Chemical equilibrium thermodynamic approach

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

The reactant mixture may be so nonideal that Equation (7.28) is inadequate. The rigorous thermodynamic approach is to replace the concentrations in Equation (7.28) with chemical activities. This leads to the thermodynamic equilibrium constant. 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

Because of the lack of high-pressure experimental reaction rate data for HMX and other explosives with which to compare, we produce in Figure 15 a comparison of dominant species formation for decomposing HMX that have been obtained from entirely different theoretical approaches. The concentration of species at chemical equilibrium can be estimated through thermodynamic calculations with the Cheetah thermochemical code.32,109... 

In the second approach, the chemical equilibrium between the reactant(s) and the transition state is expressed in terms of conventional thermodynamic functions, i.e., enthalpy and entropy changes. This method is easier to implement and provides useful insights for estimating both the preexponential factors and the activation energies. Consequently, we shall utilize the thermodynamic formulation of the TST in this paper. 

The arguments treated in the two preceding sections were developed in terms of simple equilibrium thermodynamics. The weathering of rocks at the earth s surface by the chemical action of aqueous solutions, and the complex water-rock interaction phenomena taking place in the upper crust, are irreversible processes that must be investigated from a kinetic viewpoint. As already outlined in section 2.12, the kinetic and equilibrium approaches are mutually compatible, both being based on firm chemical-physical principles, and have a common boundary represented by the steady state condition (cf eq. 2.111). 

Useful insights can undoubtedly be obtained by consideration of the likely chemical species present, and their behaviour at varying pH. Saliva is known to be metastable and supersaturated with respect to hydroxyapatite [35], which is further evidence that the purely thermodynamic approach is suspect. It does mean though that there is a significant driving force for remineralisation, as the supersaturated saliva approaches equilibrium with the consequent precipitation of hydroxyapatite. The development or arrest of a carious lesion is therefore dependent on the frequency and duration of the remineralisation and demineralisation processes, and also on their respective rates. These in turn depend on factors such as sucrose consumption, salivary flow, oral hygiene [36] and, of course, fluoride exposure [37]. It is the latter that is of greatest interest in the present chapter, and its role will be considered in detail in the next section. 

The statistical thermodynamic approach to the derivation of an adsorption isotherm goes as follows. First, suitable partition functions describing the bulk and surface phases are devised. The bulk phase is usually assumed to be that of an ideal gas. From the surface phase, the equation of state of the two-dimensional matter may be determined if desired, although this quantity ceases to be essential. The relationships just given are used to evaluate the chemical potential of the adsorbate in both the bulk and the surface. Equating the surface and bulk chemical potentials provides the equilibrium isotherm. 

The chemical equilibrium assumption often results in modeling predictions similar to those obtained assuming infinitely fast reaction, at least for overall aspects of practical systems such as combustion. However, the increased computational complexity of the chemical equilibrium approach is often justified, since the restrictions that the equilibrium constraint places on the reaction system are accounted for. The fractional conversion of reactants to products at chemical equilibrium typically depends strongly on temperature. For an exothermic reaction system, complete conversion to products is favored thermodynamically at low temperatures, while at high temperatures the equilibrium may shift toward reactants. The restrictions that equilibrium place on the reaction system are obviously not accounted for by the fast chemistry approximation. 

Alberty, R. A., and I. Oppenheimer, A Continuous Thermodynamics Approach to Chemical Equilibrium Within an Isomer Group, /. Chem. Phys., 81, 4603 (1984). 

Thermodynamics and Equilibrium Second We present chemical equilibrium from the viewpoint of thermodynamics. We believe that the quantitative formulation of equilibrium should rest on an understanding of free energy and entropy. To this end, we introduce the laws of thermodynamics before equilibrium, and we formulate equilibrium concepts in terms of standard free energies. This approach allows us to present a unified treatment of a wide range of chemical processes. 

The need to abstract from the considerable complexity of real natural water systems and substitute an idealized situation is met perhaps most simply by the concept of chemical equilibrium in a closed model system. Figure 2 outlines the main features of a generalized model for the thermodynamic description of a natural water system. The model is a closed system at constant temperature and pressure, the system consisting of a gas phase, aqueous solution phase, and some specified number of solid phases of defined compositions. For a thermodynamic description, information about activities is required therefore, the model indicates, along with concentrations and pressures, activity coefficients, fiy for the various composition variables of the system. There are a number of approaches to the problem of relating activity and concentrations, but these need not be examined here (see, e.g., Ref. 11). 

Enzymatic Catalysis. Enzymes are biological catalysts. They increase the rate of a chemical reaction without undeigoing permanent change and without affecting the reaction equilibrium. The thermodynamic approach to the study of a chemical reaction calculates the equilibrium concentrations using the thermodynamic properties of the substrates and products. This approach gives no information about the rate at which the equilibrium is reached. The kinetic approach is concerned with the reaction rates and the factors that determine these, eg, pH, temperature, and presence of a catalyst. Therefore, the kinetic approach is essentially an experimental investigation. 

Because of the relative ease of determining the system state by equilibrium calculations relative to experiments or detailed kinetics models, chemical equilibrium analysis has been the traditional approach to CVD process modeling. An extensive literature exists for the Si-Cl-H CVD system (7) and the As-Ga-Cl-H VPE process (I). The analysis of MOCVD systems has been limited by the lack of thermodynamic data. A recent equilibrium analysis of the MOCVD of GaAs (83, 84) is a good source of data for the GaAs system. 

The Mass Action Model The mass action model represents a very different approach to the interpretation of the thermodynamic properties of a surfactant solution than does the pseudo-phase model presented in the previous section. A chemical equilibrium is assumed to exist between the monomer and the micelle. For this reaction an equilibrium constant can be written to relate the activity (concentrations) of monomer and micelle present. The most comprehensive treatment of this process is due to Burchfield and Woolley.22 We will now describe the procedure followed, although we will not attempt to fill in all the steps of the derivation. The aggregation of an anionic surfactant MA is approximated by a simple equilibrium in which the monomeric anion and cation combine to form one aggregate species (micelle) having an aggregation number n, with a fraction of bound counterions, f3. The reaction isdd... 

The circumstellar chemistry is often subdivided into three main zones, which are determined by a comparison of the characteristic dynamic flow time, R/vx, with the chemical reaction times (Lafont et al. 1982 Omont 1987 Millar 1988). (i) In the region closest to the star (perhaps R 1014 cm), the density is sufficiently high that three-body chemical reactions occur in a time short compared to the dynamic time. In this regime, we expect the chemical abundances to approach thermodynamic equilibrium, (ii) Somewhat further away from the star (1014 cm < R < 1016 cm), there is a freeze-out of the products of the three-body reactions (McCabe et al. 1979). In this region, two-body reactions dominate the active chemistry, (iii) Finally, far from the star (R > 1016 cm), the density becomes sufficiently low that the only significant chemical processing is the photodestruction that results from absorption of ambient interstellar ultraviolet photons by the resulting molecules that flow from the central star. 

It follows then that the thermodynamic approach makes no reference to kinetics, while the kinetic approach is only concerned with the point at which the forward reaction equals the reverse reaction and gives no attention to the time needed to reach this equilibrium point. In nature, certain chemical events may take a few minutes to reach equilibrium, while others may take days to years to reach equilibrium such phenomena are referred to as hystereses phenomena. For example, exchange reactions... 

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