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2907
Modeling Solvent Extraction Using the Solvatochromic Parameters a,p, and T * Daniel C. Leggett Geochemical Sciences Branch, U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire 03755
A linear solvation energy relationship (LSER) employing only the solvatochromic parameters a, @,a*,and 6was shownto be adequate for describing solvent/water distribution processes for single solutes. Cavity formation is represented by the solvent a@ or a@ and T * ~ .Examples of its application are given for dimethyl methylphosphonate, phenol, aniline, and acetylacetone. This kind of model could, in principle, be used by analytical chemists and chemical engineers to design and optimize solvent extraction processes. INTRODUCTION Solvent extraction processes are important components of industrial chemical engineering operations, analytical chemistry separations, and preparative organic chemistry, among other uses. Despite their importance, there has been little effort to provide a unifying framework for the enormous amount of data that are available or to develop a comprehensive predictive model that would aid in future process design. A linear free energy model for partitioning of a solute between two solvents was first formulated by Taft et al.1 Typically, when one of the solvents is water and several extraction solvents are to be compared, the model simplifies to2 log K,, = aij2,,
+ b(r*l - c6,) + da, + e& + f
(1)
where K12 is the mole fraction distribution coefficient, a@H1 in the molar cohesive energy density of the solvent, r*1 is the solvent total dipolarity/polarizability,6 is a correction for incomplete polarization by the probe compound, a1 is the solventH-donicityor Lewis acidity,and 81is its Lewis basicity. Constants a-f are determined by multiple linear regression involving a sufficient number of solvent/water distribution data. Equation 1, however, has been found less suitable for correlating partition data than one in which 62, is replaced simply by the product ~ ~ 8 . 2 9 3Slightly better results were obtained when u*2 was also included. The resulting set of cohesion parameters represent the H-bonding and polar contributions to solvent cohesion. No dispersion terms were needed,probably because of their near cancellationin solvent to solvent transfers. Since 6 2 includes ~ dispersion and, in some cases, more bonding energy than cavity formation actually require^.^.^ I agree with Rutan et that eq 1is not generally valid. The question arises as to whether pure solvent solvatochromic parameters can be used to represent solvents (1)Taft,R. W.;Abraham,M.H.;Famini,G.R.;Doherty,R.M.;Abboud, J.-L. M.; Kamlet, M. J. J. Pharm. Sci. 1986, 74, 807. (2) Leggett, D. C. J. Solution Chem. 1993, 22, 289. (3) Rutan,S. C.; Carr, P. W.; Taft, R. W. J. Phys. Chem. 1989,93,4292. (4) Kamlet, M. J.; Doherty, R.; Taft, R.W.; Abraham, M. H. J. Am. Chem. Soc. 1983, 105,6741.
containing >0.13 mole fraction water at equilibrium.6 Some recent experimentalmeasurements suggestthat they cannot.8 However, Marcus’ found that when he used experimentally measured solvatochromicparameters for “wet”solvents(>0.13 mole fraction water) in conjunction with eq 1, his “universal“ constants derived from “dry” solvents were no longer appropriate. It is not clear whether this was due to the experimentalsolvatochromicmeasurementsbeing “artifacts” as he claimed? to the inappropriateness of eq 1, or to some other reason. In any case the approach taken here is to use the tabulated solvatochromic parameters for pure solvents regardless of their equilibrium water content and to judge the appropriateness of the parameters on a purely statistical basis.
