Znd. Eng. Chem. Res. 1995,34,373-381
373
Correlation and Prediction of Partition Coefficients of Organic Solutes between Water and an Organic Solvent with a Generalized Form of the Linear Solvation Energy Relationship Petra Meyer and Gerd Maurer* Lehrstuhl fur Technische Thermodynamik, Universitat Kaiserslautern, 0-67653Kaiserslautern, Germany
The linear solvation energy relationship (LSER) is extended to estimate partition coefficients of organic solutes in infinite dilution between water and organic solvents at 298 K. The LSER needs five parameters to characterize a solute as well as six parameters to characterize the organic solvenuwater system. To extend the applicability of the LSER, estimation rules for all parameters are desirable. In the first part of the present work rules either given in the literature or developed here are applied to determine the parameters of 101 organic substances. Predicted partition coefficients show that the estimation is reliable. Furthermore a generalized LSER equation-here called LSER36-was developed, which allows estimating infinite dilution partition coefficients of organic solutes in organic solvenuwater systems at 298 K, when no individual LSER equations are known. That generalized LSER contains 36 universal constants and for each organic solvent those 5 parameters which are used to characterize the same substance as solute. Partition coefficients predicted by LSER36 agree better with experimentell data than results from other methods like UNIFAC or Marcus’ recently published generalization of the LSER equation.
Introduction
fraction to describe concentration results in
The linear solvation energy relationship (LSER) developed by Kamlet, Taft et al. (Kamlet et al., 1983, 1988; Taft et al., 1985) is a method to correlate many different physicochemical properties like the position of maximal absorption in W/vis, IR, or NMR spectra, the solubility of organic solutes in water, and the partition coefficient of organic solutes between water and an organic solvent at infinite dilution (Meyer, 1992; Meyer and Maurer, 1993). The partition Coefficient of a solute i between two solvents A and B has t o be known for many applications, for example in searching a solvent to extract certain solutes from a multicomponent aqueous solution. The partition coefficient Ci,A si,AIB =-
p z. = p z,pure .
+ RT In xiyi
(4)
Thus the infinite dilution partition coefficient in mole fraction scale is
where y; stands for the activity coefficient of solute i in solvent j normalized according t o Raoult’s law. To convert ST& to STm, the molar density of the pure solvents A and B is required:
(1)
Ci,B
depends on temperature and composition. For preselecting a solvent for liquid-liquid extraction it is often sufficient to consider the partition coefficient at 298 K at infinite dilution Srm,298K. Applying the condition of phase equilibrium between two liquid phases results in
(2) where p; is the chemical potential of component i in the reference state, where at a concentration of 1 m o m the component i experiences the same interactions as at infinite dilution in solventj : p; = pij(T,p , ci
-
0 in j (interactions), ci 1 (concentration)) (3)
-
In the linear solvation energy relationship it is assumed that the difference in the chemical potentials of a solute at high dilution in an organic solvent and water, e.g., pyas - prw,can be estimated by summing up several contributions. Each contribution is due to a certain physical effect and is approximated by a product of two factors: one factor characterizes a specific solute property while the other stands for the influence of that property on the difference in the standard state chemical potentials in water and the organic solvent. The different additive contributionsreflect different physical effects which are responsible for concentration differences of a solute i in two coexisting liquid phases, one being an organic and the other an aqueous phase. When free volume effects, polarity and polarizability, and the ability to act as electron donors and acceptors in hydrogen bonds are the most important effects, the resulting expression for the partition coefficient is
