Solute-solvent interactions in ion-pair extraction of ... - ACS Publications

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894

J. Phys. Chem. 1981, 85, 894-901

the solubility in aqueous HC1 and aqueous NaC1. This uncertainty rises to about 10% for temperatures far from 25 "C for these systems and for all temperatures for aqueous KC1 and NH4C1,where the available experimental data are scant and of comparatively low precision. The procedure can also be used to calculate the solubility of CuCl in mixtures of soluble chlorides over the same ranges of temperature and overall concentration. Somewhat greater uncertainties are to be expected in calculations for the mixtures, since the simplified model used contains no terms to account for interactions between the cations. Practical application of these correlations can be made in any situation where CuCl is processed in solution, as for example in the preparation of CuCl for use as a catalyst. Another example is the Cymet process of receiving of copper from its ores, in which the copper is isolated as CuCl from aqueous solution, then reduced chemically to metallic copper. In both these examples, the effects of temperature and of salt concentrations on the solubility of CuCl are of major importance in the procedure. In the second example, rather complex mixtures of cations are encountered, but they should be amenable to treatment once the necessary virial parameters are established for ion pairs consisting of the cuprous complexes and the individual cations.

Appendix I. Equations for Mean-Ion Activity Coefficients

BNX

= @Nx(O)+ (2@NXc1)/cy2r) [I -(I

BNX'

(2@NX"'/cy212)[-1

+ a N 2 ) e~p(-cyl/~)]

+ (1+ C Y P+/ ~1/2cy2r) exp(-W2)]

(CMZ) = CMg, C

= 2.0 These equations are simplified versions of eq 12-15 of Pitzer and Kim,3 with molarity (M) used instead of molality (m)throughout. The symbolism is otherwise that of Pitzer and Kim.3 cy

Solute-Solvent Interactions in Ion-Pair Extraction of Tetraalkylammonium Iodides. 1. A New Approach to the Extraction Constant' Etsuro Iwamoto, Karuaki Ito, and Yuroku Yamamoto" Department of Chemistry, Faculty of Science, Hiroshima Universlty, Hiroshima 730, Japan (Received: September 22, 1980)

The extraction equilibria of tetraalkylammonium iodides R4NI(R= Me, Et, n-Pr, n-Bu, and i-Am) between water and organic solvents (nitrobenzene (NB), 1,2-dichloroethane(1,2-DCE), 1,l-dichloroethane(1,l-DCE), o-dichlorobenzene (o-DCB), dichloromethane (DCM), trichloromethane (TCM), chlorobenzene (CB), and l-chlorobutane (CBu)) were studied at 25 OC. The overall extraction constant was defined as KO = [R~N+]~[I-]~[R4NI]~02/[R4N+]w[I-]w[R4NI]wf,2 which consists of two extraction constants: one is the ionic part Ki = [R4N+],[I-]~~/[R4N+]w[I-]wf,2 and the other the neutral part K,, = [R4N1],/[R4NI],, where the subscripts o and w are ascribed to the organic and aqueous phases, respectively. These extraction constants were calculated by combining the distribution ratios of the iodides determined by use of 1311as a tracer with the ionic association constants obtained by conductivity measurements. Thereby the influences of solvent on the extractability of R4NI were split into the two parts for ionic and neutral species. The extractability of neutral species was successfully explained in terms of regular solution theory. The contribution of triple ion formation in organic solvents was also discussed. Introduction Solute-Solvent interactions in electrolyte solutions have received continuous attention in various fields of chemi ~ t r y . ~ Solvent -~ extraction6-8 is a useful technique for (1)Presented in part in the ACS/CSJ Chemical Congress, Hawaii, 1979. (2)J. F. Coetzee and C. D. Ritchie, Ed., "Solute-Solvent Interactions", Marcel Dekker, New York Vol. 1,1969; Vol. 2, 1976. (3)A. J. Parker, Chem. Rev,, 69,1 (1969). (4)A. K. Covington and T. Dickinson, Ed., "Physical Chemistry of Organic Solvent Systems", Plenum Press, New York, 1973. (5)"Ion-Ion and Ion-Solvent Interactions", Faraday Discuss. Chern. SOC.,No. 64 (1977). (6)H. L.Friedman and G. R. Haugen, J. Am. Chem. Soc., 76, 2060 (1954). (7)C. Hansch, J. E. Quinlan, and G . L. Laurence, J. Org. Chem., 33, 347 (1968). 0022-3654/81/2085-0894$01.25/0

studying solute-solvent interactions in view of direct measurements of transfer free energy changes of a solute at any concentrations from one solvent to another solvent, in contrast with the method of solubility meas~ernent."'~ Although solvent effects or relative efficiencies of different solvents for distributions of neutral species14-16 (8)J. Rais, Collect. Czech. Chem. Commun., 36, 3080,3253 (1971). (9)R. Alexander, A. J. Parker, J. H. Sharp, and W. E. Waghorne, J. Am. Chem. Soc., 94,1148 (1972). (10)C. L.De Ligny, D. Bax,M. Alfenaar, and M. G. L. Elferink,Recl. Trau. Chim., Pays-Bas, 88, 1183 (1969). (11)I. M.Kolthoff and M. K. Chantooni, J.Phys. Chem., 76, 2024 (1972). ~ - .-_ (12) M. H. Abraham, J. Chem. SOC.,Perkin Trans. 2, 1343 (1972). (13)A. J. Parker and W. E. Waghorne, A u t . J. Chem., 31,1181(1978). (14)S.Siekierski and R. Olszer, J.Inorg.Nucl. Chern., 25,1351 (1963).

