Species distribution diagram

For a weak acid the fraction of the acid in the form containing protons 

The equations that follow use protonation constants rather than dissociation constants. The stepwise protonation constant of a weak base species B is the equilibrium constant for the following reaction (charges are omitted for clarity)  

KH values are typically much greater than 1 and are often reported as logiCH values. Kq values are typically very small, and are often reported as pKg values 

It is also convenient to use the cumulative protonation constant P for the overall reaction 

The expression for the aj value for a particular protonated species is easily calculated from the expression 

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Assignment of the spectra in Fig. 16 is straightforward, as the species distribution diagrams show the four Be-containing species have... 

Classroom demonstration of complex equilibria A. R. Johnson, T. M. McQueen, and K. T. Rodolfa, Species Distribution Diagrams in the Copper-Ammonia System, J. Chem. Ed. 2005, 82,408. 

FIGURE 2.5 Species distribution diagrams for vanadate at 1.0 and 0.1 molar overall concentrations calculated for aqueous 0.6 mol/L NaCl solutions. Formation constants are taken... 

The distribution of hydrolyzed V02+ as a function of pH at a total vanadium concentration of 10 xM is shown in Fig. 3. The curves in the distribution diagram also depend on the total vanadium concentration because of the dimer formation and the precipitation reactions. While distribution diagrams of this type for V02+ are incomplete, they nevertheless illustrate the interrelationship between some of the species present and are of predictive value below pH 6 and above pH 11, and possibly in the pH 6 to 11 interval provided one starts with a solution below pH 6 and slowly adds base. The unidentified soluble hydroxide species are less likely to form under those conditions. Species distribution diagrams for a number of V02+ complexes with several common ligands are given by Kraglen34. ... 

A graphical representation of the equilibria involved in this type of systems is a plot of the distribution of the species containing M vs pL. This is called a chemical species distribution diagram it can be calculated by defining the equations of the distribution... 

These functions are monotonic (i.e., increasing or decreasing in a continuous fashion) with respect to [L] (or to pL) for the first and last species in the equilibria involved they show a maximum for the intermediate species (called ampholytes). The resulting chemical species distribution diagrams can easily be constructed by introducing these equations in a spreadsheet (e.g., Excel). See Examples 2.5 and 2.6. T/pical examples can be found in the educational literature, and several programs are available for these calculations (see, for example, Kim, 2003). 

Example 2.6 Calculate and draw the chemical-species distribution diagram for the Cu(II)-NH3 system, using the following log values of the global constants for the four sequential equilibria involved 4.10, 7.60, 10.50, and 12.50. Here, pL = pNH3, and M = Cu2+. 

As discussed above, soil pH may play a major role in its interactions with pollutants. Species distribution diagrams (see Chapter 2) set the framework to know which species are predominant at a given pH. For example, phosphates have the predominance-zone diagram shown in Figure 8.5. 

Figure 20-1. Species distribution diagram for citric acid.

Assuming activity coefficients are unity, and using the solubility expression for Ca(ox), equation (5.3), the species distribution diagram for oxalate ions can be generated, Figure 5.1. You can see that, with excess oxalate in solution, pH will play a critical role in balancing the co-precipitation of H2ox(s), Ca(ox), and the cobalt complex product. 

Given Gibbs free-energy data, be able to draw and explain a species distribution diagram for Fe(II) and Fe(III)-OH complexes as a function of pH. 

Mineral-surfactant equilibria. Mineral-surfactant equilibria determine adsorption of various surfactants on minerals, hemimicellization, interactions among dissolved mineral species and reagents and electrochemical interactions. The optimum conditions for mineral-surfactant interactions as well as flotation can be calculated from data for such parameters as the solubility product and complex formation constants and species distribution diagrams with the helps of plots of logC-pH, AG°-pH, log/3, iih-pH, etc. 

The species distribution diagrams (0-pH) for flotation reagents can be calculated from proton addition constants given in Appendices A and B. Some examples are given below. 

Fig. 2.5. Species distribution diagram of oleic acid (Somasundaran et al., 1984).

Fig. 2.7. Species distribution diagram of dodecyl amine as a function of pH (total cone. = 5x10 mol/1).

Fig. 3.4. Species distribution diagrams for calcite-water systems (a) closed and (b) open.

The species distribution diagrams calculated from these equilibria are shown in Figs. 3.6a-3.6c. For wolframite, both Mn + and Fe are dominant species for pH < 2.8. The mineral... 

Fig. 3.6. Species distribution diagrams for mineral-water open systems (a) hubnerite, (b) ferberite, and (c) scheelite (Hu and Wang, 1985).

Fig. 3.11. Species distribution diagram for covellite under open (atmospheric CO2) conditions (Acar and Soma-sundaran, 1990).

Fig. 3.15. (a) Dependence of flotation of calcite on PZC using dodecylammonium acetate (DDA) and sodium dodecylsulfate (SDS) (b) determination of PZC from species distribution diagram for calcite. 

Fig. 4.9. Oleate species distribution diagram as a function of pH. Total oleate concentration = 3x10 M.

Correlation of oleate adsorption and flotation maximum at about pH 7.5 for a variety of minerals and high abstraction (adsorption + surface precipitation) below this pH with the species distribution diagram (Fig. 4.9) suggests that the role of acid-soap dimer and precipitated oleic acid can be significant in controlling the adsorption and resultant flotation behavior. 

Due to a variety of possible solution reactions, flotation reagents exist in many forms such as undissociated molecules, ions, hydroxylated species and polymeric species under different solution conditions of pH and concentration. The fraction of species plotted as a function of the total concentration, pC, yields the species distribution diagram for the system. Such plots can be used to explain mechanisms by which reagents act in mineral flotation. 

Fig. 4.48. Species distribution diagram of Ca +, Mn -citric acid systems and flotation of calcite and wolframite using octyl hydroxamate (Wang and Hu, 1985).

Fig. 4.49. Species distribution diagrams of metallic ions-citric acid systems and its depression for mineral flotation (a) Fe(III)/quartz (b) Mn(II), Fe(II)/wolframite (Wang and Bai, 1983).

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