Using the pure substance as reference state and mole *Author to whom correspondence should be addressed. Q888-5885/95l2634-Q373$09.QQ/Q 0 1995 American Chemical Society
374 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
KO,M ,S , D, B , and A are the so-called LSER constants, which depend on the organic solvent/water system. ui, ni, di, pi, and ai are solute specific properties. ui characterizes the volume of the solute and may be the liquid molar volume or the intrinsic (van der Waals) molar volume. Leahy (1986) showed that using the intrinsic volume instead of the liquid molar volume avoids correcting the volume of cyclic (alicyclic and aromatic) solutes with an empirical factor. Kamlet et al. (1988) also used the intrinsic volume (in milliliters per mole), but divided its number by 100, so that it has roughly the same order of magnitude as the other variables. xi, pi, and ai are called solvatochromic parameters, because they can be determined by spectroscopic measurements (Kamlet et al., 1977, 1981; Kamlet and Taft, 1976; Taft and Kamlet, 1976). 7t is a polarity parameter, is a basicity parameter (hydrogen bond acceptance), and a is an acidity parameter (hydrogen bond donation). 6 is a polarizability parameter which was preset by Kamlet et al. (1988) (0.0 for nonpolychlorinated aliphatic solutes, 0.5 for polychlorinated aliphatic solutes, and 1.0 for aromatic solutes). Therefore in the LSER equation each term is a product of one parameter characterizing the pure organic solute and another parameter which characterizes the liquid-liquid two phase system, e.g., the organic solvent/water system. Only the first term does not depend on the solute. It may be interpreted as a van der Waals interaction term representing differences between water and the organic solvent alone. Kamlet et al. (1988) applied the LSER t o the correlation of the octanollwater partition coefficients at 298 K, STW',,,,,,,, for many organic solutes. They reported parameters ui, ni,6i,pi, and ai for 263 organic solutes together with experimental results for the partition coefficient of these solutes between water and octanol and fitted the solvent-dependent LSER constants. The resulting equation
log S'yodw= 0.32
+ 5.35~i- 1.04ni + 0.376, - 3.84pi
+ 0.10% (8)
correlates the octanoVwater partition coefficient reliably. That procedure was extended recently (Meyer, 1992; Meyer and Maurer, 1993)to other organic solvent/water systems. The correlation could be improved further by fitting the polarizability parameter of organic solutes to experimentally determined partition coefficients. For about 100 solutes new numbers for the polarizability are now available (Meyer and Maurer, 1993). To extend the LSER method to more solutes as well as to more organic solvedwater systems, correlations for solute parameters (e.g., ui,ni,di, pi, and ai)as well as for LSER constants (e.g., KO,M , S, D , B , and A) are required. In this paper we report about investigations on correlating the parameters of the pure substances, on results of predicting partition coefficients with correlated solute parameters, and on the correlation and prediction of partition coefficients of organic solutes between water and an organic solvent with a generalized form of the LSER equation. Correlation of Property Parameters
Kamlet et al. (1988) reported solute parameters for 263 organic compounds and divided the organic
Table 1. Parameter Estimation Rules for Inserting a CHz Group in an Aliphatic Compound or Inserting a CHz Group in an Aliphatic Side Chain of an Aromatic Compound insertion of a CH2 group Av AZ AB ha Aliphatic Compounds without H-Donor Site +0.03 fO fO alkanes $0.096 tertiary amines $0.091 -0.05 $0.03 10 acetic acid esters $0.098 -0.02 10 10 ketones +0.097 -0.02 fO fO ethers f0.097 10 fO fO Aliphatic Compounds with H-Donor Site alkohols $0.098 f0 10 carboxylic acids +0.098 -0.02 10 primaryisecondary $0.099 fO fO amines
