Ostwald s, solubility

Ostwald s solubility product, l, represents the ratio of the volume of absorbed gas to that of the liquid at the temperature and partial pressure of measurement. It is not reduced to 0° C. and 760 mm. Hence, if the measurements are made at atmospheric pressure... 

A. Solubility of Gases.1—This is usually expressed m one of two ways, namely, as Bunsen s Absorption Coefficient, ft, or as Ostwald s Solubility expression, l. These terms have already been defined (p. 36). 

Metastable crystalline phases frequently crystallise to a more stable phase in accordance with Ostwald s rule of stages, and the more common types of phase transformation that occur in crystallising and precipitating systems include those between polymorphs and solvates. Transformations can occur in the solid state, particularly at temperatures near the melting point of the crystalline solid, and because of the intervention of a solvent. A stable phase has a lower solubility than a metastable phase, as indicated by the solubility curves in Figures 15.7a and 15.7/ for enantiotropic and monotropic systems respectively and,... 

Formation of trimetaphosphate anions from those of Graham s salt also occurs in solution. In water this process is not associated with hydrolytic cleavage of the P—0—P bonds, as was at first assumed (10, 322), but is independent of it (361). Thus polyphosphates of long-chain amines which are soluble in benzene form trimetaphosphate quantitatively on warming the anhydrous solution (359). This transformation follows Ostwald s rule for successive transformations, since trimetaphosphates are more stable than polyphosphates (322). 

Ostwald (1900), using the thermodynamic relationship between vapor pressure of spherical drops and the curvature of surface, derived an equation giving the relation between solubility and particle size. Ostwald s equation was later modified by Freundlich (1909), and is as follows ... 

At present there is no trustworthy method for measuring the surface tension of most solids. An estimate for mica1 depends on the work required to cleave the crystal. Ostwald s older solubility method involves large and incalculable errors in practice. The usual methods for liquids fail, because of the non-mobility of the surface. 

Reactive crystallization operations are subject to oiling out and/or agglomeration because of the inherently high local supersaturations encountered. As indicated in Section 10.3, the formation of a crystal may be preceded by oiling out as the first physical form that may or may not be observed (see also Chapter 5, Section 5.4). This oil may separate as a second phase because of the normally extremely low solubilities of the reaction products that result from the chemical reaction. This low solubility can cause a second liquid phase to form on a time scale that is shorter than the nucleation induction time. These issues are considered in Ostwald s Rule of Stages. 

The dependence of nucleation rate on solubility is also consistent with Ostwald s (1897) law of stages regarding the preferential crystallization of metastable crystalline phases. It states that When leaving an unstable state, a system does not seek out the most stable state, rather the nearest metastable state which can be reached with minimal loss of free energy. This indicates that a metastable (more soluble) crystalline phase will generally crystallize before a more thermodynamically stable (less soluble) crystalline phase, because it will have a higher nucleation rate. 

As discussed earlier in the Thermodynamics section of this chapter, the difference in free energy between solid phases (i.e. polymorphs and solvates) is directly proportional to their relative solubilities (Equation 2). Therefore, a saturated solution of a less stable (more soluble) phase is super-saturated with respect to a more stable (less soluble) phase. Since super-saturated solutions are metastable, a more stable phase will eventually crystallize in order to establish equilibrium and remove supersaturation. According to Ostwald s (1897) Law... 

P) is the Bunsen coeff. in mL gas/mL H2O at STP. (Z) is the Ostwald coeff. in mL gas/mL H2O at stated temp. Adapted from W.F. Linke, A. Seidell s Solubilities of Inorganic and Metal-organic Compounds, American Chemical Society, 1965. ... 

In Figure 6.43b, form II is stable at temperatures below the transition temperature T and form I is stable above T. At the transition temperature both forms have the same solubility and reversible transformation between these two enantiotropic forms I and II can be effected by temperature manipulation. Figure 6.43c, however, depicts the intervention of metastable phases (the broken line extensions to the two solubility curves) which bear evidence of the importance of kinetic factors which for a time may override thermodynamic considerations. For example, if a solution of composition and temperature represented by point A (supersaturated with respect to both I and II) is allowed to crystallize it would not be unusual if the metastable form I crystallized out first even though the temperature would suggest that form II is the stable form. This would simply be an example of Ostwald s rule (section 5.7) being followed. This behaviour would occur, for example, if form II had the faster nucleation and/or crystal growth rates. However, if the crystals of form I were kept in contact with the mother liquor, transformation could occur as the more soluble form I crystals dissolve and the less soluble form II crystals nucleate and grow. 

Process changes in chemistry that increase the probability that new compounds will be isolated in amorphous or thermodynamically unstable polymorphic form have the effect of increasing the apparent aqueous solubility of newly synthesized compounds. Ostwald s rule of stages explains the common phenomenon that the physical form that is first isolated for a newly... 

At any partial pressure of gas, p, , the mole fraction solubility may be calculated from Ostwald s coefficient L as. 

Ostwald s first publication was on the equilibrium in the hydrolysis of bismuth chloride, which, as in the cases of the solubilities of zinc sulphide and calcium oxalate in acids, he found to obey the law of mass action. In the work with calcium oxalate he found that the different solubilities of the different forms of the solid phase could influence the results. ... 

For historical reasons, there are several different ways to express gas solubilities in liquids, such as Bunsen s and Ostwald s coefficients. These are not treated here in detail, and the reader is referred to Refs. [1] and [2]. Nowadays, the most common means to express gas solubilities is to turn to the equilibrium molar fractions or x) of dissolved gas A and to the temperature and pressure of the gas. From the ratio... 

Another way of expressing the solubility is given by Ostwald s coefficient, L, which is equal to the ratio of the concentration of the solute in the liquid phase to its concentration in the vapor phase. The mole fraction Xg is related to the Ostwald coefficient by... 

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