The Distribution of Electrolytes

The distribution ratios of electrolytic solutes, CA, that are practically completely dissociated into ions in both water and the solvent org, can be approximated by

DCA=( / )l ν exp[∆tG°(CA,aq→org)/RT] ( .2 64)

This expression arises from Eq. (2.40), noting that the chemical potential µCA

must be the same in the phases aq and org for equilibrium to be maintained, and that ∆tG°(CA,aq → org) = µ∞CA,org− µ∞CA,aq by definition. The approximation

is that the activity coefficients of CA are taken to be equal (near unity) at the low concentrations where Eq. (2.64) is valid.

This equation would be exact if the two phases org and aq were com- pletely immiscible.

The standard molar Gibbs energy of transfer of CA is the sumν+∆tG°(C) +

ν−∆tG°(A), where the charges of the cation C

z+

and anion Az−and the designation of the direction of transfer, (aq→ org), have been omitted. The values for the cation and anion may be obtained from tables [5–7], which generally deal with solvents org that are miscible with water and not with those used in solvent extraction. However, ∆tG°(C) depends primarily on the β solvatochromic pa-

rameter of the solvent and ∆tG°(A) on its α parameter, and these can be esti-

mated from family relationships also for the latter kind of solvents.

The general qualitative rules are that ions prefer water if they are multiply charged and small, but otherwise they may prefer solvents that have large β values (donor properties for cations) or α values (acceptor properties for anions). Consider, for example, the small cation Li+and multiply charged cation Cu2+: these cations prefer water (β = 0.47) over such solvents as methyl ethyl ketone (β = 0.48), propylene carbonate (β = 0.40), benzonitrile (β = 0.41), nitro- benzene (β = 0.30), and 1,2-dichloroethane (β = 0.00), and also 1-butanol (see later), but prefer the more highly basic (although water-miscible) solvents di- methylsulfoxide (β = 0.76), N,N-dimethylformamide (β = 0.69), and hexamethyl phosphoric triamide (β = 1.06) over water. [Note that 1-butanol (β = 0.88) is exceptional, being capable of hydrogen bond donation.] However, with propyl- ene carbonate, the preference is reversed for the large univalent cations Cs+ and tetramethylammonium, (CH3)4N+. For the tetraalkylammonium ions with n-

propyl or longer alkyl chains, the preference for the organic solvents is quite general. For the anions, water is preferred over most solvents, an exception being 2,2,2-trifluoroethanol, with α = 1.51, larger than that of water (1.17). However, very large anions may show a preference for the organic solvents, as for ClO−4with propylene carbonate and hexamethyl phosphoric triamide and for

I−3with most organic solvents. A numerical example is given at the end of sec-

tion 2.6.1, where the transfer of Na+, Cs+, and I−3from water to nitrobenzene is

salt to be extracted into nitrobenzene from water, contrary to NaI3, which cannot

(having a positive∆tG°).

A common situation is that the electrolyte is completely dissociated in the aqueous phase and incompletely, or hardly at all, in the organic phase of a ternary solvent extraction system (cf.Chapter 3), since solvents that are practi- cally immiscible with water tend to have low values for their relative permittivi- ties ε. At low solute concentrations, at which nearly ideal mixing is to be ex- pected for the completely dissociated ions in the aqueous phase and the undissociated electrolyte in the organic phase (i.e., the activity coefficients in each phase are approximately unity), the distribution constant is given by

logPCA =logcCA(org)− νlogcCA(aq) ( .2 65) The distribution ratio for the electrolyte, DCA, however, is given by

logDCA =log[cCA(org) /cCA(aq)]=logPCA− −(ν 1)logcCA(aq) ( .2 66) which is seen to be a concentration-dependent quantity. Even if the constant log

PCA can be predicted, log DCAcannot, unless some arbitrary choice is made for

the aqueous concentration.

As examples, take the extraction of nitric acid by tri-n-butyl phosphate or of hydrochloric acid by diisopropyl ether. For the former, at low acid concentra- tions, the acid is completely dissociated in the aqueous phase, but is associated in the organic phase. Therefore, DHNO3increases with the nitric acid concentra-

tion according to Eq. (2.65), up to such concentrations at which the dissociation of this acid in the aqueous phases becomes significantly lower than complete, and then D_HNO3flattens out. For hydrochloric acid, the situation is the opposite: it is dissociated in the ether phase up to about 3 M aqueous acid, so that DHClis

constant, but at higher concentrations it associates in the organic phase, and DHCl

starts to increase, again according to Eq. (2.65), when the nonidealities in both phases are taken into account.

2.9

CONCLUSION

This chapter provides the groundwork of solution chemistry that is relevant to solvent extraction. Some of the concepts are rather elementary, but are necessary for the comprehension of the rather complicated relationships encountered when the solubilities of organic solutes or electrolytes in water or in nonaqueous sol- vents are considered. They are also relevant in the context of complex and adduct formation in aqueous solutions, dealt with in Chapter 3 and of the distri- bution of solutes of diverse kinds between aqueous and immiscible organic phases dealt with inChapter 4.