+O +O
10
Aromatic Compounds without H-Donor Site +0.097 -0.02 fO
fO
Aromatic Compounds with H-Donor Site +0.098 -0.02 fO
fO
compounds into substance classes. Although in more recent publications new estimation rules were proposed (see Hickey and Passino-Reader, 19911, we considered it still to be worthwhile to follow the ideas by Kamlet et al. For each class they gave parameter estimation rules. Those rules were applied and extended. Kamlet et al. recommend two methods for estimating solute parameters. The first method is an extrapolation of experimentally determined parameters in a homologous series. Such estimation rules are summarized in Table 1. In the second method substitution rules are applied. For example there are rules for the change of a certain parameter when in an organic solute molecule a H-atom is substituted by another atom or a functional group. Those rules are summarized in Table 2. An example for the second method is given in considering doubly substituted aromatic nitro compounds. For the determination of the solute parameters of nitrophenol the parameters of phenol and nitrobenzene are needed. The volume parameter of nitrophenol is derived from the volume parameter of phenol by applying the rule for substituting in an aromatic ring (e.g., in phenol) a hydrogen atom by a NO2 group (e.g., 0.14; cf. Table 2): u =u 0.14. No distinction is made concerning the position of -OH and -NO2 in the aromatic ring. To estimate the polarity parameter of nitrophenol, one has to start from the polarity parameters of phenol and nitrobenzene: n = 0.69 and 7t = 1.01. Following the rules given in Table 2, the largest of those two numbers has to be taken and a substitution rule has to be applied. Substituting a hydrogen atom by an -OH group results in an increase of 0.1 (when the substitution is in orthoposition) or of 0.05 (when the substitution is in metaposition), whereas there is no change for a substitution in para-position. Thus the estimation procedure takes into account that a substitution in ortho-position causes the highest increase and a substitution in para-position the lowest increase of the polarity: 7Eo.fitrophenol = 1.11, nm-nitrophenol = 1.06, and np-nitrophenol = 1.01. The basicity parameter p is approximated by the maximum number of the basicity parameters of the monosubstituted compounds; for example the basicity parameter for nitrophenol is the same as that for phenol (htrophenol 0.33). For estimating the acidity parameter a solutes were
+
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 375 Table 2. Parameter Estimation Rules for the Parameter 0for Substitution of a H-Atom in Aromatic Compounds Which Has Already at Least One Substituent Substitution of H at Aromatic Compounds (Already with One Substituent at Minimum) ~~
by
note
CH3 c1 Br F
U U U U U K
NOz CH3 C1, Br, F, OH, or NO2 CH3
ortho-position meta-position para-position 1-3 groupb 4-6 groupb
C1, Br F
NOz CH3 C1, Br
F F
NOz NOz
X
no H-donor H-donor no H-donor H-donor: ortho-position meta-position para-position no H-donor H-donor: ortho-position with intramol H-bond ortho-position without intramol H-bond meta- and para-position
JP na JP
B B B B P
A
X 0.098 0.090 0.133 0.029 0.140 -0.04 fO.10
f0.05
0
0 N ,O ,..*
H
0
0
\“
bo’o\
0H,
0
0 \”
0
I
H ortho meta para Figure 1. o-, m-,and p-nitrophenol with intramolecular H-bond of o-nitrophenol.
*O -0.01 -0.02 -0.04 -0.02 *O
a a
*O *O
a a
f0.24
a a
a
fO.10 f0.08 f0.06
a
*O
a
*O
a
f0.60
a
0.30
*O
The given amount is to be added to the number of K of the higher polar compound of the two monosubstituted compounds. For substitution of 1-3 group respectively 4-6 group of the six potential substitution sites at one benzene ring. The higher number of B of the two monosubstituted compounds is taken over. a
