Activity Coefficients from Solubilities

To calculate from solubility measurements values of the activity coefficient of thallous iodate in its saturated solution in the presence of potassiiun chloride and of potassium thiocj ate. 

The solubility of thallous iodate in various salt solutions has been determined by Bdl and George (Trans. Faraday Soc. 1953, 49, 621). The values obtained for the solubility in solutions of potassium chloride and potassium thiocj anate at 25 °C are given in table 1, where s denotes the solubility and c the concentration of added electrol5 te. 

The solubility s of the thallous iodate is related to its mean activity coefficient / (both on the volume concentration scale) by 

We plot log s against c + s in fig. 1. We see that straight lines drawn through the two sets of plotted data extrapolate to give values of 

The slopes of the plots give for the solubilities and activity coefficients up to c = 0.06 mole H 

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TABLE 13.2. Activity Coefficients from Solubility Parameters and from the Wilson Equation... 

Activity Coefficients from Solubility Measurements.—The activity coefficient of a sparingly soluble salt can be determined in the presence of other electrolytes by making use of the solubility product principle. In addition to the equations already given, this principle may be stated in still another form by introducing the definition of the mean ionic concentration, i.e., c , which is equal to c+clr, into equation (109) this equation then becomes... 

Calculation of activity coefficients from mutual solubility data... 

For systems that are only partially miscible in the liquid state, the activity coefficient in the homogeneous region can be calculated from experimental values of the mutual solubility limits. The methods used are described by Reid et al. (1987), Treybal (1963), Brian (1965) and Null (1970). Treybal (1963) has shown that the Van-Laar equation should be used for predicting activity coefficients from mutual solubility limits. 

Brian, P. L. T. (1965) Ind. Eng. Chem. Fundamentals 4, 100. Predicting activity coefficients from liquid phase solubility limits. 

The most important factor in determining KQW is the aqueous-phase activity coefficient (aqueous solubility) of the organic solute. The observed partition coefficients are less than the ideal partition coefficients (K w) as result from 1) the incompatibility of the solute in water-saturated octanol and, to a lesser degree,... 

Calculation of Activity Coefficients from Mutual Solubility Data... 

We focus on the thermodynamic models that deal with the liquid mixtures in this chapter. From the two categories of activity coefficient models, the correlative one is not very useful for solubility prediction and solvent screening purposes. The main reason for this is the lack of experimental data for the binary interaction parameters of the solute-solvent, solute-antisolvent, and solvent-antisolvent systems. As an example, the activity coefficient from... 

This equation is useful for determining activity coefficients from liquid solubility data, as shown in the following illustration. 

Equations (3-6) for the potentiometric and spectrophotometric methods will provide thermodynamic pKa values. For the solubility-pH dependence method [Eqs. (7-8)], the values obtained are apparent values (pKg )/ which are relevant to the ionic strength (7) of the aqueous buffers used to fix the pH value for each solution. If the ionic strength of each buffer solution is controlled or assessed, then the apparent value can be corrected to a thermod)mamic value, using an activity coefficient from one of the Debye-Hiickel equations (Section 2.2.5). If the solubility-pH dependence is measured in several buffer systems, each with a different ionic strength, then the Guggenheim approach can be used to correct the result to zero ionic strength [Eq. (17)]. 

Furthermore, COSMO-RS is known to perform well for predictions of activity coefficients and solubilities in solvent mixtures [14,23] and in most cases reproduces solubility maxima correctly. A challenging problem case, however, the solubility of paracetamol in a water-dioxane mixture, is shown in Figure 9.3. Experimental data for the system paracetamol/water-dioxane have been taken from three different sources [31-33] and compared with COSMOt/term computations at the TZVP and the newer FINE parameterization [6]. 

Another method using liquid-solid equilibria determines solute activity coefficients from temperature-dependent solubility data. The pure solute Y, is in equilibrium with the saturated solution. With reference to the state of the infinitely dilute solution [Eqs. (91a)-(91c)], the equilibrium condition is given by the relation... 

This picture suggests that the more size-symmetric ion pairs such as KCl or NaCl should exhibit stronger attraction in solution than the size-asymmetric salt LiCl. This local argument should also have a bearing on integral thermodynamic properties such as osmotic coefficients, activity coefficients, maximal solubilities or heats of solution (compare Fig. 1). Most of these properties are difficult to obtain from simulations. The osmotic coefficient (p is comparably straightforward to calculate. It is related to the osmotic pressure O via... 

Investigations of the solubilities of aromatic compounds in concentrated and aqueous sulphuric acids showed the activity coefficients of nitrocompounds to behave unusually when the nitro-compound was dissolved in acid much more dilute than required to effect protonation. This behaviour is thought to arise from changes in the hydrogenbonding of the nitro group with the solvent. 

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). 

A.queous Solubility. SolubiHty of a chemical in water can be calculated rigorously from equiHbrium thermodynamic equations. Because activity coefficient data are often not available from the Hterature or direct experiments, models such as UNIFAC can be used for stmcture—activity estimations (24). Phase-equiHbrium relationships can then be appHed to predict miscibility. Simplified calculations are possible for low miscibiHty however, when there is a high degree of miscibility, the phase-equiHbrium relationships must be solved rigorously. 

The tlrermodynamic activity of nickel in the nickel oxide layer varies from unity in contact with tire metal phase, to 10 in contact with the gaseous atmosphere at 950 K. The sulphur partial pressure as S2(g) is of the order of 10 ° in the gas phase, and about 10 in nickel sulphide in contact with nickel. It therefore appears that the process involves tire uphill pumping of sulphur across this potential gradient. This cannot occur by the counter-migration of oxygen and sulphur since the mobile species in tire oxide is the nickel ion, and the diffusion coefficient aird solubility of sulphur in the oxide are both vety low. 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

Finally, as an example of a highly soluble salt, we may take sodium chloride at 25° the concentration of the saturated solution is 6.16 molal. The activity coefficient of NaCl, like that of NaBr plotted in Fig. 72, passes through a minimum at a concentration between 1.0 and 1.5 molal and it has been estimated2 that in the saturated solution the activity coefficient has risen to a value very near unity. Writing y = 1.0, we find that the work required to take a pair of ions from the surface of NaCl into pure water at 25° has the rather small value... 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

The temperature dependence of the activity coefficients is assumed to have a particularly simple form, and this can sometimes lead to serious error at temperatures far away from those used to evaluate the solubility parameters. 

As the components in a liquid mixture become more chemically dissimilar, their mutual solubility decreases. This is characterized by an increase in their activity coefficients (for positive deviation from Raoult s Law). If the chemical dissimilarity, and the corresponding increase in activity coefficients, become large enough, the solution can separate into two-liquid phases. 

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