For this purpose it is necessary to become acquainted, at least in a cursory fashion, with the physical and chemical properties of liquids (section 2.1.1)

and the forces operating between their molecules (section 2.1.2). Since solvent extraction depends on the existence of two immiscible liquid phases, solvent miscibility, i.e., their mutual solubility, is an important issue (section 2.2). The solvation of a solute that is introduced into a solvent, i.e., its interactions with the solvent, is described (section 2.3.1) and the thermodynamics thereof are elaborated (section 2.3.2), the case of electrolytes that dissociate into ions being given special attention (section 2.3.3).

Solution chemistry depends strongly on thermodynamic relationships that have to be mastered in order to make full use of most other knowledge concern- ing solvent extraction. Therefore, a comprehensive section (2.4) is devoted to this subject, dealing with ideal (section 2.4.1) as well as nonideal (section 2.4.2) mixtures and solutions. Then again, as solvent extraction in, e.g., hydrometal- lurgy, deals with electrolytes and ions in aqueous solutions, the relevant thermo- dynamics of single electrolytes (section 2.5.1) and their mixtures (section 2.5.2) has to be understood. In the organic phase of solvent extraction systems, compli- cations, such as ion pairing, set in that are also described (section 2.6.2).

The amount of a solute that can be introduced into a solvent depends on its solubility, be it a gas (section 2.7.1), a solid nonelectrolyte (section 2.7.2), or an electrolyte (section 2.7.3). Ternary systems, which are the basic form of solvent extraction systems (a solute and two immiscible solvents), have their own characteristic solubility relationships (section 2.8.1).

In conclusion, therefore, it should be perceived that this groundwork of solution chemistry ultimately leads to the ability to predict at least semi-quanti- tatively the solubility and two-phase distribution in terms of some simple prop- erties of the solute and the solvents involved. For this purpose, Eqs. (2.12), (2.53), (2.61), and (2.63) and the entries inTables 2.3and2.5should be particu- larly useful. In the case of inorganic ions, the entries in Table 2.4are a rough guide to the relative extractabilities of the ions from aqueous solutions. The more negative the values of ∆hydG° of the ions, the more difficult their removal

from water becomes, unless complexation (see Chapter 3) compensates for the ion hydration.

Although theories of solution (this chapter) and formation of extractable complexes (seeChapters3 and4) now are well advanced, predictions of distri- bution ratios are mainly done by comparison with known similar systems. Sol- vatochromic parameters, solubility parameters, and donor numbers, as discussed in Chapters 2–4, are so far mainly empirical factors. Continuous efforts are made to predict such numbers, often resulting in good values for systems within limited ranges of conditions. It is likely that these efforts will successively en- compass greater ranges of conditions for more systems, but much still has to be done.

Because a 10% change in the distribution ratio, which can be measured easily and accurately in the distribution range 0.01–100, corresponds to an en-

ergy change of only 0.2 kJ/mole, distribution ratio measurements offer a method to investigate low energy reactions in solutions, such as weak solute–solute and solute–solvent interactions in the organic phase. So far, this technique has been only slightly exploited for this purpose. It is particularly noteworthy to find how few thermodynamic studies have been made of the distribution or extraction constants, as enthalpy and entropy values give a good indication of the driving force of the extraction and indicate the structure of the molecular species in the organic solvent.

REFERENCES

1. Riddick, J. A.; Bunger, W. B.; Sasano, T. K. Organic Solvents, Fourth Edition, John Wiley and Sons, New York, 1986.

2. Marcus, Y. The Properties of Solvents, John Wiley and Sons, Chichester, 1998. 3. Marcus, Y. Introduction to Liquid State Chemistry, John Wiley and Sons, Chiches-

ter, 1977; 204–207.

4. Kamlet, J. M.; Abboud, J.-L.; Abraham, M. H.; Taft, R. W. J. Org. Chem., 1983, 48: 2877.

5. Marcus, Y. Ion Solvation, John Wiley and Sons, Chichester, 1985. 6. Marcus, Y. Ion Properties, M. Dekker, New York, 1997.

7. Marcus, Y. Pure Appl. Chem., 1983, 55:977.

8. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, Second Revised Ed., Butter- worth, London, 1970.

9. Harned, H. S.; Robinson, R. A. Multicomponent Electrolyte Solutions, Pergamon Press, Oxford, 1968.

10. Drago, R. S. Struct. Bonding, 1973; 15:73. 11. Marcus, Y. J. Solution Chem., 1984; 13:599.

12. Wagman, D. D.; et al., NBS Tables of Chemical Thermodynamic Properties, J.

Phys. Chem. Ref. Data, 1982, Vol. 11, Suppl. 2.

13. Marcus, Y. J. Phys. Chem., 1991;95:8886; Marcus, Y. Solvent Extract. Ion Exch., 1992, 10: 527; Migron, Y.; Marcus, Y.; Dodu, M. Chemomet. Intell. Lab. Syst., 1994, 22: 191.

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