Thermodynamic Behavior of Electrolytes in Mixed ... - ACS Publications

3 Correlation and Prediction of Salt Effect in Vapor-Liquid Equilibrium

Downloaded by UNIV OF MISSOURI COLUMBIA on June 9, 2013 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/ba-1976-0155.ch003

WILLIAM F. FURTER Department of Chemical Engineering, Royal Military College of Canada, Kingston, Ontario, Canada K7L 2W3

A review is presented of techniques for the correlation and pre diction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic con sistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties in herent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings: correlation at fixed liquid com position, extension to entire liquid composition range, predic tion from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent "special binary" approach.

n p h e use of a dissolved salt i n place of a l i q u i d component as the JL separating agent i n extractive distillation has strong advantages i n certain systems w i t h respect to both increased separation efficiency a n d reduced energy requirements. A principal reason w h y such a technique has not undergone more intensive development or seen more than specialized industrial use is that the solution thermodynamics of salt effect i n v a p o r - l i q u i d e q u i l i b r i u m are complex, and are still not w e l l understood. H o w e v e r , even small amounts of certain salts present i n the l i q u i d phase of certain systems can exert p r o f o u n d effects on e q u i l i b r i u m vapor composition, hence on relative volatility, a n d on azeotropic behavior. Also extractive and azeotropic distillation is not the o n l y important application for the effects of salts on v a p o r - l i q u i d e q u i l i b r i u m ; w h i l e used as examples, other potential applications of equal importance exist as w e l l . F o r simplicity, the discussion i n this review w i l l be l i m i t e d to the simplest 26

In Thermodynamic Behavior of Electrolytes in Mixed Solvents; Furter, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1976.

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Correlation and Prediction of Salt Effects

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system of this type possible: one consisting of two volatile components a n d a single salt, the latter considered to be completely nonvolatile. Hence, w h i l e the l i q u i d phase w i l l consist of all three components, the e q u i l i b r i u m vapor w i l l contain only the two volatile species. Most previous investigators w h o have measured v a p o r - l i q u i d e q u i l i b r i u m data i n such systems have used saturated salt concentrations throughout to determine the m a x i m u m salt effect possible at each value of l i q u i d composition. In such a case, of course, salt concentration changes as l i q u i d composition is varied (except i n the unlikely case of a salt being equally soluble i n the two l i q u i d components). H o w e v e r , a f e w investigators, recognizing that salt concentration would tend to remain essentially constant f r o m tray to tray i n an actual distillation c o l u m n (as constant, i n fact, as the concept of constant molal overflow is valid), have preferred to use salt concentrations held constant at values below saturation. T h e majority of the data reported i n the literature are for b o i l i n g systems under isobaric conditions. T h e topics of salt effect i n v a p o r - l i q u i d e q u i l i b r i u m and extractive distillation b y salt effect have been reviewed recently. T h e i r literature is treated b y F u r t e r and C o o k (1); their theory and practice b y Ciparis, Dobroserdov, and K o g a n (2), a n d b y F u r t e r (3); and the state of the art b y F u r t e r (4). C i p a r i s (5) has published a c o m p i l a t i o n of data for 188 systems. T h e selective effect that a salt can have on the volatilities of the two l i q u i d components, and hence on the composition of the equilibrium vapor, comes about p r i m a r i l y through effects exerted by the salt ions and/or molecules on the structure of the l i q u i d phase. T h e most likely effect to be expected is that the salt w o u l d induce formation of association complexes, or clusters, of molecules of the volatile components about its ions. T h i s effect w o u l d lower both of their volatilities but by d i f f e r i n g amounts d e p e n d i n g on the degree of selectivity of the particular salt i n the preference of its ions for clustering w i t h the molecules of one volatile component over those of the other. A preference for associating w i t h the less volatile component w o u l d result i n an increase i n relative volatility and hence i n ease of separation, and a preference for the more volatile component w o u l d have the opposite effect. This is not the only structural mechanism possible. F o r instance, the salt m a y alter an existing l i q u i d structure by p r o m o t i n g , destroying, or otherwise affecting interactions between the two volatile components, i n some cases i n creasing rather than decreasing the volatility of a component. Still other effects are possible. A l l , of course, are functions of the relative amounts of a l l c o m p o nents present. Also, the types of short-range forces involved i n l i q u i d structure and i n its promotion or other alteration by a salt m a y differ f r o m system to system and f r o m salt to salt. T h e great increase i n complexity i n solution thermodynamics w h i c h occurs w h e n a" salt is dissolved to substantial concentration i n a m i x t u r e of two l i q u i d components becomes f u l l y apparent i n the realization that the l i q u i d phase so created is a concentrated solution of an electrolyte whose degree of dissociation is a function of the relative proportions of the other two components present, and