RESULTS AND DISCUSSION Partition coefficients for dimethyl methylphosphonate (DMMP) between water and solvents were measured as described earlier.2 Since DMMP is poorly extracted by most water-immiscible solvents, I sought to increase its extraction by salting out together with water-soluble polar solventa.8 Extraction of DMMP from water and NaC1-saturated water are shown in Tables I and 11. The data were correlated using a linear solvation energy relationship (LSER) in which a8 and r*2replaced 6% as reported earlier.2 The final equations for fitting the data in Tables I and I1 were log K = 4 . 5 3 1 ~+~2.684~*+ 2.1308 5.049~~0 - 1 . 2 7 5 ~-* 2.325 ~ (n = 16; r = 0.998; u = 0.065; F = 410)
(2)
log K = 4.057~~ + 2.779r* + 1.27984.408~~0 - 1 . 4 5 4 ~-* 1.301 ~ (n= 19; r = 0.999; (I = 0.073; F = 958)
(3)
All parameters were significant at the 0.9999 level. Inclusion of a polarizability correction term, 6, did not measurably improve the fit. The statistical information given in parentheses is number of data points, regression coefficient, standard deviation and F-statistic. The generality of this approach is shown by correlating extraction data for phenol, which, in contrast to DMMP, is a strong acid (am= O.6Wg Solvent/water partitioning data were taken directly from Hansch and Leo10 and converted to (5) Marcus, Y. J. Phys. Chem. 1991,95,8886. (6) Migron, Y.; Marcus, Y. J. Chem. SOC.,Faraday Trans. 1991,87, 1339. (7) Marcus, Y. Solvent Extr. Ion Exch. 1992, 10, 527. (8) Leggett, D. C.; Jenkins, T. F.; Miyares, P. H. Anol. Chem. 1990, 62, 1355. (9) Kamlet, M. J.; Doherty, R. M.; Abraham, M. J.; Marcus, Y.; Taft, R. W. J. Phys. Chem. 1990,92, 6244. (10) Hansch, C.; Leo, A. Substituent Constants for Correlation Analysis in Chemistry andBiology;Wiley-Interscience: New York, 1979.
Thls artlcle not subject to U.S. Copyright. Published 1993 by the Amerlcan Chemlcal Society
2908
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993
Table I. Solvent Extraction of DMMP from Water and Solvatochromic Parameters of the Solvents solvent
fl
carbon disulfide carbon tetrachloride benzene diethyl ether trichloroethylene ethyl acetate methyl ethyl ketone nitroethane propylene carbonate nitromethane benzyl nitrile bromoform methylene chloride l,l,l-trichloroethane isobutanol chloroform
0.00 0.07 0.00 0.00 0.14 0.06
@
0.00 0.10 0.10 0.47 0.05 0.45 0.06 0.45 0.16 0.25 0.09 0.40 0.22 0.25 0.14 0.41 0.33 0.05 0.30 0.10 0.34 0.10 0.84 0.84 0.44 0.10
**a
0.11 0.28 0.59 0.27 0.53 0.55 0.67 0.80 1.17 0.85 0.99 0.62 0.82 0.53 0.40 0.58
Table 111. Solvent Extraction of Phenol from Water and Solvatochromic Parameters of the Solvents
logF
log Kc
log KP
-2.58 -1.94 -1.61 -1.49 -1.27 -1.78 -0.73 -0.50 -0.44 -0.25 -0.52 -0.34 -0.18 -0.31 -0.13 0.17
-2.05 -1.21 -0.92 -0.72 -0.57 -0.04 -0.03 0.09 0.23 0.23 0.27 0.34 0.37 0.40 0.58 0.82
-2.05 -1.19 -0.97 -0.69 -0.55 -0.14 -0.05 0.06
0.17 0.29 0.30 0.37 0.44 0.32 0.58 0.79
a References 2, 3, 11, and 12. b This work. Calculated aa K = P(Vm(solvent)/Vm(H20));see text. Fitted value from ea 2.
