Solubility as a Function of pH

Both the Hildebrand and MGSA theory can be applied to co-solvent systems by modifying the interaction parameters. 

The Hildebrand parameter for the solvent in Equation (4.8), 61, needs to be replaced by the value for the mixture determined by multiplying the pure solvent values by their volume fractions as given below for a two-solvent system. 

Where i and j represent the two solvents. In addition, the volume fraction of the solvent needs to be replaced with the sum of the volume fractions of all solvents, therefore Equation (4.8) becomes  

Additional terms can be added to this equation in order to correlate with experimental data. 

When considering the MGSA model, a similar approach can be made. Starting with Equation (4.11) the mole fraction solubility of a single solvent system can be calculated and labeled X21. The mole fraction solubility of a two solvent system can be given as X2,mix- A linear function of the solubility in the mixed solvent system can be calculated according to  

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The relative solubilities reported are very crude estimates based on equilibrium solubility products. These estimates do not take into account variations in solubility as a function of pH, ionic strength, activities of various solution species (e.g., HCO "), redox state, particle size, surface defect types and concentrations, the concentration of various types of adsorbates, including natural organic matter, on mineral surface, or the presence of different types of bacteria or microbial biofilms on mineral surfaces. 

Figure 7.2 Silica solubility as a function of pH. To determine silica solubility at a given pH, multiply the solubility as a function of temperature by the pH correction factor of the given pH of the concentrate solution.

Commonly, different metals exhibit different solution pH of zero net charge. For this reason, different metals exhibit minimum solubility at different pH values, which makes it difficult to precipitate effectively two or more metals, as metal-hydroxides, simultaneously. Thus metal-hydroxide solubility as a function of pH displays a U-shaped behavior. The lowest point in the U-shaped figure signifies the solution pH of zero net charge and is demonstrated below. Consider the solid Fe(OH)2s,... 

Figure 7 Calculated Np solubilities as a function of pH and Eh in J-13 groundwater variants (Table 5). Np205(g) and Np(OH)4(s) were assumed to be the solubility-limiting phases. Inset shows regions of solubility control versus redox control (shaded area) (Kaszuba and Runde, 1999) (reproduced by permission of American Chemical Society from Environmental Science and Technology 1999, 33, 4433).

We have already seen that the solubility of solid phases can be enhanced by ligands for example, for metal oxides, considering OH as ligands, only the total solubility as a function of pH is given by... 

Figure 4. a) Orpiment solubility as a Junction of pH and temperature in low sulfide fluids, using stability constants for HjAsOj from Webster (1990) and Pokrovski et al (1996). B) Orpiment solubility as a function of pH at in a high sulfide fluids using stability... 

For drugs with ionizable functional groups, determining solubility as a function of pH is an important preformulation task. pH-solubility probles debne the range of opportunities for liquid formulation development, and they provide baseline guidance to solubilization strategies for poorly soluble compounds. 

Figure 2. Plot of log total calcium vg pH. Dashed line, calculated solubility as a function of pH. Solid line, linear regression plot for experimental points below pH = 8.5.

Fig. 19.1. Predicted quartz solubilities as a function of pH, temperature and total sodium concentration. After Crerar and Anderson (1971)...

The value of - the slope of the metal solubility as a function of pH - is often found to be between -0.5 and -0.7 for Cd + and (McBride et al., 1997 Salam and Helmke, 1998 Gray et al., 1999 Sauve et al., 2000). If we take —0.67 as a reasonable value for Cd, then metal solubility will show a 2 3 dependence on soil solution pH. This can be handled by having GEOCHEM-PC consider the formation of a mixed solid phase with a mythical soil ligand, the MSL ... 

Impurity profiling usually, salt formation enhances purity of drug substance Partition coefficient c log P Aqueous solubility as a function of pH... 

Figure 11. Solubility as a function of pH in 3.0 M KCl, after 15 min, for subfractions of human mercaptalbumin (HMA). The HMA was chromatographed on Sephadex G-200 prior to subfractionation. O, Subfraction I A, subfraction II A, subfraction III. From Petersen and Foster (1965a).

Figure 10.7 Cerium solubility as a function of pH calculated with PHREEQC.

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