Solubility equilibrium conditions

A convenient method of interpreting water analysis for the purpose of determining the calcium carbonate solubility equilibrium conditions is embodied in the Langelier equation. The Langelier equation can be used to... 

The solubility of solids depends on particle size in a similar way. The solubility equilibrium condition is... 

Intercalation from solutions in nonaqueous solvents (S21). This method may suffer from the drawback that final stoichiometries may not correspond to equilibrium conditions, because of partial leaching out of metal halide. For this reason, some chlorides can be intercalated only from solvents in which they have limited solubility iLS). It has often been the practice to wash intercalates with solvents to remove the excess of intercalant this may lead to stoichiometries lower than the original ones. The two-ampoule method may, therefore, be preferable (H24). 

Solubility measurement at a single pH [37-39] under equilibrium conditions is largely a labor-intensive procedure, requiring long equilibration times (12h-7 days). It s a simple procedure. The drug is added to a standard buffer solution (in a flask) until saturation occurs, indicated by undissolved excess dmg. The thermostated saturated solution is shaken as equilibration between the two phases is established. After microfiltration or centrifugation, the concentration of the substance in the supernatant solution is then determined using HPLC, usually with UV detection. If a solubility-pH profile is required, then the measurement needs to be performed in parallel in several different pH buffers. 

Crystallization involves formation of a solid product from a homogeneous liquid mixture. Often, crystallization is required as the product is in solid form. The reverse process of crystallization is dispersion of a solid in a solvent, termed dissolution. The dispersed solid that goes into solution is the solute. As dissolution proceeds, the concentration of the solute increases. Given enough time at fixed conditions, the solute will eventually dissolve up to a maximum solubility where the rate of dissolution equals the rate of crystallization. Under these conditions, the solution is saturated with solute and is incapable of dissolving further solute under equilibrium conditions. In fact, the distinction between the solute and solvent is arbitrary as either component can be considered to be the solute or... 

Such a relationship describes how a chemical will partition between water and the atmosphere under equilibrium conditions and is appropriate only for dilute solutions which are typically observed in the environment. Certain hydrocarbons despite possessing relatively low vapor pressures, may tend to partition significantly toward the air. This is largely a result of their correspondingly low water solubilities which result in low values for Kw. Therefore, chemicals which have low values for Kw have a greater tendency to partition towards the air and volatilize from solution. 

The microautoclave solvent activity tests measure coal conversion in a small batch reactor under carefully controlled conditions. The tests are described as Kinetic, Equilibrium and SRT. The Kinetic and Equilibrium Tests measure coal conversion to tetrahydrofuran solubles at conditions where conversion should be monotonically related to hydrogen transfer. The Kinetic Test is performed at 399°C for 10 minutes at an 8 to 1 solvent to coal ratio. The combination of high solvent ratio and low time provide a measure of performance at essentially constant solvent composition. The measured conversion is thus related to the rate of hydrogen donation from solvent of roughly a single composition. In contrast, the Equilibrium Test is performed at 399°C for 30 minutes at a 2 to 1 solvent to coal ratio. At these conditions, hydrogen donors can be substantially depleted. Thus performance is related to hydrogen donor... 

The partial pressure of oxygen is measured with a gas detector in the atmosphere of a sewer network and found to be equal to 0.18 atm. This value is, probably because of oxygen consumption of the wastewater and limited ventilation, slightly lower than in the city atmosphere, where it was measured at 0.21 atm. Determine at 25°C the solubility of 02 (i.e., at equilibrium conditions) in the wastewater (considered as water) of the sewer. 

There is also a diffusion rate factor when polymers are exposed to any gas or liquid. Usually absorption of fluid (swelling) takes place faster than extraction of soluble constituents of the polymer and builds up to an equilibrium condition as shown in Figure 4.2 (curve A). If extraction is also taking place, for example from a plasticised material, a maximum swelling may be reached (curve B). If the absorption of fluid is accompanied by oxidation, the volume may continue to increase (curve C). 

To allow for solubility measurements by a dynamic procedure, equilibrium conditions have to be established in the extraction cell. If a sufficiently low flow rate is adjusted, the CO2 passing the extraction cell is loaded with an equilibrium substance amount in the steady state. 

General solvent extraction practice involves only systems that are unsaturated relative to the solute(s). In such a ternary system, there would be two almost immiscible liquid phases (one that is generally aqueous) and a solute at a relatively low concentration that is distributed between them. The single degree of freedom available in such instances (at a given temperature) can be construed as the free choice of the concentration of the solute in one of the phases, provided it is below the saturation value (i.e., its solubility in that phase). Its concentration in the other phase is fixed by the equilibrium condition. The question arises of whether or not its distribution between the two liquid phases can be predicted. 