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T H E R M O D Y N A M I C BEHAVIOR O F E L E C T R O L Y T E S

hence of l i q u i d composition. Unless the salt is either f u l l y associated or f u l l y dissociated at a l l l i q u i d compositions, it exists as a m i x t u r e of molecules a n d two species of ions, the relative proportions of w h i c h change w i t h l i q u i d composition. Undoubtedly, all three species play parts i n determining the overall effect of the salt o n the activities of the i n d i v i d u a l l i q u i d components. H o w e v e r , their respective contributions, while possibly interrelated, probably a l l d i f f e r f r o m each other. In one region of l i q u i d composition, one effect m a y predominate, w h i l e i n another region of the same system, it is quite possible that a different effect m a y prevail. M e r a n d a a n d F u r t e r (6) a n d others have observed the existence of such crossovers i n salt effect i n certain systems. Such complexities tend to explain w h y progress has been relatively slow, at least u n t i l recently, i n the f o r m u l a t i o n of effective relations a n d techniques for the representation of salt effect i n v a p o r - l i q u i d e q u i l i b r i u m .

Correlation at Fixed Liquid

Composition

T h e original equation for salt effect i n v a p o r - l i q u i d e q u i l i b r i u m , proposed b y F u r t e r (7) a n d e m p l o y e d subsequently b y Johnson a n d F u r t e r (8), described the effect of salt concentration o n e q u i l i b r i u m vapor composition under the condition of a fixed ratio of the two volatile components i n the l i q u i d phase. T h e equation, d e r i v e d f r o m the difference i n effects of the salt o n the c h e m i c a l potentials of the two volatile components, w i t h s i m p l i f y i n g approximations reduces to the f o r m In (a /a) s

= kN

s

(1)

In other words, the equation defines a n i m p r o v e m e n t factor, w h i c h consists of the ratio of relative volatility w i t h salt present (calculated using l i q u i d composition on a salt-free basis for direct comparison purposes) to relative volatility at the same l i q u i d composition but without salt present. It relates the l o g a r i t h m of this i m provement factor i n a direct proportionality w i t h N 3 , the m o l e f r a c t i o n of salt present i n the l i q u i d o n a ternary basis. Jaques a n d F u r t e r (17) tested the equation w i t h data taken at several constant l i q u i d compositions i n four alcoh o l - w a t e r - i n o r g a n i c salt systems, a n d observed good agreement. T h e constancy of k w i t h changing salt concentration is predicted only w h e n the ratio of volatile components i n the l i q u i d is held constant. C o n s i d e r i n g that the salt effect is believed to be a complex f u n c t i o n of interactions a n d self-interactions between a l l system components ( w h i c h i n t u r n are functions not o n l y of composition but also of degree of salt dissociation, w h i c h itself is composition-dependent), there w o u l d be little reason to expect that k should have a single value for an entire system. T h a t is, k w o u l d not be expected to r e m a i n constant over the entire l i q u i d composition range of a given system. Nevertheless, i n order to represent v a p o r - l i q u i d e q u i l i b r i u m data f o r systems c o n t a i n i n g salts, a n equation w h i c h holds over the entire composition range is r e q u i r e d . Because of the absence of any such effective relation at the time, a n d also because of the


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undoubted attractiveness of using a single-constant equation f o r representing such complex phenomena, various investigators have e m p l o y e d E q u a t i o n 1 e m p i r i c a l l y to correlate the data for entire systems.


