Phase rule dissolution

If two salts which do not react chemically to produce a double salt (contact with a quantity of solvent insufficient for complete dissolution, the composition of the solution is independent of the proportions of the two solids and is definite at a fixed temperature, as we see from the phase rule ... 

Because the ratio (aK+/ajj+) is fixed, but SiOj continues to increase as K-feldspar dissolves, kaolinite reacts to form muscovite, and the solution follows path D E, at which point the solution becomes saturated with quartz, and if equilibrium is maintained, quartz will begin to precipitate. With four components (KjO, AljOj, Si02, H2O), a maximum of four phases can coexist at our arbitrarily chosen T and P (25 °C, 1 atm) according to the phase rule. With quartz, muscovite, kaolinite, and water, this number has now been reached and cannot be exceeded (K-feldspar doesn t count it is being used as a source of solutes, and has not yet equilibrated with the solution). Therefore, if we continue to add KjO, AI2O3, and SiOj from the K-feldspar to the solution, the solution will stay at point E while kaolinite reacts with the solution to form muscovite, and quartz continues to precipitate. When kaolinite is all used up, additional dissolution of K-feldspar will drive the solution composition along E F, with the Si02 content of the solution buffered by the presence of quartz. At point F, K-feldspar finally becomes stable. 

The thermodynamic equilibria of amphiphilic molecules in solution involve four fundamental processes (1) dissolution of amphiphiles into solution (2) aggregation of dissolved amphiphiles (3) adsorption of dissolved amphiphiles at an interface and (4) spreading of amphiphiles from their bulk phase directly to the interface (Fig. 1.1). All but the last of these processes are presented and discussed throughout this book from the thermodynamic standpoint (especially from that of Gibbs s phase rule), and the type of thermodynamic treatment that should be adopted for each is clarified. These discussions are conducted from a theoretical point of view centered on dilute aqueous solutions the solutions dealt with are mostly those of the ionic surfactants with which the author s studies have been concerned. The theoretical treatment of ionic surfactants can easily be adapted to nonionic surfactants. The author has also concentrated on recent applications of micelles, such as solubilization into micelles, mixed micelle formation, micellar catalysis, the protochemical mechanisms of the micellar systems, and the interaction between amphiphiles and polymers. Fortunately, almost all of these subjects have been his primary research interests, and therefore this book covers, in many respects, the fundamental treatment of colloidal systems. 

In the previous chapters, the dissolution and micellization of surfactants in aqueous solutions were discussed from the standpoint of the degrees of freedom as given by the phase rule. The mass-action model for micelle formation was found to be better for explaining the phenomena of surfactant solutions than the phase-separation model. Two models have similarly been used to explain the Krafft point, one postulating a phase transition at the Krafft point and the other a solubility increase up to the CMC at the Krafft point. The most recent version of the first approach is a melting-point model for a hydrated surfactant solid. The most direct approach to the second model of the Krafft point rests entirely on measurements of the solubility and CMC of surfactants with temperature. From these mesurements the concept of the Krafft point can be made clear. This chapter first reviews the concepts used to relate the dissolution of surfactants to their micellization, and then shows that the concept of a micelle temperature range (MTR) can be used to elucidate various phenomena concerning dissolution... 

Various theories, ranging from qualitative interpretations to those rooted in irreversible thermodynamics and geochemical kinetics, have been put forward to explain the step rule. A kinetic interpretation of the phenomenon, as proposed by Morse and Casey (1988), may provide the most insight. According to this interpretation, Ostwald s sequence results from the interplay of the differing reactivities of the various phases in the sequence, as represented by Ts and k+ in Equation 26.1, and the thermodynamic drive for their dissolution and precipitation of each phase, represented by the (1 — Q/K) term. 

Secondary phases predicted by thermochemical models may not form in weathered ash materials due to kinetic constraints or non-equilibrium conditions. It is therefore incorrect to assume that equilibrium concentrations of elements predicted by geochemical models always represent maximum leachate concentrations that will be generated from the wastes, as stated by Rai et al. (1987a, b 1988) and often repeated by other authors. In weathering systems, kinetic constraints commonly prevent the precipitation of the most stable solid phase for many elements, leading to increasing concentrations of these elements in natural solutions and precipitation of metastable amorphous phases. Over time, the metastable phases convert to thermodynamically stable phases by a process explained by the Guy-Lussac-Ostwald (GLO) step rule, also known as Ostwald ripening (Steefel Van Cappellen 1990). The importance of time (i.e., kinetics) is often overlooked due to a lack of kinetic data for mineral dissolution/... 

Besides fluid mechanics, thermal processes also include mass transfer processes (e.g. absorption or desorption of a gas in a liquid, extraction between two liquid phases, dissolution of solids in liquids) and/or heat transfer processes (energy uptake, cooling, heating, drying). In the case of thermal separation processes, such as distillation, rectification, extraction, and so on, mass transfer between the respective phases is subject to thermodynamic laws (phase equilibria) which are obviously not scale dependent. Therefore, one should not be surprised if there are no scale-up rules for the pure rectification process, unless the hydrodynamics of the mass transfer in plate and packed columns are under consideration. If a separation operation (e.g. drying of hygroscopic materials, electrophoresis, etc.) involves simultaneous mass and heat transfer, both of which are scale-dependent, the scale-up is particularly difficult because these two processes obey different laws. 

The media represented in Table 10 contain, as a rule, a protic component but in small amounts. However, the content of proton donors can be increased appreciably hydrogenation of benzene can be effected in mixtures of water and aptotic solvents (such as diglyme, ethylenediamine, sulfolan. Table 11). Furthermore, benzene can be reduced not only in a mixture of aptotic and protic solvents but often in protic media as well. Mono- and dibasic alcohols and also water (Table 11) proved to be suitable for the purpose. Although the presence of tetrabutylammonium cations enhances to some extent the dissolution of benzene in an aqueous phase. 

It has been noted from the earliest dissolution work [39] that, for many substances, the dissolution rate of an anhydrous phase usually exceeds that of any corresponding hydrate phase. These observations were explained by thermodynamics, where it was reasoned that the drug in the hydrates possessed a lower activity and would be in a more stable state relative to their anhydrous forms [74]. This general rule was found to hold for the previously discussed anhydrate/hydrate phases of theophylline [42,44,46], ampicillin [38], metronidazone benzoate [37], carbamazepine [34,36], glutethimide [75], and oxyphenbutazone [72], as well as for many other systems not mentioned here. In addition, among the hydrates of urapidil, the solubility decreases with increasing crystal hydration [58]. 

Since the mid-1970s, a number of exceptions to the general rule have been found. For example. Fig. 8 shows that the hydrate phases of erythromycin exhibit a reverse order of solubility where the dihydrate phase exhibits the fastest dissolution rate and the highest equilib-... 

---