Saturation ratio solubility equilibrium

As before, the saturation ratio S can also be expressed as a/ao, where a and a0 are the actual and equilibrium activities, respectively, of the solutes that characterize the solubility. Once nuclei of critical size Xj+1 (in Eq. 6.1) have been formed, crystallization is spontaneous. 

The lower concentration limit of the metastable region (A-B in Fig. 7-1) is the equilibrium solubility of the compound in the solvent system. The upper limit (C-D) represents a super-saturation ratio below which nucleation is relatively slow but above which nucleation will be spontaneous. Chapters 1 and 2 give more detailed discussion on the metastable region. 

Kohler theory describes cloud droplet activation and growth from soluble particles as an equilibrium process [171], The Kohler equation takes into account two competing effects the Raoult or solute, effect which tends to decrease the equilibrium vapor pressure of water over the growing droplet, and the Kelvin, or curvature effect, which serves to increase the equilibrium vapor pressure. The Kohler curve O ig. 3) for a growing droplet describes the equilibrium saturation ratio of water as a function of droplet size and several parameters inherent to the aerosol particle [171, 172] ... 

The possibility that a separate BaC03 phase precipitated in the speed runs (at levels undetectable by x-ray diffraction) also must be noted. Since calcite is approximately three times as soluble as witherite (BaC03), the latter can precipitate from a solution at equilibrium with calcite only if the molar ratio of Ba2 to Ca2 exceeds 1 3. Starting compositions for the speed runs had Ba2 /Ca2 ratios from 3.6 x 10-if to 3.9 x 10 3 and final compositions from 2.6 x 10 3 to 2.3 x 1(T2. To exceed the solubility of witherite during these runs, in which the rapid decarboxylation supersaturates the solution relative to calcite, minimum supersaturations ranging from 14 to 130 with respect to calcite would have been required. Such supersaturations would appear difficult to achieve by decarboxylation, especially in the presence of calcite seed. Viewed in another fashion, the C032 saturation concentration of 0.11 g calcite per 200 ml solution at the start of a run is 9.1 x 10 7M. After decarboxylation to atmospheric levels of C02 and precipitation of calcite... 

The direction of a reaction can be assessed straightforwardly by comparing the equilibrium constant (Keq) and the ratio of the product solubility to the substrate solubility (Zsat) [39]. In the case of the zwitterionic product amoxicillin, the ratio of the equilibrium constant and the saturated mass action ratio for the formation of the antibiotic was evaluated [40]. It was found that, at every pH, Zsat (the ratio of solubilities, called Rs in that paper) was about one order of magnitude greater in value than the experimental equilibrium constant (Zsat > Keq), and hence product precipitation was not expected and also not observed experimentally in a reaction with suspended substrates. The pH profile of all the compounds involved in the reaction (the activated acyl substrate, the free acid by-product, the antibiotic nucleus, and the product) could be predicted with reasonable accuracy, based only on charge and mass balance equations in combination with enzyme kinetic parameters [40]. 

Strontium sulphate would dissolve in the solution of sodium carbonate in the same manner as it would in pure water until it had saturated the solution, and its solubility product, which is equal to 0.0006 X 0.0006, was reached, but for the fact that long before this could occur the solution would be supersaturated with respect to strontium carbonate, the solubility product of which is only equal to 0.00007 X 0.00007. Thus strontium carbonate is precipitated continuously as strontium sulphate dissolves and since the solution cannot become saturated with the latter as long as a large excess of carbonate ions is present, the solid salt finally remaining will consist entirely of strontium carbonate, provided a sufficient amount of sodium carbonate were employed. The reaction which takes place is, however, reversible, SrSO + Na2C03 SrCOj + NasSO, and, if strontium carbonate were boiled with a solution of sodium sulphate, the solid would change into sulphate until carbonate ions had accumulated in the solution to such an extent as to make the concentration ratio [C03 ] [SO4 ] = 1 74. When this ratio prevails, both solids are in equilibrium with the solution and no change takes place in either direction. 

The hydrophobicity of an organic molecule is quantified by means of its partition coefficient between octanol and water (Kow)- Kow is equal to the ratio of compound concentrations at saturation in n-octanol and in water at equilibrium and at a specific temperature. n-Octanol possesses structural properties analogous to lipidic tissues of organisms, and so Kow allows evaluation of the lipophilic character of the contaminant and thus of its capacity to be accumulated in the lipidic tissues of living organisms. The Kow value of hydrophobic organic pollutants (HOPs) is higher than 100. They are nonpolar molecules with a low water solubility. Their weak solubility and their hydrophobicity... 