Table 11. Solvent Extraction of DMMP from NaC1-Saturated Water and Solvatochromic Properties of the Solvents solvent
Cuo
n-hexane carbon disulfide carbon tetrachloride benzene diethyl ether tetrahydrofuran ethyl acetate methyl ethyl ketone acetone propylene carbonate nitroethane acetonitrile nitromethane 2-propanol n-propanol methylene chloride chloroform 2,2,2-trifluoroethanol 1,1,1,3,3,3-hexafluoro2-propanol
0.0
a
0.0 0.07 0.0 0.0 0.0 0.06 0.06
0.08 0.09 0.16 0.19 0.22 0.76 0.84 0.30 0.44 1.49 1.96
@
0.0 -0.08 0.0 0.11 0.10 0.28 0.10 0.59 0.47 0.27 0.55 0.58 0.45 0.56 0.48 0.67 0.48 0.71 0.40 1.17 0.25 0.80 0.40 0.75 0.25 0.85 0.90 0.48 0.84 0.52 0.10 0.82 0.10 0.58 0.00 0.73 0.00 0.65
logP
log Kc
-2.46 -1.48 -1.00 -0.67 -0.73 -0.23 -0.22 -0.08 0.02 0.07 0.17 0.42 0.49 0.40 0.55 0.66 0.97 2.18 3.08
-1.60 -0.96 -0.27 0.02 0.03 0.43 0.52 0.62 0.63 0.74 0.77 0.88 0.97 1.03 1.17 1.21 1.62 2.79 3.85
log
KP -1.52 -1.01 -0.25 -0.03 -0.06
0.51 0.53 0.62 0.68 0.72 0.80 0.88 0.95 1.03 1.22 1.18 1.51 2.93 3.80
References 2, 3,11, and 12. Reference 2. c Calculated ae K =
solvent
d
@
cyclohexane n-octane n-heptane n-pentane n-hexane n-decane n-nonane carbon disulfide tetrachloroethylene carbon tetrachloride trichloroethylene pentachloroethane bromoform iodobenzene bromobenzene xylene ethylbenzene toluene chlorobenzene chloroform mesitylene benzene l,l,2,2-tetrachloroethane methylene chloride 1,2-dichloroethane nitrobenzene o-nitrotoluene m-nitrotoluene n-pentanol diethyl ether n-hexanol n-octanol ethyl acetate n-butyl acetate methyl isobutyl ketone
0.0 0.0 0.0 0.0
0.0
0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0
0.0 0.07 0.14 0.45 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.44 0.0 0.0 0.40 0.30 0.15 0.05 0.04 0.04 0.84 0.0 0.80 0.77
0.0 0.0 0.0
0.05 0.10 0.05 0.10
0.05 0.05 0.06
0.12 0.12 0.11 0.07 0.10 0.13 0.10 0.10 0.10 0.10 0.30 0.31 0.31 0.84
0.47 0.84
0.81 0.06 0.45 0.06 0.45 0.05 0.52
**a
0.0 0.01 -0.02 -0.08 -0.08 0.03 0.0 0.11 0.28 0.28 0.53 0.62 0.62 0.81 0.79 0.49 0.53
0.55 0.71 0.58 0.47 0.59 0.95 0.82 0.81 1.01 0.97 1.02 0.40 0.27 0.40 0.40 0.55 0.51 0.63
6'
logF
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 0.5 1.0 1.0 0.5
-0.72 -0.88 -0.82 -0.70 -0.75 -0.82 -0.75 -0.26 -0.37 -0.28 0.02 0.04 0.18 0.10 0.18 0.15 0.15 0.22 0.25 0.36 0.13 0.35 0.42
0.5 0.5 1.0 1.0 1.0 0.0 0.0
0.69 0.60 0.91 0.86 0.91 1.67 1.58 1.66 1.48 1.76 1.68 2.04
0.0 0.0 0.0 0.0 0.0
log Kc
log
KP
0.06 0.16
0.08 0.19 0.09 0.12 0.11 0.00 0.11 0.00 0.22 0.23 0.25 0.17 0.26 0.38 0.38 0.40 0.45 0.58 0.72 0.69 0.87 0.91 0.87 0.78 0.89 0.86 0.95 0.90 0.98 1.00 0.99 1.03 0.99 1.01 1.00 0.93 1.01 0.87 1.02 1.02 1.05 1.00 1.19 1.33 1.24 1.24 1.67 1.68 1.73 2.35 2.35 2.39 2.43 2.50 2.55 2.88
1.19 1.21 1.69 1.76 1.73 2.34 2.38 2.42 2.41 2.62 2.50 2.83
a References 2,3,11, and 12. b Reference 10. c Calculated ae K = P(V,(solvent)/V,(HZO)); see text. Fitted value from eq 4 or 5.