0 1981 American Chemical Society


Solute-Solvent Interactions in Ion Pair Extraction undissociated in organic phase are successfully explained in terms of solubility parameters from the regular solution theory,17 those for ion pair extraction can hardly be described on the basis of a single solvent parameter because of complicated ion-solvent interactions. Irving and Lewis'* developed a model for the distribution of an ion pair between immiscible phases in which the distribution was related to ionic radii and dielectric constants, donor strengths, and internal pressures of the solvent, and applied it to data for the indium halide complex acid. However, their discussion was limited to the dissociated species. In dextromorphan halides-chloroform and -cyclohexane systems where ion pairs are almost associated, correlations of the distribution ratio with the solubility parameter, with the dielectric constant of the solvent mixtures, and with chloroform-solvate formation were discussed.1"21 The complete association and dissociation of an ion pair in organic phases are an extreme situation. Some difficulties in understanding the role of solvents seem to arise from the dissociation of ion pairs.22 We previously pointed out the importance of ionic association in ion pair extraction of metal-chelate electrolytes such as tris(1,lOphenanthroline)iron(II) halides.23 In order to understand the solvent effect on ion pair extraction we found that it would be necessary to investigate the dissociation equilibria by an independent method and to evaluate the extractability of both free ions and neutral associated species. No such attempt has been made although a number of concerning ion-pair extraction have been reported. Recently, Abraham12split the free energies of solution of tetraalkylammonium halides in various solvenh into the dissociated and the associated species parts using their solubilities, together with ionic association constants, to compare solvent effects on the free energies of solution of ion pairs with those on the free energies of transition states in some substitution reactions. In this paper, a new approach to extraction equilibria is proposed, that is, distribution ratios are combined with the association constants of the ion pair, which were determined by conductance measurements, to evaluate a newly defined overall extraction constant which consists of the two extraction constants, the ionic part and the neutral part. A homologous series of tetraalkylammonium iodides which are well extracted into a number of solvents was (15) T. Wakahayashi, S. Oki, T. Omori, and N. Suzuki, J. Inorg. Nucl. Chem., 26, 2255, 2265 (1964). (16) H. M. N. H. Irving, Ion Exch. Solvent Extr., 6 , 139 (1974). (17) J. H. Hildebrand and R. L. Scott. "The Solubilitv of Nonelectrolytes", 3rd ed, Dover, New York, 1964. (18) H. M. N. H. Irving and D. Lewis, Ark. Kemi, 32,121,131 (1970). (19) T. Higuchi, A. Michaelis, T. Tan, and A. Hurwitz, Anal. Chem., 39, 974 (1967). (20) T. Higuchi, A. Michaelis, and J. H. Rytting, Anal. Chem., 43,286 (1971). (21) H. Freiser, Anal. Chem., 41, 1354 (1969). (22) K. Behrends, 2.Anal. Chem., 250, 161 (1970). (23) (a) Y. Yamamoto, E. Sumimura, K. Miyoshi, and T. Tominaga, Anal. Chim.Acta, 64, 225 (1973); (b)Y. Yamamoto, T. Tarumoto, and E. Iwamoto, Anal. Lett., 2, 1 (1969). (24) R. L. McDonald and T. H. Hufen, J. Phys. Chem., 74, 1926

(1970). '

(25) A. G. Maddock, W. Smulek, and A. J. Tench, Trans. Faraday SOC.,58, 923 (1962). (26) R. M. Diamond, J. Phys. Chem., 61, 69, 75 (1957). (27) N. A. Gibson and D. C. Weatherburn. Anal. Chim.Acta.. 58.149. . . 159 (1972). (28) T. Sekine and D. Dyrssen, Anal. Chim. Acta, 45, 433 (1969). (29) M. KyrEi, M. Pacltova-Benesova, and J. Rais, J. Inorg. Nucl. Chem., 36, 399 (1974). (30) M . Gerin and J. Fresco, Anal. Chim.Acta, 97, 155, 165 (1978).

The Journal of Physical Chemist@', Vol. 85, No. 7, 1981 895

used as ion pairs, thereby clarifying ion size effects. In addition, the distribution ratios can easily be determined with good precision by using the radioactive tracer 1311. The organic solvents used are poor in donicity and divided into four groups: (i) nitrobenzene (high dielectric constant); (ii) 1,2-dichloroethane, 1,l-dichloroethane, o-dichlorobenzene (isodielectric constant); (iii) chlorobenzene and 1-chlorobutane (low dielectric constant); and (iv) trichloromethane and dichloromethane (low dielectric constant and hydrogen-bonding possibility).

