Equilibrium distribution of species

Because there exists an equilibrium distribution of species in the aqueous phase, removal of certain species will lead, by the law of mass action, to a readjustment of the equilibrium. The concentration of negative species will decrease to compensate for continued loss of the neutral and positive species to the organic phase (loss of the positive species is, of course, caused by complexing). This continued adjustment of equilibrium will be maintained until all of the organic lead has been removed from the aqueous phase if the organic phase is not saturated. 

The functions ty have been defined in Eq. (15), they are found for given values 6a and 0B by solving system of equations for equilibrium distribution of species (Appendix A). Inserting expressions (19) and (20) into (18), one obtains ... 

Collectively, the programs mentioned above represent the "state of the art" in the calculation of the equilibrium distribution of species in aqueous systems. As a means of examining the consistency of these programs, two test cases (a dilute river water and an average seawater analysis) were compiled and mailed to more than fifty researchers who have been active in the field of chemical modeling. These test cases may overlook many of the features of specific programs, but they provide a common basis by which most of the programs can be... 

H. L. Smith (1991b), Equilibrium distribution of species among vessels of a gradostat, Journal of Mathematical Biology 30 31-48. 

Procedures for finding the equilibrium distribution of species are based on the principle that at equilibrium the total free energy of the system is at a minimum. This total free energy is the sum of the contributions from each of the constituent chemical species in the system the contribution of each species depends on its standard free energy of formation, its activity, and the temperature and pressure of the system. 

Nickel is extracted from alkaline ammonia solutions by LIX 64N, but its equilibrium constant is five orders of magnitude smaller than that of copper.8 Also, it forms ammonia complexes more extensively than copper, which enhances the selectivity of LIX 64N for copper over nickel. Under conditions of simultaneous extraction the parameters of the chemical-reaction model for each individual metal are able to predict the iwo-metal equilibria provided that the equilibrium distribution of species in the aqueous phase is taken into account. 

Equilibrium distribution of species at long times lines drawn according to statistical model points determined experimentally by 81 NMR [95J,... 

The role of the distribution of species in solution in determining the CdS film composition and structure was studied by Rieke and Bentjen [244], who performed equilibrium analysis of the cadmium-amine-hydroxide system to predict the spe-ciation in solution. The focus was on the formation of Cd(OH)2 and Cd(NH3) species due to their importance in film growfh. If was concluded fhat for deposition of high-quality, adherent, phase-pure CdS films, a surface cafalytically active toward thiourea decomposition is desirable. The Cd(OH)2 film was thought to be responsible for this effect. 

For any initial composition of the two solntions, an equilibrium distribution of the species between the membrane, any initial composition of the two solutions, an equi-librinm distribntion of the species between the membrane, and hence also between the two solntions is attained after some time. 

The clay ion-exchange model assumes that the interactions of the various cations in any one clay type can be generalized and that the amount of exchange will be determined by the empirically determined cation-exchange capacity (CEC) of the clays in the injection zone. The aqueous-phase activity coefficients of the cations can be determined from a distribution-of-species code. The clay-phase activity coefficients are derived by assuming that the clay phase behaves as a regular solution and by applying conventional solution theory to the experimental equilibrium data in the literature.1 2 3... 

Garrels and Thompson s calculation, computed by hand, is the basis for a class of geochemical models that predict species distributions, mineral saturation states, and gas fugacities from chemical analyses. This class of models stems from the distinction between a chemical analysis, which reflects a solution s bulk composition, and the actual distribution of species in a solution. Such equilibrium models have become widely applied, thanks in part to the dissemination of reliable computer programs such as SOLMNEQ (Kharaka and Barnes, 1973) and WATEQ (Truesdell and Jones, 1974). 

Once we have calculated the distribution of species in the fluid, we can determine the degree to which it is undersaturated or supersaturated with respect to the many minerals in the thermodynamic database. Only a few of the minerals can exist in equilibrium with the fluid, which is therefore undersaturated or supersaturated with respect to each of the rest. For any mineral A , we can write a reaction,... 

For a first chemical model, we calculate the distribution of species in surface seawater, a problem first undertaken by Garrels and Thompson (1962 see also Thompson, 1992). We base our calculation on the major element composition of seawater (Table 6.2), as determined by chemical analysis. To set pH, we assume equilibrium with CO2 in the atmosphere (Table 6.3). Since the program will determine the HCOJ and water activities, setting the CO2 fugacity (about equal to partial pressure) fixes pH according to the reaction,... 

Here, we set oxidation state in the model using the dissolved oxygen content and calculate the distribution of species assuming redox equilibrium. 

Wolery, T. J. and L. J. Walters, Jr., 1975, Calculation of equilibrium distributions of chemical species in aqueous solutions by means of monotone sequences. Mathematical Geology 7,99-115. 

Pyridinecarboxaldehyde, 3. Possible hydration of the aldehyde group makes the aqueous solution chemistry of 3 potentially more complex and interesting than the other compounds. Hydration is less extensive with 3 than 4-pyridinecarboxaldehyde but upon protonation, about 80% will exist as the hydrate (gem-diol). The calculated distribution of species as a function of pH is given in Figure 4 based on the equilibrium constants determined by Laviron (9). 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

FIGURE 8.10 Equilibrium distribution of sulfur-containing species in propane-air flames with unburned gases initially containing 1% S02 (from Johnson et al. [40]). 

In polymeric models for silicate melts, it is postulated that, at each composition, for given values of P and T, the melt is characterized by an equilibrium distribution of several ionic species of oxygen, metal cations, and ionic polymers of monomeric units SiOt. ... 

The distribution of halogen species in aqueous solution depends on pH and equilibrium constants for the above reactions. Table III lists the distribution of species for each halogen at the three pH levels reported in this paper. Derivation of equations for calculation of halogen species concentration are presented in reference [1 ]. 

A enzyme kinetic technique, introduced by Britton and co-workers "", that permits one to measure the equilibrium distribution of enzyme-bound substrate(s), inter-mediate(s), and product(s). In this procedure, radiolabeled substrate or product is initially permitted to react with enzyme for sufficient time to equilibrate. At thermodynamic equilibrium, all the different enzyme-bound species will be present at concentrations reflecting their stability relative to each other. One can then add a large excess of unlabeled substrate. Under this condition, any unbound or newly released radiolabel will mix with the large unlabeled pool of substrate or product, where it will undergo substantial reduction in its radiospecific activity. This dilution effectively reduces or eliminates any significant recycling of released radiolabel. One can then... 

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