Extension to Entire Liquid Composition Range Furter (7) and Johnson and Furter (8,9) tested Equation 1 w i t h v a p o r - l i q u i d e q u i l i b r i u m data over the entire concentration range for 24 a l c o h o l - w a t e r inorganic salt systems, i n all of them discovering unexpectedly that a single best value of k for each system p e r m i t t e d correlation of the data to w i t h i n average absolute deviations of one percent or less. K o g a n et a l . (44) observed good agreement w i t h data for 14 salt-containing systems. W h e n Johnson and F u r t e r separated it into two i n d i v i d u a l salting parameters, one for salt-alcohol a n d the other for salt-water, it was observed that w h i l e the i n d i v i d u a l parameters varied considerably i n value w i t h alcohol-water proportionality, they tended to d o so i n a manner such that their difference, k, r e m a i n e d r e m a r k a b l y constant. I n these particular systems the various interaction a n d self-interaction mechanisms comprising salt effect, a l l of w h i c h are composition-dependent, tended somehow to balance each other as l i q u i d composition was varied. M o r e recent investigations have shown that this apparent b a l a n c i n g effect (that is, the insensitivity of k to l i q u i d composition) is not universal. A l t h o u g h R a m a l h o a n d Edgett (10) observed it i n certain p r o p i o n i c a c i d - w a t e r - s a l t systems; a n d O h e , Y o k o y a m a , and N a k a m u r a (11) observed it i n the methanol-ethyl acetate-calcium chloride system; Yoshida, Yasunishi, a n d H a m a d a (12) observed it w i t h certain methan o l - w a t e r - s a l t systems but not w i t h the acetic a c i d - w a t e r - s a l t systems w h i c h they tested. M e r a n d a and F u r t e r (6,13,14,15), w h o experimented w i t h a w i d e range of organic a n d inorganic salts a n d salt pairs i n a l c o h o l - w a t e r systems, observed little variation of k w i t h l i q u i d composition i n some systems a n d large variations i n others. T h e nature a n d use of E q u a t i o n 1 have been discussed not only b y F u r t e r (7) a n d b y Johnson a n d F u r t e r (8) but more recently b y F u r t e r a n d C o o k ( i ) , b y M e r a n d a a n d F u r t e r (13,14), a n d b y Jaques a n d F u r t e r (16, 17). Ramalho and Edgett (10) described a reference d i a g r a m method for using E q u a t i o n 1 w i t h data obtained at constant salt concentration. Various investigators, p a r t i c u l a r l y i n the USSR, have experimented w i t h s i m i l a r relations w i t h v a r y i n g degrees of success, often under constraints such as i n f i n i t e d i l u t i o n a n d others. T h e i r efforts have been r e v i e w e d elsewhere (1). The effect of a given salt on vapor composition i n a given system is, of course, a function of the relative proportions of the two volatile components i n the l i q u i d as w e l l as of salt concentration, a n d a n equation for correlation of salt effect at other than fixed liquid composition should contain l i q u i d composition as a factor. Hashitani and H i r a t a (18) reported some success w i t h a purely empirical equation w h i c h related the i m p r o v e m e n t factor of E q u a t i o n 1 both to salt concentration a n d to l i q u i d composition. G u y e r , G u y e r , a n d Johnsen (19) proposed a n e m p i r i c a l relationship between vapor composition change a n d the concentration


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of one volatile component i n the l i q u i d w h i l e m a i n t a i n i n g a f i x e d ratio of the concentrations of the other volatile component and salt. Sada, K i t o , Yamaji, and K i m u r a (20), by considering vapor pressure lowering caused b y the salt, derived an equation similar otherwise to Equation 1 but with the right hand side m o d i f i e d to a n expression of salt concentration a l l o w i n g for the numbers of cations a n d anions per salt molecule p r o d u c e d b y dissociation, a n d c o n t a i n i n g no e m p i r i c a l parameter. T h e y reported test results for the equation, w h i c h is restricted to systems i n w h i c h the salt is soluble i n only one of the t w o volatile components, w i t h data for three benzene-ethanol-salt systems tested. Bedrossian a n d C h e h (21) proposed two e m p i r i c a l correlations a n d tested t h e m w i t h data for one system. L u (22) proposed a correlation i n v o l v i n g m o d i f i e d expressions of l i q u i d composition w h i c h were intended to relate the relative contributions of the two volatile components to the overall salt solution. L i q u i d composition was expressed i n pseudo mole fractions based on relative vapor pressure lowerings b y the salt i n question. A l v a r e z et al. (23, 24) have proposed a n d tested various e m p i r i c a l equations, i n certain cases a d o p t i n g the pseudo mole fraction approach of L u . T h e classical work relating l i q u i d phase activity coefficients to the concentrations of electrolyte and nonelectrolyte species present i n aqueous solution, a n d to the respective electrostatic interactions involved, was published b y L o n g a n d M c D e v i t (25). H a l a (26) developed a generalized expression for characterization of v a p o r - l i q u i d e q u i l i b r i u m i n m u l t i c o m p o n e n t systems containing both electrolyte and nonelectrolyte components. In his method a ternary system, for instance, is treated as three binaries. C o r r e l a t i o n w i t h excess free energy of m i x i n g is achieved through extrapolation of dilute solution behavior to standard states. Jaques a n d F u r t e r (16, 27) d e r i v e d an equation relating the salt effect to both l i q u i d composition a n d salt concentration b y subtracting f r o m the L o n g - M c D e v i t equation i n its ten-constant f o r m the R e d l i c h - K i s t e r equation written i n a four-constant f o r m . T h e resulting six-constant equation was tested w i t h data for a total of 12 systems, and, not surprisingly, y i e l d e d a better fit than d i d the one-constant E q u a t i o n 1. Prediction from Pure-Component