Experimental Section Materials. Five iodide salts, Me4NI, Et4NI, Pr4NI, Bu4NI, and i-Am4NI,were commercial products (Wako Pure Chemical Industries, Ltd.). All salts were purified by several recrystallizations from the following solvents: water for Me,NI, methanol for Et4NI, ethanol-ether mixtures for Pr4NI,and acetoneether mixtures for Bu4NI and i-Am4NI. Me4NI and Et4NI were recrystallized by evaporating the solvents at -40 "C under reduced pressure. Great care was taken to ensure that the ether was peroxide free. The salts were dried in vacuo at -50 "C and stored in brown-colored glass bottles in desiccators over calcium chloride. The purity of all products was checked by analysis. Nitrobenzene (Wako Pure Chemical Industries, Ltd.) was washed with sulfuric acid, sodium carbonate solution, and distilled water, successively. It was then dried over anhydrous calcium chloride for 1week. The filtrate was passed through a molecular sieve (4 A) and fractionally distilled under reduced pressure (below 10 mmHg), and the middle fraction was collected. The distillation was done twice. Density (d, in g ml-l) and viscosity (q, in cP) of the pure solvent at 25 "C were d, = 1.1983 (1.1986,31 1.197732),qp = 1.847 (1.83932),and density (dJ and viscosity (qe)of the solvent saturated with H20 at 25 "C were d, = 1.1973 (1.19730)and qe = 1.814 (1.8230). Values in parentheses are from the literature. 1,2-Dichloroethane (1,2-DCE),dichloromethane (DCM), 1,l-dichloroethane (l,l-DCE), o-dichlorobenzene (0-DCB), chlorobenzene (CB), and 1-chlorobutane (CBu) were all commercial products (Katayama Chemical Industries, Ltd.). Each of the six solvents was washed with 5% sodium hydrogen carbonate solution and then with water, dried over calcium chloride for 1week, and fractionally distilled. The middle portion was collected. For 1,2-DCE, d, = 1.2456 (1.246OB), d, = 1.2447, qp = 0.7846 (0.783433),and q, = 0.7804; for l,l-DCE, d, = (1.166731),de = 1.1626, 7, = 0.4688 (0.46534), and q, = 0.4692; for DCM, d, = 1.3161, d, = 1.3153, qp = 0.4160, and qa = 0.4240; for o-DCB, d, = 1.3003 (1.300735) d, = 1.3002, qp = (1.27235),and q, = 1.286; for CB, d, = 1.1010, qs = 0.7554; for CBu, d, = 0.8808 and q s = 0.4330. Spectrograde trichloromethane (Wako Pure Chemical Industries, Ltd.) was washed with water several times and equilibrated with water at 25 "C just before use: d, = 1.4783 and qls = 0.5482. The carrier-free radionuclides 1311and 13'Cs were obtained as sodium iodide from Commissariat AL'Energie Atomique and as cesium chloride from the Radiochemical Centre, Amersham, respectively. Apparatus and Measurements. In distribution and conductance experiments all the organic solvents used were (31) E. G. Taylor and C. A. Kraus, J.Am. Chem. SOC.,69,1731 (1947). (32) H. Sadek and R. M. Fuoss, J. Am. Chem. Soc., 76,5905 (1954). (33) J. J. Zwolenik and R. M. Fuoss, J. Phys. Chem., 68,903 (1964). (34) F. H. Healey and A. E. Martell, J. Am. Chem. SOC.,73, 3269 (1951) (35) E. K. Ralph, 111,and W. R. Gilkerson,J.Am. Chem. Soc., 86,4783 (1964).


896

The Journal of Physical Chemistry, Vol. 85, No. 7, 1981

saturated with water and water for extraction was equilibrated with each organic solvent just before use. A glass tube with cocks at the both ends, 2.5 cm in diameter and 60 mL in volume, was used as a separatory funnel for extraction. The shaking for extraction was carried out with an incubator (Taiyo Model M-1) equipped with temperature control (*0.05 "C) and 200 strokes m i d of shaking frequency. Organic solvents (15 mL) and aqueous solutions (15 mL) containingtetraalkylmmonim iodides, a tracer concentration of 1311, and a reductant (sodium thiosulfate, 0.0095 mol L-l; sodium hydrogen carbonate, 0.020 mol L-l; sodium carbonate,0.0025 mol L-l) were equilibrated at 25 "C by shaking for 20 min after temperature equilibration and then allowed to stand for 30 min for phase separation. Both phases were completely separated by centrifugation. The reducing agent was required to prevent iodide ion oxidation, In preliminary experiments each shaking time of 15,20,30, and 60 min gave the same distribution ratio within experimental error. The radiometric assay was carried out at the 0.364-MeV y peak of 1311 for iodine and at the 0.661-MeV y peak of 137Csfor cesium, using a well-type scintillationcounter with a sodium iodide crystal and a multichannel analyzer (type Omega-1, Camberra Industries). The aliquot portions (5 mL) taken from each phase was assayed consecutively. The distribution ratio is defined as D = [specific activity (cpm mL-') of organic phase] / [specific activity (cpm mL? of aqueous phase]. Conductances were measured by using a conductometer (Model MY-7, Yanagimoto Mfg. Co.) with a Wheatstone bridge (800 Hz), which was calibrated with a standard resistance box (Shimazu Seisakusho Co.). The two conductance cells used were of the Kraus-Erlenmeyer type with lightly platinized electrodes. The cell constants, 0.04701 and 0.1137, were determined with standard aqueous solutions of potassium chloride, using the constants of Lind, Zwolenik, and F u o ~ s .Potassium ~ chloride was recrystallized twice from conductivity water and dried at -500 "C. All measurements were carried out in a water bath thermostated to 25 f 0.01 "C. Stock solutions were accurately prepared by weight. About 80 mL of solvent was accurately weighed into the cell and its resistance was measured after temperature equilibration. Then 20 mL of the solvent was pippetted out and an appropriate volume of the stock solution was added to the cell to give an appropriate concentration. Measurements were carried out with the dilution technique. The specific conductances (mho cm-') of the solvents were as follows: NB, 3.8 X (dry NB, 2-4 X 1,2-DCE, 1.5 x lo*; l,l-DCE, 1.8 X lo4; DCM, 1.0 X o-DCB, 1.8 X lo*; CB, 2.5 X 10-l'; CBu, 2.8 X TCM, 6.9 X Solubilities of water in organic solvents 25 "C were measured coulometrically by using a Hiranuma AQ-3 aquacounter; in mole fraction: 0.0170 in NB; 0.0101 in 1,2-DCE; 0.00481 in 1,l-DCE; 0.00271 in o-DCB;0.00927 in DCM, 0.00249 in CB; 0.00328 in CBu; 0.00596 in TCM. Gerin and Frescomreported that the dielectric constant of water-saturated nitrobenzene was 34.87 compared with 34.82 for pure nitrobenzene. In this study dielectric constants of pure solvents3' were used: NB, 34.82; 1,2-DCE, 10.36; l,l-DCE, 10.0; DCM, 8.90; o-DCB, 9.93; TCM, 4.72; CB, 5.62; CBu, 7.4. Viscosities were measured in Ubbelohde viscometers modified for use in a closed, dry atmosphere at 25 f 0.01 OC. Densities were measured by using an Anton Paar Model DMA 02D digital N

(36) L. Lind, J. Zwolenik, and R. M. Fuoss, J. Am. Chem. SOC., 81, 1557 (1959). (37) R. C. Weast, Ed., "Handbook of Chemistry and Physics", 47th Chemical Rubber Co., Cincinnati, OH, 1966.

