Equilibrium in heterogeneous systems

Degree of Saturation of Condensed Phases and Affinity to Equilibrium in Heterogeneous Systems... 

Fuerstenau") was the first who used the Stern-Grahame model of EDL to describe the adsorption of long-chain surfactants for the equilibrium in heterogeneous systems. The adsorption density in the Stem plane is given by the equation... 

Equilibrium in heterogeneous systems, in the absence of electrical, capillary, Or gravitational effects—The Phase Rule and some of its applications—The theory of Allotropy... 

Chemical equilibrium in heterogeneous systems (from the thermodynamic standpoint) when capillary or electrical effects are of importance—Adsorption—Donnan s theory of membrane equilibria—Micelle theory of colloidal electrolytes... 

Solution of this contradiction often depends on the nature of the studied objects and on the type of set tasks. As a rule, for calculations of equilibrium in heterogeneous systems as basis components are used chemical elements, more rarely dissociated ions of water solutions. Craig M. Bethke (2008) proposed to subdivide basis components into the following groups ... 

But in writing such equations, we assumed that our system is homogeneous—that its values for intensive properties are uniform throughout. Here we want to generalize the development so we can identify equilibrium in heterogeneous systems, especially those in which the heterogeneity results from the presence of more than one part, such as multiple phases. For such systems, the fundamental equation (7.1.1) takes the form... 

Since at equilibrium in heterogeneous systems the fugacity of a component is the same in all phases, then if the same standard state for a substance is chosen for each phase, the activities of the substance in all phases are equal. The ratio a/x is termed activity coefficient y and for ideal solutions... 

Let us begin an analysis of the process of formation of chemical compounds in heterogeneous systems with the simplest case of growth of a solid layer between elementary substances A and B which form, according to the equilibrium phase diagram of the A-B binary system, only one chemical compound ApBq, p and q being positive numbers (Fig. 1.1). The substances A and B are considered to be solid at reaction temperature 7, and mutually insoluble. 

The analysis of stationary and nonstationary flow distributions in multiloop hydraulic systems with lumped, regulated, and distributed parameters and in heterogeneous systems was given in (Gorban et al., 2001, 2006 Kaganovich et al., 1997). In the concluding section of Section 5 the abundant capabilities of the flow MEIS are illustrated by the simplest example of stationary isothermal flow distribution of incompressible fluid in the three-loop circuit. It is shown how the degrees of order (laminar or turbulent modes) on the branches of this circuit are determined from calculation of the final equilibrium. 

Equilibrium Displacements in Heterogeneous Systems Passage of a Component from one Phase to another. 

A variety of equilibria occur in heterogeneous systems that involve solids and liquids as well as gases and dissolved species. Molecular species cross the interfaces between phases in order to participate in reactions. A whole class of examples (Chapter 16) is based on the dissolution of slightly soluble salts, where the dissolved ions are in equilibrium with the pure solid. Another class includes the reaction of pure metals with acids to produce hydrogen gas ... 

Equilibrium m heterogeneous systems, 1 e equilibrium between components in different phases... 

In Vol I the question of heterogeneous equilibnum, i e equilibrium in a system consisting of more than one phase, was considered from the kinetic standpoint, the generalisation employed being the Distribution Law of Nernst We now take up the study of heterogeneous equilibnum from the standpomt of thermodynamics... 

To calculate thermodynamic equilibrium in multicomponent systems, the so-called optimization method and the non-linear equation method are used, both discussed in [69]. In practice, however, kinetic problems have also to be considered. A heterogeneous process consists of various occurrences such as diffusion of the starting materials to the surface, adsorption of these materials there, chemical reactions at the surface, desorption of the by-products from the surface and their diffusion away. These single occurrences are sequential and the slowest one determines the rate of the whole process. Temperature has to be considered. At lower substrate temperatures surface processes are often rate controlling. According to the Arrhenius equation, the rate is exponentially dependent on temperature ... 

We then move to the more complex cases reactions taking place in heterogeneous systems and multiple reactions. To this purpose we consider first the Phase Rule and the Duhem theorem - as they apply to reacting systems - and discuss the methodology for identifying the number of independent reactions for the formation of a given equilibrium mixture. 

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