Properties

Pure-component properties f r o m w h i c h prediction of salt effect i n v a p o r l i q u i d e q u i l i b r i u m might be sought, i n c l u d e vapor pressure l o w e r i n g , salt solubility, degree of dissociation a n d ionic properties (charges a n d radii) of the salt, polarity, structural geometry, a n d perhaps others. It has been generally held, at least u n t i l recently, that a salt dissolved i n the l i q u i d phase w o u l d enrich the e q u i l i b r i u m vapor i n the component i n w h i c h it was less soluble and impoverish it i n the component i n w h i c h it was more soluble. It was also assumed that the m a g n i t u d e of the effect on vapor composition depended not only on how m u c h salt was present but also on the degree of difference between the solubilities of the salt i n the two l i q u i d components taken separately. Various investigators, i n c l u d i n g T u r s i a n d T h o m p s o n (28) a n d F o g g (29), have tried to relate the salt effect to this solubility difference alone, but their success


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31


has not been m a r k e d since such other factors as degree of dissociation a n d the ionic properties of the salt are neglected. F u r t e r (7) a n d Johnson a n d F u r t e r (8) demonstrated that the p r e d i c t i o n that a salt w o u l d alter vapor composition i n favor of the component i n w h i c h it was less soluble was mathematically rigorous i n the l i m i t e d case of systems possessing festoon-like solubility curves. T h e y also proposed an empirical equation expressing the relationship between salt saturation concentration a n d l i q u i d composition i n terms of the two pure-component salt solubilities and one other parameter. T h e expectations for prediction of the salt effect f r o m solubility factors alone have been l a i d to rest b y m o r e recent discoveries of systems w h i c h behave anomalously i n respect to the earlier-held generalities relating m a g n i t u d e of salt effect to pure-component solubilities. M e r a n d a a n d F u r t e r (6,13,14) a n d Newstead a n d F u r t e r (30), for instance, reported systems i n w h i c h a reversal i n the salt effect takes place at some point i n the l i q u i d composition range even though the salt is clearly m o r e soluble i n one component than i n the other, others i n w h i c h a salt was observed to e n r i c h the vapor throughout i n the component i n w h i c h it is more, rather than less, soluble, a n d still others i n w h i c h a large change i n vapor composition is caused b y a salt having little difference between its pure-component solubilities i n the two l i q u i d components. T h e possibilities f o r p r e d i c t i n g the salt effect f r o m ionic properties alone are likewise improbable. General orders of effectiveness for anions and cations have been observed to exist b y various investigators, including L o n g and M c D e v i t (25), Prausnitz a n d T a r g o v n i k (31), Johnson a n d F u r t e r (7, 8), C i p a r i s a n d Smorigaite (32), a n d others. I n general, f o r s i m i l a r l y charged ions, the order of decreasing effectiveness follows the order of increasing ionic radius. Although the anion order is reasonably independent of the cation a n d vice versa i n some systems, the u n i f o r m i t y decreases considerably w h e n the l i q u i d components are polar. I n general, orders of i o n effectiveness are only approximate a n d tend to exhibit some variance f r o m system to system. F o r relating salt effect to ion radius and charge, the degree of dissociation, the number of ions per molecule, and the salt concentration must be considered so that i o n parameters are isolated f r o m the latter factors. The literature pertaining to ion order is reviewed i n more detail elsewhere (1). O v e r the years, various other theories a n d models have been proposed for p r e d i c t i n g salt effect i n v a p o r - l i q u i d e q u i l i b r i u m , i n c l u d i n g ones based o n h y dration, internal pressure, electrostatic interaction, a n d v a n d e r W a a l s forces. These have been r e v i e w e d i n detail b y L o n g a n d M c D e v i t (25), Prausnitz a n d T a r g o v n i k (31), F u r t e r (7), Johnson a n d F u r t e r (8), a n d F u r t e r a n d C o o k (I). Although the electrostatic theory as m o d i f i e d for m i x e d solvents has had l i m i t e d success, no single theory has yet been able to account for or to predict salt effect on e q u i l i b r i u m vapor composition f r o m pure-component properties alone. Use of Correlations Based on the Gibbs-Duhem