Iwamoto et al.

1.0

0.5

-

0 0 0

5 -0.5

-

-1.0

-

-1.5

-

- 20 I

1

-4.0

I

-3.0

-2.0

6

-1.0

log ci

Figure 1. Dependence of distribution ratios on the ion-pair concentration at 25 "C: 0,NB; A, DCM; 0, 1,2-DCE; A,TCM; CD, 1,l-DCE; 0 , 0-DCB.

density meter at 25 f 0.01 "C. Results The distribution ratios were measured at an initial salt concentration (Ci) of 0.001 mol L-l in aqueous solutions for all systems. The average values for three to ten runs in each system were tabulated in Table I. For the systems without values in Table I, the y-counting ratios were comparable to those of the blank solutions without R4NI, showing hardly any extraction of ion pairs. The equilibration was checked by using 13'Cs and measuring the distribution of CsI. The values obtained by using 137Cs were in good agreement with those obtained when 1311was used. Figure 1 shows the concentration dependence of distribution ratio for Bu4NI in which for concentrations larger than 0.07 mol L-l the salt was initially dissolved in organic solvents and was partitioned. The distribution ratios greatly depend on the concentration of ion pairs. The trend is much more marked for solvents with a lower dielectric constant such as TCM than for NB with a higher dielectric constant. This suggests that the degree of dissociation of ion pairs in organic solvents plays an important role. In NB, 1,2-DCE, l,l-DCE, o-DCB, and DCM the values of association constant, K,,, and the limiting conductance, AO, were determined by the method of Shedlovsky.= The conductances at five to seven concentrations of the salts mol L-I were covering the range from 6 X lo-" to 3 X measured. All calculations were carried out by an electronic computer, HITAC-8700. The errors in the value of K,, were found to be less than 2.5% except for that of Pr4NI in o-DCB where the error was 10%. The theory of triple ion f o r m a t i ~ npredicts ~ ~ ~ ~their ~ formation in a medium with a dielectric constant of less than 26.2 for a pair of a mean distance of approach of, for example, 8 A. For Bu4NI in l,l-DCE, DCM, and o-DCB the conductances were also measured over the ranges of 7 X 10-2-2 x and 2 X lO-"2 X lo4 2 X 10-I-1 x (38) T. Shedlovsky, J. Franklin Inst., 226,739 (1938).


Solute-Solvent Interactions in Ion Pair Extraction

em..

000 rlrlri

x x x omTirl nnn

"199

0000 +I

+I

+I

+I

P-mt-rn ??~~ W Y W

e

m

n

-

0000 rldrlri

x x x x rlwmrim n-nn

"99Cu.e

00000 +I

+I +I +I

+I

The Journal of Physical Chemistty, Vol. 85,No. 7, 1981 897

mol L-l, respectively. For DCM a minimum conductance which indicates formation of triple ions appeared a t 3 X mol L-l, whereas for another two solvents no minimum conductance was observed in the working concentration range. The conductances of R4NI (R = Et, Pr, Bu, and i-Am) in TCM and Bu4NI and i-Am4NIin CB and CBu were measured over the ranges of 1 X 10-z-l X 1X lO+-l X and 1 X lO"-l X mol L-I, respectively. For all salts in TCM a minimum conductance was observed a t -3 X mol L-l which is expected from the FuossKraus theory: C, = $13 X 104.39@Since the equivalent conductances in TCM, CB, and CBu are too low to be treated by the Shedlovsky method, the limiting equivalent conductances of each salt were estimated from the average Walden's product of each salt in 1,2-DCE, l,l-DCE, and DCM. These conductances were analyzed by using the Fuoss-Kraus equation40 AC1l2g(C) = Ao/Ka,1/2+ (A2Ka3/KaO1/')(l - A/Ao)C (1) where g(C) is given by g(C) = e~p[-2.303A~(CA/A~)~/~]/[l AA(CA/A~)'/"?/A~](~ - A/Ao)l/' The constant Ka3is the triple ion association constant and is assumed to be the same for both possible ion triplets Ka3= [R4NII-]/[R4NI][I-] = [ R W % N + I/[R4NII [ R N I A30 is the limiting conductance of triple ions, and Af and AA are the limiting slopes of the DebyeHuckel theory and of the Onsager theory, respectively. A plot of AC1I2g(C) against (1- A/Ao)C should yield a straight line with an intercept Ao/Ka,1J2and a slope A,OKa3/Ka;I2. If Ao and A: are known, K , and Ke3can be determined. Assuming A:/Ao = 1/2,4l the conductances were analyzed. A straight line in each case was obtained. Because of the low solubility of Me4NI in all the organic solvents, its association constant could not be obtained. In Table I1 are summarized the values of Kaoand Ka3,in which the values of K,, in parentheses were obtained from eq 1. The literature values in pure solvents for some cases were also included in Table 11. Discussion (a) Definiton of Extraction Constants. Although an advantage of solvent extraction over that of solubility measurements is the direct measurement of transfer energies of a solute at any concentrations, solvent extraction suffers one disadvantage which is the mutual saturation of solvents. Furthermore, on extraction water is coextracted or salted-in with ion pairs in the organic phasesm' and organic solvents are also salted-in in the aqueous p h a ~ e . Some ~ ~ ~iodides ~ ~ coextract 1 mol of water per (39) H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions", 3rd ed, Reinhold, 1958, Chapter 7. (40) R. M. Fuoss and C. A. Kraus, J.Am. Chem. Soc., 55,2387 (1933). (41) A value A l / A o = 0.82 was employed for Bu4NN03in anisole (G. S. Bien, C. A. Kraus, and R. M. Fuoss, J. Am. Chem. SOC.,56, 1860 (1934)). A larger value of A30/Ao gives a smaller Ka3value. So if a value larger than 1/2 is used, the triple ion contribution discussed later becomes smaller. (42) E. Hirsch and R. M. Fuoss, J. Am. Chem. Soc., 82, 1018 (1960). (43) R. L. Benoit and C. Louis,Inorg. Nucl. Chem. Lett., 6,817 (1970). (44) F. Accascina, E. L. Swarts, P. L. Mercier, and C. A. Kraus, Proc. NatE. Acad. Sci. U.S.A.,39, 917 (1953). (45) (a) T.Kenjo and R. M. Diamond, J.Phys. Chem., 76,2454 (1972); (b) J. Inorg.Nucl. Chem., 36, 183 (1974). (46) Y. Yamamoto, T. Tarumoto,and T.Tarui, Bull. Chem. SOC.Jpn., 46, 1466 (1973). (47) E. M. Arnett, B. Chawla, and N. J. Hornung, J. Solution Chem., 6, 781 (1977).