The apparent permeability of 11 test compounds was measured in the presence and absence of human serum albumin in the donor compartment, and by solving the differential equations describing the kinetics of membrane permeability, membrane retention and protein binding, the authors were able to obtain the Kd. With the protein in solution rather than immobilized and without the need for mass balance or equilibrium conditions, this approach provides an attractive alternative to existing methods with the potential to be applied to an array of other soluble proteins. 

Most metals of practical importance are actually mixtures of two or more metals. Recall from Section 1.1.3 that these intimate mixtures of metals are called alloys, and when the bond between the metals is partially ionic, they are termed intermetallics. For the purposes of this chapter, and especially this section, we will not need to distinguish between an intermetallic and an alloy, except to note that when a compound is indicated on a phase diagram (e.g., CuAb), it indicates an intermetallic compound. We are concerned only with the thermodynamics that describe the intimate mixing of two species under equilibrium conditions. The factors affecting how two metal atoms mix has already been described in Section 1.1.3. Recall that the solubility of one element in another depends on the relative atomic radii, the electronegativity difference between the two elements, the similarity in crystal structures, and the valencies of the two elements. Thermodynamics does not yet allow us to translate these properties of atoms directly into free energies, but these factors are what contribute to the free energy of... 

T. Clark 6 found tetrasodium pyrophosphate to be less readily soluble in water than the disodium hydrophosphate, Na2HP04. The equilibrium conditions and transition points have not yet been worked out. According to A. B. Poggiale (1863), 100 parts of water dissolve ... 

In the following discussion, only the basic equations that allow the calculation of the solubility of a solid material (solute, component 2) in a dense gas will be reported. The equilibrium condition for component 2 is ... 

Water solubility is defined as the saturation concentration of a compound in water, that is the maximum amount of the compound dissolved in water under equilibrium conditions. The most common units used to express water solubility are... 

Polymer structures that hold silanols at the interface. Good examples of hydrolytically stable crosslinked structures are silica and silicate rocks. Although every oxane bond in these structures is hydrolyzable, a silicate rock is quite resistant to water. Each silicon is bonded to four oxygens under equilibrium conditions with a favorable equilibrium constant for bond retention. The probability that all four bonds to silicon can hydrolyze simultaneously to release soluble silicic acid is extremely remote. With sensitive enough analytical techniques it is possible to identify soluble silica as it -leaches from rocks, but an individual rock will survive in water for thousands of years. 

The fact that silanol persistence can be favored by equilibrium conditions rather than control of condensation kinetics by steric or electronic factors is usually not considered. The phase separation which results from highly condensed systems continuously removes material from deposition solutions, depleting soluble silane species. While condensed silanols or siloxanes are typically not regarded as participating in a reversible reaction with water or alcohol, they do indeed participate in an equilibrium reaction. Iler [16] has shown that even hydrated amorphous silicon dioxide has an equilibrium solubility in methanol, which implies the formation of soluble low molecular... 

For the measurement of solubility the traditional dissolution-equilibrium procedure is employed, i.e., put both the crystals and the mother liquor into a container submerged in a water bath continuously stirred, control the temperature inside the container rigorously at a given value, with the fluctuation no greater than +0.1°C. When the dissolution equilibrium is achieved, measure the concentration of the solute in the liquid phase as the solubility at the temperature given. The equilibrium condition is judged by the criterion that the relative deviation of the values obtained in, at least, three times of adjacent measurements is not greater than %c. 

Of the elements considered in this study (see Table II), nickel, palladium, antimony, and lead are particularly sensitive to the presence of reduced sulfur species (S2, HS") in the groundwater. For each of these radionuclides, if sulfur speciates under thermodynamic equilibrium conditions, solid sulfide phases will control their solubility at low Eh values. The implication of this fact is illustrated in Figure 1 by a bold, dashed line that corresponds to the solubility of nickel in the reference groundwater and a patterned zone representing the total range... 

The fluid phase that fills the voids between particles can be multiphase, such as oil-and-water or water-and-air. Molecules at the interface between the two fluids experience asymmetric time-average van der Waals forces. This results in a curved interface that tends to decrease in surface area of the interface. The pressure difference between the two fluids A/j = v, — 11,2 depends on the curvature of the interface characterized by radii r and r-2, and the surface tension, If (Table 2). In fluid-air interfaces, the vapor pressure is affected by the curvature of the air-water interface as expressed in Kelvin s equation. Curvature affects solubility in liquid-liquid interfaces. Unique force equilibrium conditions also develop near the tripartite point where the interface between the two fluids approaches the solid surface of a particle. The resulting contact angle 0 captures this interaction. 

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