Infinite-dilution

Activity-coefficient data at infinite dilution often provide an excellent method for obtaining binary parameters as shown, for example, by Eclcert and Schreiber (1971) and by Nicolaides and Eckert (1978). Unfortunately, such data are rare. 

Figure 4-11. Activity coefficients for noncondensable solutes at infinite dilution.

VSTR is useful for estimating partial molar volumes at infinite dilution but is not used here because of Equation (4-17)... 

GAMMA calculates activity coefficients for N components (N 20) at system temperature. For noncondensable components effective infinite-dilution activity coefficients are calculated. 

Activity coefficients for condensable components are calculated with the UNIQUAC Equation (4-15)/ and infinite-dilution activity coefficients for noncondensable components are calculated with Equation (4-22). ... 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

Thus, if the activities of the various species can be detennined or if one can extrapolate to infinite dilution, the measurement of the emf yields the standard free energy of the reaction. 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

The solute-solvent interaction in equation A2.4.19 is a measure of the solvation energy of the solute species at infinite dilution. The basic model for ionic hydration is shown in figure A2.4.3 [5] there is an iimer hydration sheath of water molecules whose orientation is essentially detemiined entirely by the field due to the central ion. The number of water molecules in this iimer sheath depends on the size and chemistry of the central ion ... 

At infinite dilution, the assumption of a constant relaxation time is reasonable and, using Stokes law as well, we have... 

With the knowledge now of the magnitude of the mobility, we can use equation A2.4.38 to calculate the radii of the ions thus for lithium, using the value of 0.000 89 kg s for the viscosity of pure water (since we are using the conductivity at infinite dilution), the radius is calculated to be 2.38 x 10 m (=2.38 A). This can be contrasted with the crystalline ionic radius of Li, which has the value 0.78 A. The difference between these values reflects the presence of the hydration sheath of water molecules as we showed above, the... 

From equation A2.4.38 we can, finally, deduce Walden s rule, which states that the product of the ionic mobility at infinite dilution and the viscosity of the pure solvent is a constant. In fact... 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

Orr W J C 1947 Statistical treatment of polymer solutions at infinite dilution Trans. Faraday Soc. 43 12-27... 

In most colloidal suspensions tire particles have a tendency to sediment. At infinite dilution, spherical particles with a density difference Ap with tire solvent will move at tire Stokes velocity... 

The salts had a high electrical conductivity, and it was claimed that the values of the molar conductances at infinite dilution showed the formation of a binary and ternary electrolyte respectively. 

PARTIAL MOLAR EXCESS ENTHALPY AT INFINITE DILUTION OF THIAZOLE IN VARIOUS SOLVENTS AT SIS.IS K... 

Absorption coefficient, linear decaidic a. K Aqueous solution at infinite dilution aq, CO... 

The solution of 1 mole of HCl gas in a large amount of water (infinitely dilute real solution) is represented by ... 

The equivalent conductivity of an electrolyte is the sum of contributions of the individual ions. At infinite dilution A° = A° -f A, where A° and A are the ionic conductances of cations and anions, respectively, at infinite dilution (Table 8.35). 

As written, equation 6.5 is a limiting law that applies only to infinitely dilute solutions, in which the chemical behavior of any species in the system is unaffected by all other species. Corrections to equation 6.5 are possible and are discussed in more detail at the end of the chapter. 

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). 

Extrapolation to infinite dilution requites viscosity measurements at usually four or five concentrations. Eor relative (rel) measurements of rapid determination, a single-point equation may often be used. A useful expression is the following (eq. 9) (27) ... 

Eor given biaary pair, two-phase behavior likely when infinite dilution activity coefficient of either component ia other component is >7.5. 

A composite curve of heat of infinite dilution of oleum from reported data (3,88—90) is presented in a compiled form in the Hterature (91), where heats of formation of oleums from Hquid or gaseous SO are also reported (Tables 5 and 6). Heat of vaporization data are also available (92). Oleum heat capacity data are presented in Figure 18 (76) solubiUty data for SO2 in oleum can be found in Reference 69. 

The properties of calcium chloride and its hydrates are summarized in Table 1. Accurate data are now available for the heats of fusion of the hexahydrate, the incongment fusion of the tetrahydrate, and the molar heat capacities of the hexahydrate, tetrahydrate, and dihydrate (1). These data are important when considering the calcium chloride hydrates as thermal storage media. A reevaluation and extension of the phase relationships of the calcium chloride hydrates, has led to new values for the heats of infinite dilution for the dihydrate, monohydrate, 0.33-hydrate, and pure calcium chloride (1). 

Experimentally deterrnined equiUbrium constants are usually calculated from concentrations rather than from the activities of the species involved. Thermodynamic constants, based on ion activities, require activity coefficients. Because of the inadequacy of present theory for either calculating or determining activity coefficients for the compHcated ionic stmctures involved, the relatively few known thermodynamic constants have usually been obtained by extrapolation of results to infinite dilution. The constants based on concentration have usually been deterrnined in dilute solution in the presence of excess inert ions to maintain constant ionic strength. Thus concentration constants are accurate only under conditions reasonably close to those used for their deterrnination. Beyond these conditions, concentration constants may be useful in estimating probable effects and relative behaviors, and chelation process designers need to make allowances for these differences in conditions. 

Terminal activity coefficients, 7°, are noted in Figure 3. These are often called infinite dilution coefficients and for some systems are given in Table 1. The hexane—heptane mixture is included as an example of an ideal system. As the molecular species become more dissimilar they are prone to repel each other, tend toward liquid immiscihility, and have large positive activity coefficients, as in the case of hexane—water. 

Hquid-phase activity coefficient (eq. 6) terminal activity coefficient, at infinite dilution constant in Wilson activity coefficient model (eq. 13)... 

The most common method for screening potential extractive solvents is to use gas—hquid chromatography (qv) to determine the infinite-dilution selectivity of the components to be separated in the presence of the various solvent candidates (71,72). The selectivity or separation factor is the relative volatihty of the components to be separated (see eq. 3) in the presence of a solvent divided by the relative volatihty of the same components at the same composition without the solvent present. A potential solvent can be examined in as htfle as 1—2 hours using this method. The tested solvents are then ranked in order of infinite-dilution selectivities, the larger values signify the better solvents. Eavorable solvents selected by this method may in fact form azeotropes that render the desired separation infeasible. 

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