Equation

E m p i r i c a l relations w h i c h w o r k w e l l for a variety of systems c a n be useful



32


for correlating a n d , i n l i m i t e d cases, even p r e d i c t i n g data but cannot be considered as criteria for judging their thermodynamic consistency. T h e criterion for t h e r m o d y n a m i c consistency of v a p o r - l i q u i d e q u i l i b r i u m data is that they must be consistent w i t h the G i b b s - D u h e m equation. Therefore o n l y those relations which themselves are consistent with the G i b b s - D u h e m equation can be deemed reliable for judging the thermodynamic consistency of such data or for correlating t h e m i n a t h e r m o d y n a m i c a l l y consistent manner. T h e p r i n c i p a l correlations a n d consistency tests for v a p o r - l i q u i d e q u i l i b r i u m i n use today, i n c l u d i n g those of van L a a r , Margules, R e d l i c h - K i s t e r , Scatchard, Renon, W i l s o n , a n d others, can a l l be considered approximations to the integration of the G i b b s - D u h e m equation. F o r systems of the type under consideration, that is, consisting of two volatile components and a salt, there has been controversy over whether binary or ternary forms of correlating equations should be used, a n d over whether the presence of the salt should be i n c l u d e d i n the l i q u i d mole fraction data used to calculate l i q u i d activity coefficient values for the two volatile components. O n e point, however, is absolutely clear. It w o u l d be t h e r m o d y n a m i c a l l y incorrect not to acknowledge the presence of the salt i n c a l c u l a t i n g liquid-phase activity coefficients. If the two volatile components are designated A a n d B respectively, a n d component A is used as an example, the mole fraction of component A i n the l i q u i d expressed on a salt-free basis is ^

moles A

^

moles A + moles B However, if activity coefficient data were calculated for component A using the pure component vapor pressure a n d l i q u i d composition data on a salt free basis, the activity coefficient values w o u l d not n o r m a l i z e (i.e., a p p r o a c h u n i t y as X\ approaches unity) unless the salt were insoluble i n component A . A better l i q u i d composition expression w o u l d be moles A

—

(3) moles A + moles B + moles salt H o w e v e r the question of whether the salt should be considered as a molecular or ionic constituent is raised. T h e laws of solution theory suggest the latter. Hence, unless the salt is either fully associated or f u l l y dissociated over the entire l i q u i d composition range, the v a r y i n g degree of salt dissociation over this range is important. In other words, since both species of i o n a n d salt molecules contribute to the total effect caused b y a partially dissociated salt, the total n u m b e r of salt particles (ions a n d molecules) present should be considered. T h i s w o u l d suggest that an even more correct expression of l i q u i d composition for use i n calculating l i q u i d phase activity coefficients w o u l d be X\

* " A

m

o

l

e

s

A

moles A + moles B + n moles salt


(4)