assigned to two groups, one representing substances whose molecules possess a hydrogen bond donor site (a t 0) and the other representing substances without such a site (a= 0). The acidity parameter of substances of the second group is not changed by substituting a hydrogen atom by a NO2 group, whereas such a substitution in a molecule of the first group increases the ability to act as an hydrogen donor in a hydrogen bond. Substituting a hydrogen atom by a NO2 group in a molecule possessing a H-donor site therefore increases the acidity parameter by the empirically found differences 0.60 or 0.30 (when the NO2 group is in orthoposition or in meta- and para-position respectively to the H-donor atom). Those rules do not hold for substances like o-nitroaniline and o-nitrophenol. These compounds are able to build intramolecular hydrogen bonds, and therefore they show no ability for intermolecular hydrogen bonding (cf. Figure 11,resulting in a = 0. On the other side benzoic acid is a hydrogen bond donor (a= 0.59), but substituting a NO2 group in ortho-position does not lead to an intramolecular hydrogen bond. Therefore o-nitrobenzoic acid has the largest acidity parameter among all nitrobenzoic acids (cf. Table 3). Table 3 give parameters as estimated applying the rules given in Tables 1 and 2 for 101 solutes. To test the reliability of the estimation procedure, these parameters were used together with individual LSER equations for 30 organic solvent/water systems as published recently (Meyer and Maurer, 1993) t o predict partition coefficients. The predictions were
compared to experimental results taken from the data collection of Hansch and Leo (1979). A special comparison is quantified in Table 4. The comparison is restricted to nitroaniline, nitrophenol, and methylnitrophenol. For the ortho-isomers of these substances 27 predicted partition coefficients are compared to experimental data, taking intramolecular hydrogen bonding into account on one side and neglecting that effect on the other side. Considering intramolecular hydrogen bonds improves the prediction considerably. For 82 partition coefficients the average absolute deviation in log sT0&,298K is reduced from 0.72 to 0.35, while the number of cases where a wrong preference of a solute for a phase is predicted, is reduced from 13 to 4. A quantitative review over all predictions is summarized in Table 5 . Estimated solute properties were used to calculate 332 partition coefficients for 63 substances in 29 different organic solvenffwater systems. The average absolute deviation in log sT0dw,298K between predicted and measured partition coefficients is 0.33. The corresponding number for those 947 data points for 263 solutes and 30 organic solvenffwater systems which were used to develop the individual LSER equations is 0.12. For seven (e.g., 2%) partition coefficients applying estimated solute parameters yields a wrong preference for a solute in a phase. The corresponding number for the data base used to develop the LSER equations is 13, e.g., about 1.4%. That comparison demonstrates that combining estimated solute parameters with individual LSER equations developed recently (cf. Meyer and Maurer, 1993) yields in most cases reliable results for the partition coefficient. Figure 2 shows a comparison between predicted and measured partition coefficients for the benzenelwater system. As the partition coefficient s ~ 0 d w , 2 9 8 Kranges from about 0.001 to about 1000, a logarithmic scale was chosen. Two different data sets are shown: partition coemcients calculated with estimated solute properties on the one side and those calculated using “experimentally determined” solute parameters on the other side (Meyer and Maurer, 1993). As was to be expected, the “truly”predicted partition coefficients deviate more from the experimental results than those used for developing the LSER relation.
Generalization of LSER To expand the applicability of the LSER to more organic solvent/water systems than those 30 systems for which individual LSER equations are known, a generalization of the LSER would be useful. The aim of generalizing the LSER is t o estimate the partition coefficient of an organic solute between water and an
