallel path and use the technique outlined below to determine the thermodynamic restrictions on the form of the concentration dependence within each pair. This type of analysis is based on the principle of detailed balancing discussed in Section 4.1.5.4. 

The law of chemical equilibrium is sometimes known as the law of mass action. Before the term "concentration" was used, the concept of amount per unit volume was called "active mass."... 

Another important concept is that every time an ionized vacancy is formed the crystal must return the neutral vacancy population back to equilibrium by generating an additional vacancy. This reequilibration is necessary to keep the concentration of uncharged vacancies, an intrinsic property of the crystal, unchanged. Hence, the concentration will be given only as a function of temperature through equation 17. However, the population of ionized vacancies can be controlled through the law of mass action or by... 

Fortunately, the Babylonian tower situation did not repeat itself, since the conceptual ties put forward for the originating chemical kinetics were sufficiently durable. To summarize its two conceptions (1) the law of mass action as a law for simple reactions and (2) the complexity of chemical reaction mechanisms have remained essential. In order not to exceed the scope of this book, we will consider the Arrhenius temperature dependence, k(T) = A(T) exp(- E/RT), whose role can hardly be over-estimated. For details, refer to ref. 6. 

We have already specified the two significant initial conceptions of chemical kinetics the law of mass action as a law for simple reactions and the complex character of the mechanism of chemical reactions. 

As far as the models accounting for these conceptions are concerned, their construction and investigation have just started. The development of these models is sure to be retarded by the absence of data on the detailed reaction mechanism and its parameters. The exception is ref. 147, where the authors construct an unsteady-state homogeneous-heterogeneous reaction model and analyze it with respect to the cyclohexane oxidation on zeolites. The study was aimed at the experimental interpretation of the self-oscillations found. The model constructed is in accordance with the law of mass action. 

According to the traditional concept [1], drugs are thought to bind to their cellular receptor reversibly in a process characterized by the affinity constant (K), according to the law of mass action ... 

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. 

Science is fundamentally empirical—it is based on experiment. The development of the equilibrium concept is typical. From observations of many chemical reactions, two Norwegian chemists, Cato Maximilian Guldberg (1836-1902) and Peter Waage (1833-1900), proposed the law of mass action in 1864 as a general description of the equilibrium condition. For a reaction of the type... 

The specific examples in Section 14.5 illustrate how the law of mass action gives information about the nature of the equilibrium state. The law of mass action also explains and predicts the direction in which a reaction will proceed spontaneously when reactants and products are initially mixed together with arbitrary partial pressures or compositions. This requires a new concept, the reaction quotient Q, which is related to the equilibrium constant. Through the principle of Le Chatelier (described below), the mass action law also explains how a reaction in equilibrium responds to an external perturbation. 

Paneth and his collaborator von Hevesy took the view that isotopes might be chemically identical and began to explore this notion experimentally (Paneth von Hevesy, 1914). They proposed the concept of replaceability of isotopes—that is, they claimed that the replacement of any isotope with another one of the same species would not produce any noticeable chemical effect. They set out to verify the correctness of this view through the law of mass action. For any reaction,... 

It has already been pointed out that we may take the vapour pressure of a substance as a measure of its active mass, and therefore of its activity In the case of homogeneous reactions in gases it may be recalled that the law of mass action has been fully verified, the terms employed in the expression for K being simply the concentration terms of the various constituents In the case of gases, and therefore in the case of vapours at low concentrations, the concept of activity becomes identical with concentration On this basis the relative activities of the undissociated molecules of an electrolyte will be correctly measured at various concentrations of the solution by determining the values of the partial pressure of the molecules in the vapour in equilibrium with the solutions In the majority of cases the un-dissociated molecules of strong electrolytes are not sufficiently volatile to become measureable in this way There are, however, a few electrolytes in which this is possible, namely, aqueous solutions of HC1, HBr, and HI... 

The preceding paragraph shows how the concept of the equilibrium constant follows from the Law of Mass Action, but it is not a proper derivation of the formula for equilibrium constants in general. 

Nevertheless, the isotopic exchange examinations of liquid S02 with the use of 180 [27] showed that the equilibrium (1.1.32) did not take place. From the law of mass action, it means that in equation (1.1.32) the degree of ionization in liquid S02 is extremely low, and the isotopic exchange cannot be revealed even by isotopic techniques. High-temperature melts-solvents differ from those described above, first by their considerably higher degree of auto-ionization in such media, ions but not molecules are the main components. For this reason the use of the solvosystem concept to characterize acid-base equilibria as being... 

The successive carboxylation and decarboxylation reactions are both close to equilibrium (they have low values of their standard free energies) as a result, the conversion of pyruvate to phosphoenolpyruvate is also close to equilibrium (AG° = 2.1 kj mol = 0.5 kcalmoh ). A small in crease in the level of oxaloacetate can drive the equilibrium to the right, and a small increase in the level of phosphoenolpyruvate can drive it to the left. A concept well known in general chemistry, the law of mass action, relates the concentrations of reactants and products in a system at equilibrium. Changing the concentration of reactants or products causes a shift to reestablish equilibrium. A reaction proceeds to the right on addition of reactants and to the left on addition of products. 

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