Mass actions, law

Chemical reactions can be described by thermodynamics (chapter 1.1.2) and kinetics (chapter 1.2). Reactions expressed by the mass-action law (chapter 1.1.2.1), are thermodynamically reversible and independent of time. In contrast, kinetic processes are time dependent reactions. Thus, models that take into account kinetics can describe irreversible reactions such as decay processes that require finite amounts of time and cannot be reversed under a given set of conditions. 

In principle, any chemical equilibrium reaction can be described by the mass-action law. 

K = thermodynamic equilibrium or dissociation constant (general name) 

In particular, the term K is defined in relation to the following types of reactions using the mass-action law  

If one reverses reactants and products in a reaction equation, then the solubility constant is K =l/K. Hence it is important always to convey the reaction equation with the constant. 

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The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

The mass action law or Saha equation for thermal ionisation of seed atoms is... 

This was first demonstrated ia 1862 by Berthelot and Saint-Gibes (32), who found that when equivalent quantities of ethyl alcohol and acetic acid were abowed to react, the esterification stopped when two-thirds of the acid had reacted. Sinularly, when equal molar proportions of ethyl acetate and water were heated together, hydrolysis of the ester stopped when about one-third of the ester was hydroly2ed. By varyiag the molar ratios of alcohol to acid, yields of ester >66% were obtained by displacement of the equbibrium. The results of these tests were ia accordance with the mass action law shown ia equation 5. 

Ion Exchange A useful tool is provided by the mass action law for describing the general exchange equilibrium in fully ionized exchanger systems as... 

The inaccuracy seems not to prohibit study of the structural properties of associating fluids, at least at low values of the association energy. However, what is most important is that this difficulty results in the violation of the mass action law, see Refs. 62-64 for detailed discussion. To overcome the problem, one can apply thermodynamical correspondence between a dimerizing fluid and a mixture of free monomers of density p o = P/30 = Po/2 and dimer species [12]. The equation of state of the corresponding mixture... 

Manganese, D. of - continued with magnesium and zinc, (ti) 334 Mannitol 299, 581 Masking agents 12, 312 Mass action law 16 applications to electrolyte solutions, 23 Matrix effects 733, 794 Maxima in polarography 597 suppression of, 597, 611 Mean deviation 134 relative, 134 standard, 134 Measuring cylinders, 87 flasks, 81... 

For both cases, the assumption is valid that only one helical sequence exists and that products with the same number of hydrogen bonds have the same stability. Considering the statistical weights of the possible intermediates, the whole measurable degree of conversion, t0,ai, is computed by the mass-action law and can be derived from Eq. (6)149. ... 

Connection between the reversible target binding and the change in fluorescence intensity can be easily established based on the mass action law. In the simplest case... 

Non-stoichiometric compounds Mass action law treatment of defect equilibria... 

This type of defect equilibrium treatment has been used extensively to model the defect chemistry and non-stoichiometry of inorganic substances and has the great advantage that it easily takes several simultaneous defect equilibria into account [22], On the other hand, the way the mass action laws are normally used they are focused on partial thermodynamic properties and not on the integral Gibbs energy. The latter is often preferred in other types of thermodynamic analyses. In such cases the following solid solution approach is an alternative. 

The system to be solved involves five unknown concentrations which, for sake of illustration, are made equal to the corresponding activities. An identical number of equations must be found that include component conservation plus a number of mass action laws corresponding to the formation of as many species as the excess of species over components. We first write the recipe, i.e., the mass balance for the components, not including the components of water. Calcium mass balance reads... 

The six equations in the six unknowns xlt x2,..., x6 are the electroneutrality condition, conservation of mercury and chloride components, plus the three mass action laws corresponding to water dissociation and mercury complexation by Cl- and OH-. The condition of electroneutrality reads... 

In thermal equilibrium, within a quantum statistical approach a mass action law can be derived, see [12], The densities of the different components are determined by the chemical potentials ftp and fin and temperature T. The densities of the free protons and neutrons as well as of the bound states follow in the non-relativistic case as... 

Calculations of the composition (112/ns) of symmetric nuclear matter (np = nn, no Coulomb interaction) are shown in Fig. 3 [7], At low densities, the contribution of bound states becomes dominant at low temperatures. At fixed temperature, the contribution of the correlated density 112 is first increasing with increasing density according to the mass action law, but above the Mott line it is sharply decreasing, so that near nuclear matter density (ns = ntot = 0.17 fm-3) the contribution of the correlated density almost vanishes. Also, the critical temperature for the pairing transition is shown. 

Kinetic methods describing the evolution of distributions of molecules by systems of kinetic differential equations (obeying either the classic mass action law of chemical kinetics or the generalized Smoluchowski coagulation process). 

In the case of classic chemical kinetics equations, one can get in a few cases analytical solution for the set of differential equations in the form of explicit expressions for the number or weight fractions of i-mcrs (cf. also treatment of distribution of an ideal hyperbranched polymer). Alternatively, the distribution is stored in the form of generating functions from which the moments of the distribution can be extracted. In the latter case, when the rate constant is not directly proportional to number of unreacted functional groups, or the mass action law are not obeyed, Monte-Carlo simulation techniques can be used (cf. e.g. [2,3,47-52]). This technique was also used for simulation of distribution of hyperbranched polymers [21, 51, 52],... 

Empirical Models vs. Mechanistic Models. Experimental data on interactions at the oxide-electrolyte interface can be represented mathematically through two different approaches (i) empirical models and (ii) mechanistic models. An empirical model is defined simply as a mathematical description of the experimental data, without any particular theoretical basis. For example, the general Freundlich isotherm is considered an empirical model by this definition. Mechanistic models refer to models based on thermodynamic concepts such as reactions described by mass action laws and material balance equations. The various surface complexation models discussed in this paper are considered mechanistic models. 

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