376 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 Table S. Organic Compounds with Estimated Property Parameters no. compound formula 1 methane 2 ethane 3 propane 4 butane 5 nonane 6 tributylamine 7 acetic acid pentyl ester 8 2-octanone 9 1-heptanol 10 1-octanol 11 1-nonanol 12 1-decanol 13 1-undecanol 14 1-tridecanol 15 n-heptanoic acid 16 n-octanoic acid 17 n-nonanoic acid 18 n-undecanoic acid 19 n-dodecanoic acid 20 n-tridecanoic acid 21 n-tetradecanoic acid 22 n-pentadecanoic acid 23 n-hexadecanoic acid 24 n-heptadecanoic acid 25 n-octadecanoic acid 26 n-nonadecanoic acid 27 butoxybenzene 28 phenylpentanoic acid 29 phenylbutanol 30 phenylpentanol 31 phenylhexanol 32 pentachlorobiphenyl hexachlorobiphenyl 33 34 methylamine 35 n-heptylamine 36 n-octylamine 37 n-nonylamine 38 dimethylamine 39 dipentylamine 40 decane 41 undecane 42 dodecane 43 tridecane 44 tetradecane 45 pentadecane 46 hexadecane 47 acetic acid hexyl ester 48 acetic acid heptyl ester 49 acetic acid octyl ester 50 2-nonanone 51 2-decanone 52 2-nitrophenol 3-nitrophenol 53 54 4-nitrophenol 55 2-methylphenol 56 2-fluorophenol 57 3-fluorophenol 4-fluorophenol 58 3-trifluoromethylnitrobenzene 59 2-chlorobenzaldehyde 60 3-chlorobenzaldehyde 61 4-chlorobenzaldehyde 62 63 2-chloroacetophenone 2-fluoroacetophenone 64 3-fluoroacetophenone 65 66 2-bromoacetophenone 67 3-bromoacetophenone 68 2,3-dimethylphenol 2-fluoronitrobenzene 69 70 3-fluoronitrobenzene 4-fluoronitrobenzene 71 72 2,3-difluoronitrobenzene 3,4-difluoronitrobenzene 73 74 2,3,4-trifluoronitrobenzene 3,4,5-trifluoronitrobenzene 75 76 2-methylnitrobenzene 2-ethylphenyl 77
U
n
0.167 0.263 0.360 0.456 0.938 1.259 0.814 0.864 0.790 0.888 0.985 1.082 1.180 1.375 0.813 0.911 1.010 1.206 1.304 1.402 1.500 1.598 1.696 1.794 1.892 1.990 0.921 1.042 0.928 1.026 1.124 1.370 1.460 0.237 0.830 0.929 1.028 0.341 1.117 1.034 1.131 1.227 1.324 1.420 1.516 1.613 0.912 1.010 1.108 0.960 1.057 0.676 0.676 0.676 0.634 0.565 0.565 0.565 0.816 0.696 0.696 0.696 0.780 0.719 0.719 0.823 0.823 0.732 0.660 0.660 0.660 0.689 0.689 0.718 0.718 0.732 0.732
-0.19 -0.16 -0.13 -0.11 0.04 0.13 0.49 0.59 0.40 0.40 0.40 0.40 0.40 0.40 0.50 0.48 0.46 0.42 0.40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0.65 1.13 0.93 0.91 0.89 0.45 0.50 0.32 0.31 0.31 0.31 0.25 0.25 0.07 0.10 0.13 0.16 0.18 0.21 0.24 0.47 0.45 0.43 0.57 0.55 1.11 1.06 1.01 0.68 0.82 0.77 0.72 1.12 1.02 0.97 0.92 1.00 1.00 0.95
6 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.08 0.18 0.28 0.37 0.47 0.67 -0.06 -0.04 -0.02 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 1.00 1.00 1.00 1.00 1.00 2.00 2.00 0.32 0.37 0.38 0.39 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 1.03 1.03 1.03 1.00 1.00 1.oo 1.00 1.oo 1.00 1.00 1.oo
1.00 1.00 1.00
1.00
1.00
0.95 0.64 1.11 1.06 1.01 1.16 1.06 1.16 1.21 1.01 0.66
1.00 0.64 1.00 1.00 1.00 1.00 1.00 1.oo 1.00
1.03 1.00
B
a
0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.72 0.45 0.48 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.30 0.55 0.55 0.55 0.55 0.06 0.03 0.70 0.69 0.69 0.69 0.70 0.70 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.45 0.45 0.45 0.48 0.48 0.33 0.33 0.33 0.34 0.28 0.28 0.28 0.25 0.40 0.40 0.40 0.45 0.47 0.47 0.45 0.45 0.35 0.28 0.28 0.28 0.26 0.26 0.24 0.24 0.30 0.34
0.00 0.00 0.00 0.33 0.33 0.33 0.33 0.33 0.33 0.55 0.55 0.55
0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
0.00 0.55
0.33 0.33 0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.91 0.91 0.58 0.71 0.69 0.67 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00
0.55 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.58
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 377 Table 3 (Continued) no. compound 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
formula
2-propylphenol 2-isopropylphenol 2-tert-butylphenol 4-tert-butylphenol 2-chlorobenzoic acid 2-fluorobenzoic acid 3-fluorobenzoic acid 4-fluorobenzoic acid 2-bromobenzoic acid n-decylamine dibutyl ether 2,4-dimethylphenol 2,5-dimethylphenol 2,6-dimethylphenol 3,4-dimethylphenol 3,5-dimethylphenol 2-methyl-4-pentanone dipentyl ether 2-nitroaniline 3-nitroaniline 4-nitroaniline 2-nitrobenzoic acid 3-nitrobenzoic acid 4-nitrobenzoic acid