log K = 3.7138+ 2.081(** - 0.1486)2.2150$ - 1.317~*~ + 0.165
(n = 26;r = 0.998;u = 0.07;F = 886)
(4)
log K = 3.9268 + i.228(** - 0.4786)- 2 . 2 6 + ~ 0.154 ~~~
P (V,(solvent)/VdHaO)): see text. d Fitted value from ea 3. (n = 24;r = 0.997;IJ = 0.077;F = 929) the mole fraction scale. Slightly different results are obtained if log P is regressed directly, and I have argued elsewhere that the mole fraction scale should be usede2 Table I11 presents the results for 35 solvents for which reliable solvatochromic parameters were available.2t8J1J2 The resulting group of solvents has a broad range of properties and consists of 7 aliphatic hydrocarbons, 9 halogenated aliphatics, 11 aromati ics, 3 alcohols, 2esters, 1 ether, 1 ketone, and carbon disulfide. Considering the unknown quality of the input data, the resulting correlations were remarkably good and very few statistical outliers were eliminated from the original dataset.10 There was a systematic difference between halogenated aliphatic and aromatic solvents, which lowered the overall regression coefficient. Therefore, I segregated these groups and combined each of them with the remaining aliphatic solvents, obtaining two regression equations: (11) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft,R.W. J. Org. Chem. 1983,48,2817. (12) Marcus, Y.J. Solution Chem. 1991,20, 929.
(5)
Equation 4 is for aromatics plus nonhalogenated aliphatics. Equation 5 is for all aliphatics. The main difference is in the coefficient of 6, which is 3 times greater for the halogenated aliphatic group. This indicates that halogenated aliphatic solvents are less polarizable by phenol than are aromatics, which seems reasonable from an electronic standpoint. As expected, solvent basicity is the dominant factor. Phenol extractability into alcohols, however, is mitigated by their high cohesive strength, and more efficient extraction occurs with the less H-bonded esters and ketones. Extraction data for aniline are shown in Table IV. Aniline is interesting because it is amphoteric as well as dipolar (a, = 0.26;Bm = 0.50;?r* = 0.73).9 This is reflected in the best-fit equation: log K = 1.7648 + 1.138~* + 1.123~~ 2.744~~8 - 0.253~*~ + 0.844
(n = 15;r = 0.998; u = 0.05;F = 364)
(6)
ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993
Table IV. Extraction of Aniline from Water and SolvatochromicParameters of the Solvents log Kc
log KP
-0.11 -0.05 0.03 0.5 0.60
0.80 0.81 0.81 1.33
0.82 0.75
0.0 1.0 1.0 1.0 1.0 1.0 0.0 0.5 0.0 0.5
0.90 0.72 0.83 1.00 0.86 0.90 1.25 1.32 1.40 1.45
1.84 1.55 1.60 1.70 1.63 1.65 2.12 1.97 2.14 2.22
0.65 0.0
1.55
2.83 2.82
ap
n-heptane n-hexane cyclohexane carbon tetrachloride n-octanol xylene toluene benzene bromobenzene chlorobenzene butyl acetate chloroform ethyl acetate 1,1,2,2-tetrachloroethane tributyl phosphate
0.0 0.0 0.0 0.07
0.0 -0.02 0.0 -0.08 0.0 0.0 0.10 0.28
0.0 0.0 0.0
0.77 0.0 0.0 0.0 0.0 0.0 0.06 0.44
0.81 0.12 0.11 0.10
0.06
0.80
@
**a
0.40 0.49 0.55 0.59 0.79 0.71 0.46 0.58 0.55 0.95
0.06
0.07 0.45 0.10 0.06 0.45 0.40 0.10
Table V. Solvent Extraction of Acetylacetone from Water and Solvatochromic Parameteme of the Solvents
logP
P
solvent
0.84
1.38 1.84 1.55 1.59 1.60 1.69 1.65 2.10 1.97 2.18 2.21
*
References 2,3,11, and 12. Reference 10. c Calculated aa K = P(V,(solvent)/V,(HzO)); see text. Fitted value from eq 6. a
where a, 8, and A* are about equally important in describing the partitioning of aniline between water and 15 organic solvents. The 6 correction term was not significant in this case, probably because of the relativelysmall number of data. In any case, the fit to the solvatochromic LSER is excellent and robust as it includes both strongly acidic and strongly basic as well as polar and nonpolar solvents. A final example of application of LSER theory to solvent extraction is for acetylacetone,which is an important organic chelatingagent.13 The extensivedata base10 includesa diverse group of solvents. The results of this analysis are shown in Table V. Solvent acidity and cohesion are extremely important, with the acidity of alcohols largely nullified by cohesive interactions and performing no better than carbon tetrachloride as extractants. The best extractants were the more acidic chlorinated solvents, especially those with large dipole contributions: tetrachloroethane, methylenechloride, and chloroform. The final regression equation was log K = 1.603a 0.933~*+ 0.2508 -
+
+
2.346aB - 0 . 3 3 8 ~ * ~0.989
= 0.046; F = 229) was not significant.