Crystals form in supersaturated solutions in which the solute concentration exceeds its solution solubility. Supersaturation is usually expressed as either of the ratios dc or (c — c )lc, where c is the concentration of solute before crystallization and is the solute equilibrium saturation concentration. Supersaturated solutions are thermodynamically metastable. Equilibrium can be restored by reducing the solute concentration through precipitation or formation of nuclei and subsequent crystal growth. The super saturation requirements for nucleation and... 

The estimation of transfer activity coefficients was reviewed by Popovych. One method for measurement of transfer activity coefficients for electrolytes or neutral molecules is by measurement of solubility. When the solubility is low, the effects of contamination by traces of water can be profound. Furthermore, reliable solubility values even in water are difficult to obtain. Nevertheless, if saturated solutions of a substance in water and another solvent are considered, and if each solution can be shown to be in equilibrium with the same solid, the value of y, is given by the ratio of the solubility products ( sp)water/( sp)soivent electrolyte producing n ions. For... 

One of the primary aims in the study of the geochemistry of carbonates in marine waters is the calculation of the saturation state of the seawater with respect to carbonate minerals. The saturation state of a solution with respect to a given mineral is simply the ratio of the ion activity or concentration product to the thermodynamic or stoichiometric solubility product (Equation (3)). In seawater the latter is generally used and Hmingjai is the symbol used to represent the ratio. If H = 1, the solid and solution are in equilibrium if H < 1, the solution is undersaturated and mineral dissolution can occur, and if H > 1, the solution is supersaturated and precipitation should... 

FIG. 63. Equilibrium solubility of SO3 (wt.%) in melts of the system Si02—Na20 with component ratios of 4 to 1.5 at 1200 in terms of partial pressure of SO2 + O2. The dashed line indicates saturation (Holmquist, 1966). 

The two solids CuBr(s) and AgBr(s) are only very slightly soluble in water lsmall amount of KBr is added and dissolves completely. Compute the ratio of [Cu ] to [Ag ] after the system reestablishes equilibrium. 

The second hypothesis considers the solid as a multi-component solid-solution, capable of adjusting its composition in response to the aqueous solution composition, given the long equilibration period, the relatively high solubility of the solid and relatively low solid to solution ratio. In this case, the assumption of thermodynamic equilibrium may apply. If the equilibration period is too short for thermodynamic equilibrium to have been achieved, but if an outer surface layer of the solid has been able to recrystallise (because of the high solubility of the solid), the concept of primary saturation may apply. 

The equilibrium water saturation of a polymeric system increases with the number of polar groups present in the polymeric matrix. Circumstances like the accessibility of the polar groups, the relative strength of the water-water versus water-polymer bonds and for semi-crystalline polymers the degree of crystallinity, hamper a straightforward correlation between the number of polar groups and the solubility. Van Krevelen [1] presents the amount of water per structural group at equilibrium (expressed as molar ratio), as what he calls the best possible approach to the sorptive capacity of (amorphous) polymers versus water. 

A partition coefficient is defined by the ratio of the concentrations of a compound in two immiscible phases that are at equilibrium. It is common, though not necessary, for one phase to be water and the second an organic solvent, such as hexane, benzene, ether, and so on. It is important to emphasize that Aqw is not the ratio of the solubilities of the compound in octanol and water, because, since the two liquids are at equilibrium, the octanol phase will be saturated with water and the water with octanol. The use of n-octanol dates from the late nineteenth century when water-octanol was chosen as a surrogate to reflect uptake of pharmaceuticals into organisms. In retrospect, this turned out to be a wise choice and over the past 30 years there has been a continuing interest in the study of initially stimulated... 

That is why the value of the ratio in parentheses on the right may be used in the same way as power exponent of solution D,. saturation. Both parameters tend to 1 with water saturation, and the closer the solution and mineral to equilibrium, the smaller the difference between them. Relative saturation of ground water with a specific mineral often is evaluated graphically (Figure 2.27). We will review the graphic determination of mineral solubility limit in water on an example of barite and orthoclase. 

Dimroth measured the rate of rearrangement (intramolekulare Umlager-ung) in different solvents and used an equation given by van t Hoff if are the equilibrium concentrations of two forms in a solution and s y the solubilities (saturation concentrations), the ratio of the relative concentrations is independent of the solvent ( aAa) ( b/%) = const. 

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