898

Iwamoto et at.


TABLE 11: Association Constants, K,, and K,,, in Water-Saturated Solvents at 25 'Ca salt Et,NI Pr,NI

Bu4NI

i-Am4NI


f

NB

1,P-DCE

35 2gb 33

lo3 7.39 x l o 3 5.86 x l o 3

1,l-DCE

0-DCB

CBu

CB

DCM 6.30 X

9.04X

33 2yC

7.9

29

5.24 x l o 3

x

103d

lo4 5.33 x lo4 (4.8 x io4) 1of 5.24 x

lo4

lo5 1.62 x l o 5 1.68 x

6.54 x

(1.6 x 10') 6 5f 1.6 x 1 0 5 d 1 . 5 6 ~1 0 5 e 1.67 x l o 5

Values in parentheses were obtained from eq 1. Values of triple-ion formation constant, K,, .

+

[R4N+lO[I-l,[R4NIl, f,2 (3) [R4N+lw[I-lw[R4NIlw where f is the activity coefficient. The constant KO is divided into two equilibrium constants. One is the ionic part of extraction constant

KO =

2

[R4N+l,[I-lo f,2 (4) [R4N+1 ,[I-I w and the other the neutral part of extraction constant, or the distribution coefficient of the neutral species Kn = [R"./ tR4NIlw (5) We get the relation KO= KiK, If the ion pair is completely dissociated in the aqueous Ki =

3.94 x 104 (4.3x goof

lo7)

(2.6 x l o 8 ) 1200f

(3.4 x 800f

lo7)

(3.6 x lo8) 2100f

Reference 52.

iodide ion into NB.45346The organic solvents used here dissolve only a small amount of water (below 0.01 mol fraction in most solvents). So it is unlikely that the dissolved water has a significant effect on the solvent nature, as seen by the viscosities. However, the association constants of Bu4NIin dry NB,DCM, and 1,2-DCE were found to be 10-1570 larger than those in the water-saturated solvents. It is thus obvious that the water in organic solvents solvates the iodide ion. The association constants determined in water-saturated solvents could, to some extent, take into account the effects of hydration on extraction equilibria. In aqueous phases the presence of sodium salts as reductant (ionic strength = 0.056) is helpful for keeping the activities of water and the salted-in organic solvents constant. Therefore in the following equilibrium expressions it was assumed that the water activity is unity and the hydrated species of the iodide ion are treated as nonhydrated species and that the effect of the organic solvent salted-in is also disregarded. The contribution of coextraded water and organic solvents to the extractability of R4NI will be discussed in more detail in a subsequent paper of this series. The overall extraction process can be thus represented simply as R4NIw+ R4N+, + I-, + R4NI, (2) R4N+, + I-, where the subscripts w and o are ascribed to the aqueous and organic phases, respectively. No terms for triple ions are introduced because the fraction of triple ions is usually very small as shown later. For eq 2 the overall extraction constant KOis defined as

2

(48)F. A. Long and W. F. McDevit, Chem. Rev., 51, 119 (1952). (49)(a) E. Iwamoto, Y. Hiyama, and Y. Yamamoto, J. Solution Chem., 6,371 (1977);(b)E. Iwamoto, Y. Tanaka, H. Kimura, and Y. Yamamoto, J. Solution Chem., in press.

TCM

lo4

Reference 42.

3.26 x lo4 (3.3 x i o 4 ) 15f 2.90 x

Reference 43.

lo4 e

(3.1 x 640f (1.8 x 53Qf (1.3 x 5oof

lo8)

(9.6 x 4 5Of

lo7)

108)

lo8)

Reference 44.

phase, the overall extraction equilibrium can be written as (7) 2R4N+, 21-, + R4N+, + I-, + R4NI, In this case the overall extraction constant

+

where K', is the neutral ion-pair extraction constant defined as (9)