(n = 31; r = 0.989; The 6 correction to A*
~7
2909
(7)
CONCLUSIONS These are but a few examples which serve to show the applicabilityand power of LSER equationsto simulatesolvent (13) Minmweki,J.; Chweetowska,J.; Dybezynski, R. Separation and heconcentration Methods in Inorganic Trace Analysis; John Wiley New York, 1982.
log
solvent
a0
B
6'
n-heptane n-octane n-nonane heptene n-pentanol n-hexanol carbon tetrachloride n- heptanol n-octanol n-nonanol dipentyl ether xylene cumene toluene benzene chlorobenzene bromobenzene iodobenzene o-dichlorobenzene phenetole 1,2-dibromoethane ethyl trichloroacetate trichloroethylene methyl chloroacetate methyl isobutyl ketone nitrobenzene 1,2-dichloroethane 1,l-dichloroethane methylene chloride chloroform 1,1,2,2-tetrachloroethane
0.0 0.0 0.0 0.0
0.0 0.0
0.84 0.80 0.07 0.79 0.77 0.75 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.12 0.14
0.84
-0.02 0.0 0.04 0.01 0.0 0.08 0.02 0.0 -0.01 0.08 0.0 0.23 0.40 0.0 0.43 0.40 0.0 0.45 0.28 0.5 0.51 0.40 0.0 0.32 0.40 0.0 0.34 0.40 0.0 0.26 0.24 0.0 0.26 0.49 1.0 0.52 0.51 1.0 0.56 0.55 1.0 0.62 0.59 1.0 0.73 0.71 1.0 0.78 0.79 1.0 0.79 0.81 1.0 0.79 0.80 1.0 0.72 0.69 1.0 0.68 0.75 0.5 0.80 0.61 0.0 0.74 0.53 0.5 0.93 0.75 0.0 0.94 0.63 0.0 0.80
0.0 0.07
0.84 0.10 0.82 0.81 0.81 0.46 0.12 0.12 0.11 0.10 0.07 0.06
0.05 0.03 0.30 0.0 0.25 0.05 0.08 0.32 0.05 0.52 0.05 0.15 0.26 0.30 0.44 0.40
0.30 0.10 0.10 0.10 0.10 0.10
1.01 0.81 0.48 0.82 0.58 0.95
P
1.0 0.5 0.5 0.5 0.5 0.5
0.90 1.10 1.10 1.31 1.40 1.44
log
log
Kc
K&
0.95 1.04 0.99 1.12 1.21 1.29 1.24 1.22 1.28 1.25 1.31 1.35 1.45 1.39 1.46 1.53 1.56 1.58 1.52 1.53 1.48 1.63 1.63 1.63 1.64
0.97 1.00 1.01 1.08 1.21 1.22 1.34 1.26 1.28 1.29 1.31 1.39 1.41 1.43 1.45 1.50 1.53 1.54 1.53 1.56 1.50 1.62 1.61 1.65 1.60
1.66 1.74 1.77 1.86 2.05 2.21
1.71 1.75 1.74 1.96 2.04 2.14
*
a References 2,3,11, and 12. Reference 10. Calculated aa K = P(V,(solvent)/V,(H~O)); see text. d Fitted value from eq 7.
extraction processes. There is every reason to believe that the descriptors a,@ and P* are generally appropriate for this purpose. A number of alcohoh and other wet solvents were included in the correlations,and no statistical anomalieswere detected. This certainly does not mean that wet solventscan be treated as dry in all applications, but suggests that in this instance the errors associated with that assumption were no greater than those of the input parameters of both wet and dry solvents taken as a whole, and thus statistically insignificant. Overall, the approach used here would lend itself to custom design of extraction processes for both analytical separations and chemical engineering applications.
RECEIVED for review January 27, 1993. Accepted July 8, 1993.' ~
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Abstract published in Advance ACS Abstracts, September 1,1993.
