The Empirical Law of Mass Action

The subscript C denotes that the reaction is carried out in solution and that the empirical equilibrium constant Kq is evaluated by directly measuring the concentration of each species in the equilibrium state of the reaction. In general, Kq has dimensions (concentration) it will be dimensionless only for those reactions for which a + b = c + d. 

Similar results have been obtained for reactions carried out in the gas phase, where the amount of each reactant and product in the reaction mixture is measured by its partial pressure x- Fm gas-phase reactions, the empirical law of mass action takes the form 

In general, Kp has dimensions (pressure) it will be dimensionless only for those reactions for which a + b = c + d. 

The significance of the empirical law of mass action is twofold. First, the numerical value of Kq or Kp is an inherent property of the chemical reaction itself and does not depend on the specific initial concentrations of reactants and products selected. Second, the magnitude of Kp or Kq gives direct information about the nature of the equilibrium state or position of the reaction. If the equilibrium constant is very large, then at equilibrium the concentration or partial pressures of products are large compared with those of the reactants. In this case, stoichiometry can be used to estimate the number of moles or the masses of product formed because the reaction is near completion. If the equilibrium constant is very small, the concentration or partial pressures of reactants are large compared with those for products, and the extent of reaction is very limited. If the equilibrium constant has a value close to 1, both reactants and products are present in significant proportions at equilibrium. 

Many reactions are conveniently carried out entirely in the gas phase. Molecules in the gas phase are highly mobile, and the collisions necessary for chemical reactions occur frequently. Two examples are the key steps in the production of hydrogen from the methane in natural gas. The first is the reforming reaction  

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Section 14.2 provides a thorough discussion of procedures for writing the empirical law of mass action for gas-phase, solution, and heterogeneous reactions, with specific examples for each. 

Sections 14.4 and 14.5 present a variety of equilibrium calculations based on the empirical law of mass action. 

An ion is an atom with an electric charge due to gain or loss of electrons. Ion exchange equilibria have been described by empirically and theoretically derived equations. They follow the form of the general law of mass action, which is... 

The two basic laws of kinetics are the law of mass action for the rate of a reac tion and the Arrhenius equation for its dependence on temperature. Both of these are strictly empirical. They depend on the structures of the molecules, but at present the constants of the equations cannot be derived from the structures of reac ting molecules. For a reaction, aA + hE Products, the combined law is... 

The interpretation of kinetic data is largely based on an empirical finding called the Law of Mass Action In dilute solution the rate of an elementary reaction is... 

The tools we created in Chapter 3, Physical/Chemical Models, form the core of the fitting algorithms of this chapter. The model defines a mathematical function, either explicitly (e.g. first order kinetics) or implicitly (e.g. complex equilibria), which in turn is quantitatively described by one or several parameters. In many instances the function is based on such a physical model, e.g. the law of mass action. In other instances an empirical function is chosen because it is convenient (e.g. polynomials of any degree) or because it is a reasonable approximation (e.g. Gaussian functions and their linear combinations are used to represent spectral peaks). 

The second important characteristic of the micellar solution that relates to solubilization is the micelle size. Poor aqueous soluble compounds are solubilized either within the hydrocarbon core of the micelle or, very commonly, within the head group layer at the surface of the micelle or in the palisade portion of the micelle. Predictions of the micelle size have relied on the use of empirical relationships employed within a thermodynamic model, for instance the law of mass action where micellization is in equilibrium with the associated and unassociated (monomer) surfactant molecules (Attwood and Florence, 1983). 

To characterize the process defined by Eq. (1), Smoluchowski applied the empirical [1] Guldberg-Waage [2] law of mass action. In his papers [3,4] published in 1916 and 1917 he derived and examined the set of differential kinetic equations equivalent to... 

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... 

Despite their success in giving the correct expressions for the mass action law, the empirical procedures leave unanswered numerous fundamental questions about chemical equilibrium. Why should the law of mass action exist in the first place, and why should it take the particular mathematical form shown here Why should the equilibrium constant take a unique value for each individual chemical reaction What factors determine that value Why does the value of the equilibrium constant change slightly when studied over broad ranges of concentration Why should the equilibrium constant depend on temperature Is there a quantitative explanation for the temperature dependence ... 

The chemical kineticists of the previous century developed a phenomenological understanding of chemical change that provided an accurate description of many chemical reactions in vitro. This description is known as the Law of Mass Action and is now rationalized in terms of certain probability considerations, which in turn can be represented by empirically determined rate constants and the concentrations of reactants. Let us begin with two elementary cases. 

Data regressions based on the law of mass action are generally adequate for most situations. However, this model only retains validity in liquid-phase reactions at equilibrium without cooperativity. Reactions that involve solid-phase, multiple cooperative binding, and not reaching equilibrium, deviate from the model. Therefore, empirical equations that are not based on the law of mass action have been used for curve fitting also. Among these, polynomial (205) and spline functions are often used (206-209). Polynomial regression can be a second-order (parabolic) or third-order (cubic) function ... 

MA and IMA are the malonic and the iodomalonic acid, respectively. For the CDIMA case in the usual experimental conditions, it is appropriate to assume that the only dynamical variables are [I-] and [C1C>2 ], the other concentrations staying essentially constant. In addition, the two first reactions in (3.44) follow the law of mass action, whereas the third one proceeds at a rate which is empirically given... 

The exchange equilibrium can be expressed by an empirical distribution ratio Rj = [=Zr]/[Zr] where [=Zr] is the total Zr concentration bound to the resin (mol/g) and [Zr] the total Zr concentration in the aqueous phase (M) at equilibrium. The law of mass action yields ... 

We can illustrate how the law of mass action was discovered empirically and demonstrate that the equilibrium constant is independent of starting concentrations by examining a series of experiments involving dinitrogen tetroxide and nitrogen dioxide ... 

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