Only either Ki or K,' has so far been used for the extraction constant of an ion pair in a solvent.7~8~23-30 Evans and Kay60 reported association constants, K,,, of 3.1 and 2.0 for Bu4NIand of 2.1 and 1.0 for Pr4NI in water at 25 "C, using the Fuoss-Onsager equation5' Association constants of 1.0 for Et4NI by K ~ r t u m using ~ ~ the FuossKraus equation53and of 1.8 for Me4NI by L e ~ i e using n~~ the Fuoss-Onsager equation5' were reported. Evaluation of such a very small degree of association depends upon a theoretical equation used for analysis of the conductivity measurements and it is difficult to obtain reliable values. We assumed the association constant K,, to be unity for all the ion pairs. This assumption gives the relation, K,,' = K,, since thereby [R,NIIw = ~R4N+lw[I-3wfw2 (10) The newly defined extraction constants KO,or K,,and Ki were calculated at each concentration of Bu4NI for all the solvents by using the distribution ratios (Figure l),the association constants (Table 11),and the Debye-Huckel equationM(f = exp{-A(Ca)'/2/[1 + BU(C~~)'/~]) with a value for a of 6 A for activity Coefficients where A and B are the Debye-Huckel constants and a is degree of dissociation corrected for triple ion concentrations. An iterative calculation was used to reproduce the association constant K,, within 0.01%, each concentration of the species being determined. Activity coefficients for Et4NI and Pr4NI of more than 0.1 mol kg-' in the aqueous phase were reported by Lindenbaum and Boyd.% Since in the present work the concentration in the aqueous phase is less than 0.03 mol L-I and the reductant was added, the Debye-Huckel (50)D. F. Evans and R. L. Kay, J. Phys. Chem., 70,366 (1966). (51) R. M. Fuoss and F. Accascina, "Electrolytic Conductance", Interscience, New York, 1959. (52)G. Kortum, S. D. Gokhale, and H. Wilski, Z. Phys. Chem. (Frankfurtam Main), 4, 286 (1955). (53)R.M. Fuoss and C. A. Kraus, J. Am. Chem. SOC.,55,476(1933). (54)B. J. Levien, Aust. J. Chem., 18, 1161 (1965). (55)R.A. Robinson and R. H. Stokes, "ElectrolyteSolutions", revised, Butterworths, London, 1970,Chapter 9. (56)S.Lindenbaum and G. E. Boyd, J . Phys. Chem., 68,911 (1964).

The Journal of Physical Chemistry, Vol. 85, No. 7, 198 1 890


TABLE 111: Ion Fraction f o r Bu4NIin Organic Phases a t 25 "C solvent

NB 0-DCB DCM TCM

CB

Ci,' mol L-'

~ , , bmol

1.0 x 2.0 x 1.0 x 2.0 x 1.0 x 2.0 x 1.0 x 1.0 x 1.0 x

7.46 x 1.57 X 1.80 x 2.99 x 5.39 x 1.65 X 3.65 x 7-62 x 2.61 X


Initial concentration.

10-3 10-3 10-3

10-3 10-3

L-I

10-4 10.' 10-5 10-3 10-4

10-4 10-3

Bu4NI 012 0.019 0.178 0.537 0.905 0.708 0.799 0.992 0.978 0.961

single i o n a1

0.981 0.822 0.462 0.06 2 0.287 0.126 0.0051 0.0018 0.0384

t r i p l e ion

a3 0.0 0.0 0.0003 0.0110 0.0016 0.0250 0.0009 0.0068 0.0001

fo

0.905 0.713 0.929 0.701 0.700 0.304 0.890 0.546 0.981

Concentration in organic phase. a 1 = [I-],/C,;a2 = [Bu4NI],/CO;a3 = [Bu,NIBu,N'],/C,.

E

-4

-3

log ci

-2

Figure 2. Dependence of extraction constants on the ion-pair concentration at 25 OC: for NB, A, log KO;A, log K,; A, log K,; for 0-DCB, 0,log KO; 0 , log Ki; 0, log K,.

equation was also used. The activity coefficients of associated species were assumed unity at the concentration of interest here. Table I11 shows some examples of ion fractions in organic phases at initial concentrations of 1.0 X 1.0 X and 2.0 X mol L-' and Figures 2-4 show the concentration dependence of the extraction constants of Bu4NI. Satisfactory constancy of all the extraction constants, especially below Ci = 2 X was observed. This shows that the thermodynamically quantitative extraction constants can be written by eq 3-5. The deviation from constancy above 2 X mol L-l may be due to the inadequate application of the Debye-Huckel equation to such concentrated solutions and to the formation of higher aggregates. So while the rather small concentration dependence of the distribution ratios (Figure 1)for NB of higher dielectric constant can be attributed almost entirely to the decreases in activity coefficients, the strong dependences for other five solvents are due not only to the rapid decreases in activity coefficients but also to the formation of triple ions and higher aggregates with increasing concentration. The contribution of triple ion formation to the extraction constants defined here was found to be very small and negligible if the distribution ratios at Ci = 1.0 X are used. For example, for DCM in which the largest mole fraction of triple ions was found (Table 111) at Ka3= 15 and Ci = 1.0 X log KO=2.326 (2.100),log K,, = 3.419 (3.306), and log Ki = -1.093 (-1.206), while at Ka3= 0, log KO= 2.331 (2.185), log K , = 3.422 (3.349), and log Ki = -1.090 (-1.164) where the values in parentheses correspond to values at Ci = 2.0 X Table IV gives the extraction calculated by use of constants, log Ki, log K,,, and log KO,

-3

-L

log

ci

-2

-1

Figure 3. Dependence of extraction constants on the ion-pair concentration at 25 'C: for 1,2-DCE, A,log KO;A,log K,; A,log K,; for l,l-DCE, 0,log KO;0 , log K,, 0 , log K,.

A

6

H

A

A 4 A

A

p p a

2

A

A

A

~

0

..

-I*

= = =

-A

-3 log

ci

-2

-1

Figure 4. Dependence of extraction constants on the ion-pair concentration at 25 ' C : for DCM, A, log KO;A, log K,; A, log K,; for TCM, 0,log KO;0 , log Ki; 0 , log K,.

the distribution ratios in Table I. The solvent effects of ion-pair extraction can thus be discussed in terms of each effect for ionic and neutral species. ( b )Application of Regular Solution Theory to K,,. The results in Table IV show as a general trend of extractability that the larger the cation, the larger the extraction constant in all solvents. The extraction free energies for NB cal-

900

Iwamoto et al.