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where n is a factor accounting for the degree of dissociation of the salt and is the statistical average number of particles (ions and molecules) of the salt i n solution per molecule of salt dissolved. F o r example, for the salt N a C l , n = 1 f u l l y associated, n = 2 f u l l y dissociated, and n lies between these limits f o r partial dissociation. (Note that n is not a constant but is rather a f u n c t i o n of the relative proportions of the volatile components A a n d B present i n the l i q u i d phase.) H o w e v e r even E q u a t i o n 4 is not an ideal expression; an even more sophisticated approach w o u l d be to have the value of n also take account of i o n r a d i i a n d charges. T h e real problem, of course, is i n k n o w i n g the degree of salt dissociation as a function of l i q u i d composition i n a boiling system, and is a major reason w h y so little progress has been m a d e over the years o n t h e r m o d y n a m i c correlation of salt effect i n v a p o r - l i q u i d e q u i l i b r i u m . In s u m m a r y , to be t h e r m o d y n a m i c a l l y rigorous, the salt presence must be recognized i n calculating activity coefficients f o r use i n correlating equations; its degree of dissociation as a function of l i q u i d composition, among other factors, must be considered also. Conversely, it m a y be possible to a p p l y data that are believed to be consistent to a consistency test i n order to calculate degree of dissociation as a f u n c t i o n of l i q u i d composition. Various investigators have encountered the difficulties of attempting to correlate data f o r systems containing salts b y one or another of the c o m m o n correlating equations or consistency tests for v a p o r - l i q u i d e q u i l i b r i u m data, often i n their binary versions, using activity coefficients computed f r o m salt-free l i q u i d composition data. A m o n g them are L i n d b e r g and Tassios (33), Rius and Alvarez (34), Costa and Moragues (35), and other investigators such as Kogan, Rozen, and their associates whose w o r k has been r e v i e w e d elsewhere (1). Recently, Sada a n d M o r i s u e (36) attempted to derive a relationship consistent w i t h the G i b b s D u h e m equation b y expressing salt effect on vapor composition as a f u n c t i o n of l i q u i d composition. T h e l i q u i d composition expression w h i c h they used acknowledged both the presence of the salt and the number of ions per salt molecule, but not ionic charges or radii, or variation i n degree of salt dissociation w i t h l i q u i d composition.

The Special Binary

Approach

Jaques and F u r t e r (37,38,39,40) devised a technique for treating systems consisting of two volatile components and a salt as "special binaries" rather than as ternary systems. I n this pseudo b i n a r y technique the presence of the salt is recognized i n adjustments m a d e to the pure-component vapor pressures f r o m w h i c h the liquid-phase activity coefficients of the two volatile components are calculated, rather than b y inclusion of the salt presence i n l i q u i d composition data. In other words, alteration is m a d e i n the standard states o n w h i c h the activity coefficients are based. I n the special b i n a r y approach as a p p l i e d to saltsaturated systems, for instance, each of the t w o components of the b i n a r y is considered to be one of the volatile components i n d i v i d u a l l y saturated w i t h the



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salt. T h e pure-component vapor pressures used to calculate liquid-phase activity coefficient values f o r the volatile components are the vapor pressures of the volatile components each saturated with salt at the temperature i n question, rather than of the volatile components alone. Instead of defining the reference fugacity as the saturated vapor pressure of the pure component, it is defined as that of the pure component as depressed b y the presence of the salt. I n other words, the activity coefficients of the volatile components, are based o n standard states consisting of each volatile component saturated i n d i v i d u a l l y w i t h the salt. A l though only data for salt-saturated systems have been tested so far, the technique is not l i m i t e d to saturation; f o r salt concentrations below saturation the standard-state vapor pressures w o u l d be those of the volatile components each depressed i n d i v i d u a l l y b y the salt, at the salt concentration a n d temperature i n question. T h e temperature i n question is, of course, the b o i l i n g point of the salt-containing l i q u i d phase at the composition for w h i c h an activity coefficient is calculated. T h e advantage of the approach is that any of the c o m m o n correlating equations or t h e r m o d y n a m i c consistency tests based on approximations to the G i b b s - D u h e m equation can then be used i n their standard b i n a r y forms, and w i t h l i q u i d compositions calculated on a salt-free basis. H e n c e the method obviates the necessity for k n o w i n g the relationship between degree of salt dissociation and l i q u i d composition that w o u l d otherwise be r e q u i r e d to calculate activity coefficients, information w h i c h for most systems is not generally k n o w n . T h e special b i n a r y approach, w h i l e s e m i - e m p i r i c a l , has been e m p l o y e d successfully b y Jaques a n d F u r t e r both i n testing for t h e r m o d y n a m i c consistency and i n the correlation of data. Jaques and F u r t e r (37,39) tested the t h e r m o d y n a m i c consistency of literature data for 23 alcohol-water-salt systems and Jaques (41) studied 17 additional systems using the H e r i n g t o n method as adapted to their special b i n a r y technique. Jaques a n d F u r t e r (38, 40) also a p p l i e d the special b i n a r y approach to the correlation and prediction of salt effect i n v a p o r - l i q u i d e q u i l i b r i u m using the W i l s o n equation as the correlating relation. F o r a total of 22 systems tested, the average deviations between observed and calculated vapor compositions ranged f r o m

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