Ideal solution maximum solubilities

Another important factor to be considered is the effect of temperature in the washing process. Chlorine has its maximum solubility at 4 °C, but it has been shown that the chlorinated washing water should ideally have a temperature that is at least 10 °C higher than that of the product. Results from a study by Zhuang et al. (1995) showed that a significantly higher number of Salmonella cells was taken up by the core tissue when tomatoes at a temperature of 25 °C were dipped in a chlorine solution held at 10 °C. 

Because the entropy of formation in Hildebrand theory is ideal, this approach should be restricted to those systems in which there are no structure effects due to solute-solvent and solvent-solvent interactions. The implication of this is that the solute should be non-ionic and not have functional groups which can interact with the solvent. According to Equation (4.8), the maximum solubility occurs when the Hildebrand parameter of the solvent is equal to the Hildebrand parameter of the solute. That is, when plotting the solubility versus the Hildebrand parameter, the solubility exhibits a maximum when the solubility parameter of the solvent is equal to the solubility parameter of the solute. 

In an ideal solution, the maximum solubility of a drug substance is a function of the solid phase in equilibrium with a speciLed solvent system at a given temperature and pressure. Solubility is an equilibrium constant for the dissolution of the solid into the solvent, and thus depends on the strengths of solute solvent interactions and solute solute interactions. Alteration of the solid phase of the drug substance can inLuence its solubility and dissolution properties by affecting the solute solutc molecular interactions. 

Metal-Hydroxides. Most heavy metals may precipitate via strong bases (e.g., NaOH and KOH) as metal-hydroxides [M(OH)n]. These precipitation reactions are described in Chapter 2. As noted, metal-hydroxide solubility exhibits U-shape behavior and ideally its lowest solubility point in the pH range allowed by law (e.g., pH 6-9) should be lower than the maximum contaminant level (MCL). However, not all heavy metal-hydroxides meet this condition. The data in Figure 12.1 show the various metal-hydroxide species in solution when in equilibrium with metal-hydroxide solid(s). In the case of Pb2+, its MCL is met in the pH range of 7.4-12, whereas the MCL of cadmium (Cd) the MCL is not met at any pH. Similar information is given by the solubility diagrams of Cu2+, Ni2+, Fe3+ and Al3+. 

The graph in Fig. 2 can be used to address the most fundamental question regarding insulin iontophoresis—is it theoretically possible, under the most favorable conditions, to deliver the required dose Based on the discussion in Section 2.1, the needs are a basal delivery rate of 1-2 units per hour coupled with a bolus of up to 20 units over about a half-hour. Figure 2 indicates that a delivery rate of 40 units per hour could be achieved with a 1 mM solution of insulin, which is equivalent to about 4mg/ml or 100 units/ml. Regular (currently marketed human, pork, or beef) insulin has a water solubility that exceeds this value. Thus, it is theoretically possible to iontophorese insulin at the required rate. However, an idealized model has been used to reach this conclusion. Specifically, it was assumed that insulin exists as an ideal solution (with a MW of 5800), that the mobility of insulin is independent of pH and has a value close to its maximum value, and that the molecule is not degraded on its way through the skin. For regular insulins, these assumptions are not true. In the next section, the physicochemical properties of insulin that impact its deliverability by iontophoresis are described. 

Benzene and naphthalene form a nearly ideal liquid solution. However, these two substances are nearly insoluble in each other s solid phase since they cannot both fit into a single crystal lattice. Figure 6.8 schematically shows the vapor pressure and chemical potential of naphthalene in a liquid solution with benzene near room temperature. The standard state of naphthalene for the liquid solution is supercooled liquid naphthalene, which has a higher chemical potential than solid naphthalene. There is a range of mole fractions of naphthalene near unity in which the chemical potential of naphthalene in the solution would exceed that of the solid naphthalene. The mole fraction of naphthalene at which its chemical potential equals that of the solid represents the maximum solubility of naphthalene in a solution with benzene. A solution with this composition is said... 

Dissolution indicates the rate-limiting step for compound absorption when drugs are administered orally. The solubility of a pharmaceutical compound represents its maximum concentration in an aqueous buffer. Additional compound will not dissolve above this concentration. The solubility value is often heavily dependent upon pH and temperature and is typically measured at physiologically important pH levels and body temperature. The standards for dissolution testing are determined by the United States Pharmacopoeia (USP). Testing typically requires sampling of a solution at 15, 30, 45, and 60 min for immediate-release products. /./Pl.C is ideally suited for use in conjunction with USP apparatus types I or II and can rapidly analyze multiple time points or replicate samples. 

Solubility and speciation. Minimum requirements for reliable thermodynamic solubility studies include (i) solution equilibrium conditions (ii) effective and complete phase separation (iii) well-defined solid phases and (iv) knowledge of the speciation/oxidation state of the soluble species at equilibrium. Ideally, radionuclide solubilities should be measured in both oversaturation experiments, in which radionuclides are added to a solution untU a solid precipitates, and undersaturation experiments, in which a radionuchde solid is dissolved in aqueous media. Due to the difference in solubilities of crystalline versus amorphous solids and different kinetics of dissolution, precipitation, and recrystalhzation, the results of these two types of experiments rarely agree. In some experiments, the maximum concentrahon of the radionuchde source term in specific water is of interest, so the sohd that is used may be SF or nuclear waste glass rather than a pure radionuclide solid phase. 

The properties of SFs make them ideal for extracting analytes from solid matrices such as soils, agricultural products, foods, and solid sorbents. Supercritical fluids have the ability to maximize the extraction selectivity by controlling the temperature and pressure of the supercritical fluid (Figure 11.27) (85). Initially, the solubility of an analyte in a supercritical gas is dependent on solute vapor pressure thus the solubility of the analyte in the gas first decreases with a rise in pressure reaching a point of minimum solubility. As the gas is compressed into the critical phase, there is a rapid increase in analyte solubihty, which ends at a maximum pressure that is determined by the extraction temperature. Any additional increase in pressure will only slightly increase analyte solubility. Also, in... 

These expressions are applicable to drugs and drug-related ionizable substances, such as asparagine, aspartic add, caffeine, leucine, nalidixic acid, paracetamol, salicylic acid, and sulfanilamide. However, the log-linear expression (8.17) or the first two terms on the right-hand side of Equation 8.18 and even its modificafion in terms of the complete Equation 8.18 cannot model cases where the solubility curve exhibits a maximum as is observed in many cases, a problem solved when fluctuation theory is employed in the calculations as pointed out by Ruckenstein and Shulgin, [57]. If the solute is rather poorly soluble in the solvents and their mixtures, then solute-solute interactions can be ignored and the mutual interactions of the solvent components can then be treated either as ideal or as non-ideal. The molar volume of the binary solvent mixture is expressed as VJ +s) = where c is an empirical parameter that in... 

The normal melting temperature of phenanthrene is 96.3°C. Its enthalpy change of fusion is 18.6kJmol. Find the solubility (maximum mole fraction) of phenanthrene in a liquid solution with naphthalene at 82.0°C. Assume that the liquid solution is ideal and that no solid solubility occurs. 

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