Applications of the Mass Action Law

Disturbance of Equilibrium One way to disturb a preexisting equilibrium would be to add a certain amount of one of the starting substances to the reaction mixture. Gradually, a new equilibrium would be established where the new equilibrium concentrations differ from the original ones. However, in all, the relations (6.19) and (6.21), respectively, remain fulfilled. 

As an example, we consider the equilibrium in aqueous solution between iron hexaquo complex cations and thiocyanate anions on the one hand and the blood red iron thiocyanate complex on the other which can be described in the following simplified manner  

If the blood red solution is diluted with water, the concentration and therefore also the chemical potential of the dissolved substances decrease for all substances by the same amount. This is indicated by an arrow placed above the formulas of the substances  

Experiment 6.1 Iron(III) thiocyanate equilibrium If Fe or SCN solutions are added to the pale orange dilute iron thiocyanate solution, it will turn red again in both cases. 

By adding excess iron (III) ions (1st case), their concentration in the solutirai and therefore also their potential increase the reaction runs backwards and correspondingly the color deepens again to blood red. Adding excess thiocyanate ions shows the same result the pale orange solution turns red again (2nd case). Both cases can be illustrated again by arrows above the chemical formulas. 

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Contrary to the preceding treatment the so-called mass-action model develops apparently more naturally from the application of the mass action law applied to the overall aggregation process... 

FRO] Fronaeus, S., On the application of the mass action law to cation exchange-equilibria, Acta Chem. Scand., 7, (1953), 469-480. Cited on pages 266, 269, 280, 287, 290. 

Pressure. Pressure, like temperature, can affect the rate of reaction as well as the equilibrium position. The rate of reaction is generally increased by increasing pressure, because a gas phase is usually present, and increased pressure gives increased concentration. In general, increased concentration speeds up a reaction. Pressure increases the equilibrium yield in a hydrogenation reaction when there is a decrease in the volume of the reaction as it proceeds. This is the simple application of the mass-action law, or Le Chdtelier s principle. In hydrogenation reactions, there is usuaUy a decrease in volume. 

This is esterification in its narrow sense and is what is usually meant when the term esterification is used. It has been extensively studied by both organic and physical chemists. It has been one of the most useful reaction in preparative organic chemistry, one of the best examples of the application of the mass-action law, and has involved one of the most baffling problems in homogeneous catalysis. 

The application of mass action law to heterogeneous elementaiy reactions is somewhat refined by treating the adsorption of the species S on unoccupied site a(0) as bimolecular combination of S and elementary reaction is thus expressed as proportional to 0 0(0), where <7 is the concentration of S in gas and 0(0) the probability of the site a being unoccupied. The approximation of Langmuir adsorption isotherm is precisely in line with this refinement of the application of the mass action law, which will be called the extended mass action law in what follows. The application of the extended mass action law to the hydrogen electrode reaction leads now to the value of a, which decreases from 2 to 0 with the increase of rj passing through the observed value ea 0.5 (6). The value of tj at a = 0.5 is however far too low and the interval of ij, in which a stays near 0.5, far too short as compared with observations. 

Once the mass balances for each chemical species are written using the corresponding reactor type model, it is necessary to write an explicit expression for the reaction rate (production and consumption) of each chemical species Ri. This is done by the application of the mass action law. This law, in one of its versions, establishes that for an elementary reaction... 

For a batch reactor, the application of the mass action law considering only these two kinetic steps results in... 

The DEE approach starts with the application of the mass action law to the overall ligand system. In this case, the metal binding to the substrate is represented as (dropping charges for simplicity)... 

As an example of the application of the mass-action law to ion-exchange equilibria, we will consider the reaction between a singly charged ion B with a sulfonic acid resin held in a chromatographic column. From a neutral solution, initial retention of B ions at the head of the column occurs because of the reaction... 

Most gases dissolve monatomically in liquid metals. For example, the solution reactions may be written as H2 -> 2H, N2 —> 2N, O2 —> 20, where the underlining signifies the element is in solution. Sievert s law for diatomic gases is an application of the mass action principle. It states that the solubility is proportional to the square root of the partial pressure of the gas. For example,... 

We have only discussed two of the sixteen fields given in the figure, the prediction of the direction in which a reaction can proceed spontaneously by means of the chemical potential and the temperature and pressure dependence of p and its application. A next step would be to go over to mass action, i.e., the concentration dependence of p. This leads directly to the deduction of the mass action law, calculation of equilibrium constants, solubilities, and many other data. An expansion of the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc., is easily possible. Furthermore, the same tools allow solving problems even at the atomic and molecular level that are usually treated by quantum statistical methods. 

