Infinite-dilution solubility

In Eq. 1.19, the sum is over all charged species in the solution. In the limit of infinite dilution, soluble complexes should make a negligible contribution to Ief. If this is true, then Eqs. 1.16 and 1.18 can be combined into the following single equation ... 

FIGURE 20.4-1 Linesr relationship between the infinite dilution solubility coefficient and ihe amorphous fraction in the polymer. The data are for polyethylene al 25°C,S... 

In this section, we test the behavior of the NET-GP procedure for a gas-polymer mixture whose solubility has been characterized in both equilibrium and non-equilibrium conditions, that is, above and below the glass transition temperature Tg of the polymer. In Figure 2.1 we plot the value of the infinite dilution solubility coefficient of CO2 in poly(bisphenol-A) carbonate (PC) as a function of the inverse absolute temperature, as measured by Wang and Kamiya l The infinite dilution solubility coefficient, Sq, expressed in cm (STP)/(cm atm), is the slope of the solubility isotherm, in the limit of very low pressures ... 

An infinite dilution solubility parameter for the polymer in terms of measurable thermodynamic quantities may be defined [60] ... 

The inverse phase gas chromatography method has the advantage of providing values for the infinite dilution solubility parameter, over a range of temperatures. This is particularly valuable for the prediction of phase equilibria at elevated temperatures. The value of at 25°C can be estimated by using the expected temperature dependence for X (Eq. B 18) of... 

If the mutual solubilities of the solvents A and B are small, and the systems are dilute in C, the ratio ni can be estimated from the activity coefficients at infinite dilution. The infinite dilution activity coefficients of many organic systems have been correlated in terms of stmctural contributions (24), a method recommended by others (5). In the more general case of nondilute systems where there is significant mutual solubiUty between the two solvents, regular solution theory must be appHed. Several methods of correlation and prediction have been reviewed (23). The universal quasichemical (UNIQUAC) equation has been recommended (25), which uses binary parameters to predict multicomponent equihbria (see Eengineering, chemical DATA correlation). 

Calculation of Liquid-to-Gas Ratio The minimum possible liquid rate is readily calculated from the composition of the entering gas and the solubility of the solute in the exit liquor, saturation being assumed. It may be necessaiy to estimate the temperature of the exit liquid based on the heat of solution of the solute gas. Values of latent and specific heats and values of heats of solution (at infinite dilution) are given in Sec. 2. 

The critical hydrogen content for the ductility loss increased with increasing hydrogen solubility in the alloy. The fracture surfaces were not characteristic of those found under conditions of SCC. In terms of hydrogen and deuterium solubility in a similar series of bcc alloys, the equilibrium constants were determined at infinite dilution as a function of temperature The free energy function was expressed in terms of the bound-proton model. 

It is not only the solid state of a drug that suffers from ambiguities, but also the aqueous state. The state relevant for the intrinsic solubility is the state of the saturated solution of the neutral species. Since most aqueous drug solubilities are small, direct interactions of the drug molecules are usually rare. Hence, this state is usually very similar to the state of the drug at infinite dilution in water. Most computational methods disregard saturation effects. Usually this is a good approximation, but one should keep in mind that this approximation may result in some moderate, but systematic errors at the upper end of the solubility scale. 

Salts such as silver chloride or lead sulfate which are ordinarily called insoluble do have a definite value of solubility in water. This value can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductivity, KV, is equal to the equivalent conductivity at infinite dilution which according to Kohlrausch s law is the sum of ionic conductances or ionic mobilities (ionic conductances are often referred to as ionic mobilities on account of the dependence of ionic conductances on the velocities at which ions migrate under the influence of an applied emf) ... 

Bartle et al. [286] described a simple model for diffusion-limited extractions from spherical particles (the so-called hot-ball model). The model was extended to cover polymer films and a nonuniform distribution of the extractant [287]. Also the effect of solubility on extraction was incorporated [288] and the effects of pressure and flow-rate on extraction have been rationalised [289]. In this idealised scheme the matrix is supposed to contain small quantities of extractable materials, such that the extraction is not solubility limited. The model is that of diffusion out of a homogeneous spherical particle into a medium in which the extracted species is infinitely dilute. The ratio of mass remaining (m ) in the particle of radius r at time t to the initial amount (mo) is given by ... 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Haines, R.L.S., Sandler, S.L. (1995) Aqueous solubilities and infinite dilution activity coefficients of several polycyclic aromatic hydrocarbons. J. Chem. Eng. Data 40, 835-836. 

This equation has the expected behavior that AG< becomes more positive with decreasing solubility of the solute. However, free energies of solvation for different solutes cannot be related to their relative solubilities unless the vapor pressures of the different solutes are similar or one takes account of this via Equation 76. Furthermore, if the solubility is high enough that Henry s law does not hold, then one must consider finite-concentration activity coefficients, not just the infinite-dilution limit. 

A wide range of values (one decade ) could be obtained using correlations as well as using different experimental methods [34, 38, 43]. As for solubility, diffusion coefficient at infinite dilution should be determined experimentally using the real liquid phase. Experimental methods are, however, more complex to carry out and correlations are widely used. 

The solubilities of ammonia, carbon dioxide, and hydrogen sulfide were obtained from binary data and expressed in terms of a Henry s constant for infinite dilution and an interaction parameter ... 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

Table 5.3 Solute and solvent solubility isotope effects for (benzene-water) solutions at 306.2 K obtained from IE s on Henry s Law coefficients, Ki and Kn- [Isotope effects on free energies of transfer, ideal gas to solution in the limit of infinite dilution] (Dutta-Choudhury, M., Miljevic, N.

The thermodynamic connection between IE s on gas solubility, infinite dilution Henry s law constants, and transfer free energy IE s, implies that gas-liquid chromatography should be a convenient way to study solvent effect IE s. That in fact is the case, and many authors have reported on chromatographic isotope separations and on the interpretation of the separation factors in terms of the transfer free energy IE s (Section 8.5). 

Wright, D.A., Sandler, S.I., and DeVoll, D. Infinite dilution activity coefficients and solubilities of halogenatedhydrocarbons in water at ambient temperature, iinviron. Sci. Tec/mo/., 26(9) 1828-1831, 1992. 

Zielenjiewicz, W., Golankiewicz, B., Perlovich, G.L., and Kozbial, M. Aqueous solubilities, infinite dilution activity coefficients and octanol-water partition coefficients of tricyclic analogs of acyclovir. /. Solution Chem., 28(6) 731-745,1999. 

For an ionic solute dissociating into v ions, the temperature coefficient is 1/v times the right-hand side of Eq. (2.60). Again, it is assumed that the solubility is sufficiently low for the mean ionic activity coefficient to be effectively equal to unity and independent of the temperature. When this premise is not met, then corrections for the heat of dilution from the value of the solubility to infinite dilution must be added to Asoi //°b in Eq. (2.60). 

Calorimetric measurements are time consuming and very expensive because of the amount of the IL taken to the experiment. The results usually show the same type of interaction as in other experiments as the activity coefficients at the infinite dilution or solubility measurements. Prom calorimetric measurements it can be observed that the molar heat capacities depend linearly on the temperature and increase proportionally to the alkyl chain length of the cation. 

---