TABLE IV: Extraction Constants a t 25 "C salt NB 1,2-DCE

1,l-DCE

0-DCB

CBu

CB

DCM

TCM

- 5.60

- 9.41


log Ki Et,NI R,NI Bu,NI i-Am,NI

- 2.70 - 0.82

- 5.34 - 3.08

1.00 2.37

-0.97 0.57

Et,NI Pr,NI Bu,NI i-Am,NI

-1.15 0.70 2.51 3.84

-1.38 0.79 2.80 4.29

Et4NI Pr,NI Bu,NI i-Am,N I

- 3.85 - 0.12

-6.72 - 2.30 1.83 4.87

3.51 6.21

-6.16 -4.04 - 2.47

-4.97 - 2.71 -0.97

- 3.42 -7.78 - 5.79

- 5.00

-6.29

- 0.92

0.57 2.27

-0.80 1.18 3.42 4.96

- 6.40 - 2.24

- 10.32 - 6.65 - 1.88

log Kn - 0.94

-0.16 2.02 3.75

1.17 2.76

- 0.15 1.74

1% KO - 5.13

- 7.10

-0.69 2.78

- 2.88

n Flgure 5. Extraction free energles as a function of chain length, ((C&+,),NI), for NB at 25 'C: 0,-AG;; 0 , -AG?; a,-AGn0.

culated by using the relation -AGO = 2.303RT log K,, where R is the gas constant and K,, is the extraction constants were plotted against the number n of carbon in (CnH2n+1)4NI (Figure 5). Fairly good linear relationships were found among Et4NI,Pr4NI, and Bu4NI with normal alkyl chains although a drift of the plot from a straight line was clearly observed for i-Am4NI. The extraction free energies of R4NIare made up of additive contributions for the extractability of the methylene groups. The following equations were obtained: -AGio(NB) = 2.52n - 8.70 -AGno(NB) = 2.50n - 6.57 -AG,o,NB) = 5.02n - 15.26

The contribution per methylene group is so very nearly the same for both the ionic and neutral parts, indicating that the charge for R4N+is well shielded. For different solvents they have almost the same slope for each extraction free energy. The average values are 3.01 f 0.08 for -AGr, 2.87 f 0.08 for -AG,", and 5.88 f 0.13 for -AG,". Therefore we can obtain 0.63 kcal mol-l for NB and 0.73 kcal mol-l for other solvents as the contribution to the extraction free energies per methylene group. The additivity due to a methylene group has been already found experimentally for several cases: in kcal mol-l of -CH2-, 0.8 for aliphatic a m i n e ~ - C H C l ~0.74 , ~ ~ for tetraalkyl-

0.29

-7.93 -4.05

- 7.45

-1.09 0.50

- 7.85

- 7.28 - 4.02

2.33 5.46

-3.23

0.80 3.12 4.75

1.52

ammonium picrates-DCM and CHC13,%0.76 for carboxylic a ~ i d - N B 0.82 , ~ ~ for carboxylic acid-l,l-DCEt9 and 0.75 for trialkylammonium halide~-NB.~O Comparing the methylene group contribution for tetraalkylammonium salts with that for the monoalkyl salts, the former appears to be a little smaller than the latter. This may be compatible with the result that an increase in partial molal volume per methylene group for R4N+up to n = 4 is 15.5 mL mol-l 60@1 while that for RH3N+is 16.5.62163 The application of the regular solution theory to ion-pair extractions has been a controversial problem.16Je-21 As mentioned in an earlier section, the newly defined extraction constant K , is the distribution coefficient of the neutral species R4NI. Therefore it is very interesting to see whether or not regular solution theory could interpret the distribution of R4NI. Regular solution theory successfully predicts the extraction free energy -AG,O of a solute (solubility parameter 6, and molar volume V,) from water (6, and V,) to organic solvent (6, and V,) by the equation14-17 -AG;/(6, - 6,) = V,(6, + 6,' - 26,) (11) where 6,' is given by 6, + RT(l/V, - 1/Vw)/(6, - 6,) 6', provided the concentration of solute in both phases is sufficiently small. Furthermore, if it is assumed that an additional methylene group does not produce any appreciable change in solubility parameters of compounds having the same functional from eq 11 we arrive at A(-AG,O) = AVJ(6, - 6J2 - (6, - ad2] (12) where A(-AG,O) and AV, are the difference of extraction free energy and molar volume of homologous compounds. When eq 12 with a 6, value of 17.5515 and an increment in molar volume per methylene group of 15.5, and the slopes in plots of -AGn0 vs. n, was used the solubility parameter was calculated as 11.1 for NB and 10.7 for the other solvents. Equation 11 was applied to the distribution coefficients K,,as an example, for B a N I in Table IV using values of solubility parameter and molar volume in Table V. Figure 6 shows plots of -AGn/ (6, - 6), against (57)D. Dyrssen, Sven. Kem. Tidskr., 77, 387 (1965). (58) (a) K.Gustavii and G.Schill, Acta Pharm. Suecica, 3,241 (1966); (b) K. Gustavii, ibid., 4, 233 (1967). (59)I. Kojima, M.Yoshida, and M. Tanaka, J. Znorg, Nucl. Chem., 32,987 (1970). (60)B.E.Conway, R. E. Verrall, and J. E. Desnoyers, Trans. Faraday SOC.,62,2738 (1966)). (61)F. Franks and H. T. Smith, Trans. Faraday SOC.,63,2586 (1967). (62)J. E.Desnoyers and M. Arel, Can. J . Chem., 45,359 (1967). (63)A. E.Rheineck and K. F. Lin, J . Paint Technol., 40,611(1968).

