Solubility coefficient overall

Treatment of class (c) membranes, on the other hand, presents a considerably more complicated problem. Here, S and DT in Eqs. (1) and (2) are functions of the spatial coordinates. The problem becomes much more acute if S and DT are also dependent on C 4,5). Under these conditions, transformation of Eqs. (2) into (3) is not generally possible and there are no standard methods, as in the previous cases, of fully characterizing the membrane-penetrant system 3 "5). There is usually no difficulty in determining an overall or effective solubility coefficient but the definition of useful effective diffusion coefficients is a more difficult matter, which, not surprisingly, is a major concern of current research in the field. 

If the component phases denoted by A and B are of sufficient, but still microscopic, size (cf. introductory section) and do not interact appreciably, their individual sorption and diffusion properties may be deduced from measurements on the pure bulk phases. Then, the overall solubility coefficient is given by an additive relation analogous to Eq. (5), except that the volume fractions vA, vB( = 1 — vA) of the respective components in the membranes must be taken into account ... 

Intrinsic reaction rate constant, s overall apparent rate constant, s solubility coefficient, cur liquid-atm/mol stirrer speed, RPM partial pressure, atm... 

For illustration, rubbery polymeric membranes, whose polymeric network is sufficiently elastic and mobile to allow comparatively large organic compounds to diffuse through it (Table 3.6-2), are in general used for the recovery of organic compounds from aqueous solutions. Because of its small size, the bulk solvent, water, unfortunately diffuses through the membrane even better. This is why in organo-philic pervaporation the selectivity is mainly achieved and determined by the ratio of the solubility coefficients (sorption selectivity. Table 3.6-2). Membrane selectivity, as defined in Eq. (7), is an intrinsic parameter and can differ from the overall process selectivity, as wiU be shown later. 

The positive diffusional activation energy is larger in absolute value than the negative AH, and so the overall permeability increases as temperature increases, but to a lower degree than the diffusion coefficient itself It should be noted that the use of equation 34 is only strictly valid when the diffusion and solubility coefficients are independent of concentration. 

An increase in size in a series of chemically similar permeants generally leads to an increase in their solubility coefficients due to their increased boiling points, but will also lead to a decrease in their diffusion coefficients due to the increased activation energy needed for diffusion. The overall effect of these opposing trends is that the permeability generally decreases with increasing permeant size, since for many polymer/permeant pairs the sorption coeffcient will only increase by perhaps a factor of ten whilst the diffusion coefficient can vary by ten orders of magnitude, as previously described. 

The horizontal portion of the plot in Figure 23.6 represents the equilibrium mass uptake—the amount absorbed at equilibrium whose magnitude is influenced by the solubility parameter 8 (Section 23.4.3.1). In reality, coefficient D quite often varies with concentration, so that the overall plot takes on a sigmoid shape (see Section 23.4.4.3), although a horizontal portion is still usually achieved eventually if it is not, the elastomer is possibly a two-phase material (a blend), with one phase much slower at absorbing the incoming liquid. 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

The correlation (or lack of correlation) of other physiochemical characteristics has not yet been established. For instance, are all surfactants irritants Can one classify severity by the size of the molecule Can octanol water partition coefficients predict irritation potential does a propensity to partition out of the ocular fluid mean that a compound presents more of an irritation hazard than one which is more water soluble Theoretically, these data should reflect the ability of a compound to penetrate the eye and cause an irreversible lesion. However, until definitive data are available, physical and chemical parameters will probably have limited utility in an overall assessment of irritation. 

The influence of the solubility of the gas on the shape of the equilibrium curve, and the effect on the film and overall coefficients, may be seen by considering three cases in turn — very soluble, almost insoluble, and moderately soluble gases. 

A solution containing 23 per cent by mass of sodium phosphate is cooled from 313 to 298 K in a Swenson-Walker crystalliser to form crystals of Na3P04.12H20. The solubility of Na3P04 at 298 K is 15.5 kg/100 kg water, and the required product rate of crystals is 0.063 kg/s. The mean heat capacity of the solution is 3.2 kJ/kg deg K and the heat of crystallisation is 146.5 kJ/kg. If cooling water enters and leaves at 288 and 293 K, respectively, and the overall coefficient of heat transfer is 140 W/m2 deg K, what length of crystalliser is required ... 

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