The current treatments of elementary reactions in terms of the mass action law are now reviewed in this section as based on the generalized theory of elementary reactions developed in the previous sections. It will be seen that the current treatment is applicable under the condition where the impenetrability alone is significant, as exemplified in this section, but is hardly reasonable in the case of the interaction operative. 

A solution to these difficulties is a blend of the chemical picture in which clustered ion configurations are described by the mass action law, while the interactions between the various entities are treated by methods applying the high-temperature approximations of the /-functions, e.g. by the MSA. The Debye-Hiickel (DH) theory [26], although derived from classical electrostatics, is also a high-temperature approximation, whose range of applicability can be extended by supplementing a mass action law for ion pair formation [27],... 

Chemical equilibrium model Most reactive transport formulations use the mass action law to solve the chemical equilibrium equations. In this formulation an alternative (though thermodynamically equivalent) approach is used, based on the minimization of Gibbs Free Energy. This approach has a wider application range extending to highly non-ideal brine systems. 

Method of constant equilibrium (physicochemical) is based on the search of such water composition, at which activities or concentrations of components would be tied between themselves by equilibrium constants, according to the mass-action law. This method is commonly used in physical chemistry, especially in the chemistry of complex compounds, as it solves most of their problems. Its application in hydro-geochemistry is due to the fact that computer programs developed on its base are simpler and, as a rule, take less time for calculations. 

The conditions in which slow reactions of relative simplicity become accessible to precise measurement are not normally obvious, and have to be discovered. Even when they have been found, the phenomena which become apparent would be, in the eyes of many, little more than curiosities. Nevertheless, the development of any phenomenon in time has a fascination of its own, and the laws which it follows have an attraction to those interested in the quantitative aspect of things. The application of the so-called law of mass action led to the idea of reaction order, and provided a basis for a rational classification of slow chemical changes. Examples of reactions of different orders were sought and found, and indeed the existence of this convenient system of grouping not infrequently led to the oversimplification of the real relations. But the obvious molecular explanation of the order in terms of collision probability did not fail to arouse interest in the statistical theory of reaction rates. Even so, an unconscious tendency to compare chemical changes with phenomena of viscous flow or movement under friction persisted, terms such as chemical resistance were endowed with a fictitious significance, and catalysts were likened to lubricants. 

In addition to the direct methods for determining chemical drives and potentials, respectively, there are numerous indirect methods that are more sophisticated and therefore more difficult to grasp, yet more universally applicable. These include chemical (using the mass action law) (Sect. 6.4), calorimetric (Sect. 8.8), electrochemical (Sect. 23.2), spectroscopic, quanmm statistical, and other methods to which we owe almost all of the values that are available to us today. Just as every relatively easily measured property of a physical entity that depends upon temperature (such as its length, volume, electrical resistance, etc.) can be used to measure T, every property (every physical quantity) which depends upon fi can be used to deduce fi values. 

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 defect structure gets more involved as defect cOTicentrations increase so that the mass-action-laws are no longer applicable. This basic logical framework can also be extended by taking into account defect associates or long range interactions in terms of activity coefficients of defects. 

The rates of many reactions are not represented by application of the law of mass action on the basis of their overall stoichiometric relations. They appear, rather, to proceed by a sequence of first- and second-order processes involving short-lived intermediates which may be new species or even unstable combinations of the reaclants for 2A -1- B C, the sequence could be A -1- B AB followed by A -1- AB C. 

The deduction adopted is due to M. Planck (Thermodynamik, 3 Aufl., Kap. 5), and depends fundamentally on the separation of the gas mixture, resulting from continuous evaporation of the solution, into its constituents by means of semipermeable membranes. Another method, depending on such a separation applied directly to the solution, i.e., an osmotic process, is due to van t Hoff, who arrived at the laws of equilibrium in dilute solution from the standpoint of osmotic pressure. The applications of the law of mass-action belong to treatises on chemical statics (cf. Mel lor, Chemical Statics and Dynamics) we shall here consider only one or two cases which serve to illustrate some fundamental aspects of the theory. 

It will be of interest to illustrate some applications of the law of mass action to homogeneous gaseous equilibria. Two types of reaction would be considered (i) those in which no change in the total number of molecules occurs consequent to the reaction and (ii) those involving changes in the total number of molecules. A reaction of the first type can be generally presented as ... 

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