The Journal of Physical Chemistry, Vol. 85,No. 7, 198 1 901


TABLE V : Solvent Parameters solvent NB 1,P-DCE 1,l-DCE 0-DCB CB CBu DCM TCM

H,O

va

€ib

PC

103 79 84 113 102 105 64 81 18

1l.ld 9.9 9.1 10.0 9.5 8.4 9.7 9.3 17.55e

4.27 1.75 2.05 2.30 1.56 2.11 1.54 1.02 1.84

I - 4c

Molar volume (mL mol-'). Solubility parameter (from ref 17 and 74). Dipole moment. M. Tanaka (Nagoya University), private communication and from ref 75. e From ref 15.


0.6

-8

-10

1

\

\

70

I

I

0

2

I

1

4

6

8

log Kao

Flgure 7. Correlation of ionic extraction free energies with logarithmic association constant for Bu,NI: 1, NB; 2, 1,P-DCE; 3, DCM; 4, 1,lDCE; 5, 0-DCB; 6, TCM; 7, CBU; 8, CB.

5.5

6.0

6.5

7.0

S' Flgure 6. Correlation of extraction free energies of Bu,NI with solvent solubility parameter (eq 11): 1, NB; 2, DCM; 3, 1,P-DCE; 4, TCM; 5, 1,l-DCE; 6, 0-DCB; 7, CB; 8, CBU.

,'a,

in which the solid line corresponds to values of V , = 310 and 6, = 11.3. Regular solution theory roughly interprets the distribution of associated species. The deviation from the straight line for DCM and TCM would be due to hydrogen bonding to the ion pair. The extractability of the neutral species by o-DCB, CB, and CBu is less than expected from their solubility parameters. The trend of decreased extractability for the three solvents is also seen for the ionic species as shown later. ( c ) Contribution of Specific Solvation. The extractability of ions decreases in the order NB > 1,2-DCE > DCM > 1,l-DCE > o-DCB > TCM > CB > CBu. A better linear relationship was found for -AGF vs. log K , plots of BQNI, leading to a general rule that, the stronger the ionizing power of the solvent, the more extracted into the solvent are the dissociated ions. The dipolar aprotic solvent, NB,. is a very good solvent for the extraction of a number of ion pairs.8,22i27-29,64~8 This is due mainly to the higher dielectric constant. The drastic variation in the association constants of 1,2-DCE,l,l-DCE, and o-DCB in spite of their almost similar dielectric constants, was interpreted by the difference between solvent-ion and solvent-ion pair interaction energies appreciably due to the solvent dipoles.m A clearer explanation for the smaller association constant in 1,2-DCE70is that the effective dielectric constant of the (64)Y. Yamamoto, T.Tarumoto, and E. Iwamoto, Anal. Chim. Acta, 64,1 (1973). (65) S. L. Law and R. L. McDonald, J. Phys. Chem., 72,1617 (1968). (66)M.Pivoiikovd and M. KyrB, J. Znog. Nucl. Chem., 31,175(1967). (67)P.R.Danesi, R. Meider-Gorican, R. Chiarizia, and G. Scibona, J. Znorg. Nucl. Chem., 37, 1479 (1975). (68)T.Iwachido, Bull. Chem. SOC.Jpn., 45, 1746 (1972). (69)W.R. Gilkerson, J. Chem. Phys., 25, 1199 (1956). (70)Y.H.Inami, H. K. Bodenseh, and J. B. Ramsey, J. Am. Chem. SOC.,83,4745 (1961).

solvent in the vicinity of an ion is appreciably greater than the macroscopic dielectric constant due to an increase in the ratio of gauche to trans molecules of 1,2-DCE by the ionic field. For neutral species, the order is DCM > TCM > NB > 1,S-DCE > 1,l-DCE > o-DCB > CB > CBu. The associated species are extracted more into DCM and TCM than into NB. We also found strong evidence for specific interactions between R4NI and DCM or TCM from the temperature dependences of distribution ratios, that is, the transfer enthalpy of R4NI from water to DCM or TCM is negative but those for other solvents are positive.7l These can be explained in terms of hydrogen bonding between the iodide ion and the solvents and the efficiency for hydrogen bonding appears to be independent of the type and degree of ionic a s s o c i a t i ~ n . These ~ ~ results clearly demonstrate that specific interactions, especially hydrogen bonding, can be more important than the dielectric constant in determining the properties of an ionic solution. If the chloride series is used, a more drastic contribution of hydrogen bonding may be observed since the chloride ion is much more solvated in protic solvents than in dipolar aprotic solvents while the iodide ion is at least as solvated in dipolar aprotic solvents as in protic solvents, as can be seen from the solubility data.73 It can be concluded that there are three important properties of the solvent for ion-pair extractions: the dielectric constant for the ionic solution, the solubility parameter for the neutral, and the hydrogen bonding power for both. In this connection, NB is the best solvent for ion-pair extractions and DCM is the second best. More precise examinations of the contribution of dielectric constant and solubility parameter will be given in a subsequent paper for the nitrobenzene-carbon tetrachloride system.

Acknowledgment. Thanks are due to the Ministry of Education for financial support (Grant No. 443013 and 454183). We also thank Mr. H. Ohmori for his assistance in the experimental work. (71)Y. Yamamoto, E. Iwamoto, T. Sakai, K. Ito, and H. Ohmori, unpublished results. (72)(a) R. P. Taylor and I. D. Kuntz, Jr., J. Am. Chem. Soc., 92,4813 (1970); (b) J. Phys. Chem., 74,4573 (1970). (73)14. J. Parker, Q.Reu. Chem. SOC.,16, 163 (1962). (74) 4.F.M.Barton, Chem. Rev., 75,731 (19715). . (75) - - - M. . ,- H. - - -.Abraham and J. Liszi, J. Chem. SOC.,Faraday Tram. 1 , 74,1604 (1Y78). 2

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