Table 4. Comparison between Predicted and ExperimentallyDetermined Numbers of log S~d,,,2g,K for Nitroaniline, Nitrophenol, and Methylnitrophenol without consideration of with consideration of intramolecular H-bonds intramolecular H-bonds ortho metdpara all ortho metdpara all 27 55 82 55 82 nexp 27 0.35 0.35 0.35 0.35 0.72 dabs 1.48 nrs 9 4 13 0 4 4 Table 5. Comparison between the Correlation of Partition Coefficients with the Individual LSER Equations and the Prediction of Partition Coefficients with the Individual LSER Equations for Solutes with Estimated F'roDerty Parameters correlation prediction nexp 947 332 dabs 0.12 0.33 nrs 13 7
organic solvent from measured or estimated parameters of the solvent as well as the solute. The idea of that generalization is that the six LSER constants of the individual LSER equations (KO, M, 5,D,B, and A in eq 7) depend on the properties of the organic solvent used. Intentionally no distinction is made between parameters when the component is either a solvent or a solute. It has been proven in recent publications by several groups (see, for example, Leahy et al., 1992a,b) that such an distinction has some advantages and gives a better picture of the microscopic behavior. Nevertheless for the sake of the often demanded simplicity in engineering work, we did not follow that line. Furthermore, while several groups are currently working on improvements of the linear solvation energy relationship and/or developing new experimental techniques to determine the solvent and solute parameters (see, for example, Abraham et al., 1991; Abraham and Walsh, 1992; Abraham and Taft, 1993; Abraham, 1993; Carr, 1993; Eltayar et al., 1991,1992; Fan et al., 1990; Li et al., 1991;Raevsky et al., 1989, 1992; Test and Klier, 1991), the new methods are not yet regarded as being in a state for engineering applications. Therefore the LSER constants were developed with the properties of the solvent corresponding to the description of a single LSER equation. Thus the following equation for the partition
U
n
6
B
C.
0.830 0.830 0.928 0.928 0.740 0.679 0.679 0.679 0.783 1.127 0.892 0.732 0.732 0.732 0.732 0.732 0.864 1.084 0.702 0.702 0.702 0.790 0.790 0.790
0.64 0.64 0.62 0.62 0.84 0.84 0.79 0.74 0.89 0.12 0.27 0.64 0.64 0.64 0.64 0.64 0.59 0.27 1.11 1.06 1.01 1.11 1.06 1.01
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.00 0.00 0.64 0.64 0.64 0.64 0.64 0.00 0.00 1.25 1.25 1.25 1.03 1.03 1.03
0.34 0.34 0.34 0.34 0.36 0.38 0.38 0.38 0.36 0.68 0.47 0.35 0.35 0.35 0.35 0.35 0.48 0.47 0.50 0.50 0.50 0.40 0.40 0.40
0.58 0.58 0.58 0.58 0.83 0.83 0.63 0.63 0.83 0.00 0.00 0.55 0.55 0.55 0.55 0.55 0.00 0.00 0.00 0.56 0.56 1.19 0.89 0.89
4,
/
benzene/water
T y , ,, -4.0
-3.0
-2.0
-1.0
I
,
0.0
1.0
2.0
3.0
.O
Figure 2. Partition coefficients in the system benzendwater at compared 298 K calculated (e.g., predicted ( 0 )or correlated (0)) to experimental data.
coefficient of a solute i between water (w) and an organic solvent (os) at high dilution is derived:
Kk,Mk,Sk,Dk,Bk, and Ak are the "universal LSER constants'' of the generalized LSER equation. To characterize an organic substance, the property parameters already used for an organic solute (index i) are also used for an organic solvent (index os), e.g., volume parameter u , polarity parameter n, polarizability parameter 6, basicity parameter p, and acidity parameter a. That method is here called LSER36. The 36 universal constants were fitted to 826 experimental partition coefficients of organic solutes at infinite dilution in 20 organic solvent'water systems a t 298 K.
378 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 Table 6. Universal Constants of the GeneralizedLSER (LSER36)from Fitting to 826 Partition Coefficients of Organic Solutes between Organic Solvents and Water
k
Kk
Mk
sk
Dk
Bk
1 2 3
0.180 0.594 1.652 -0.752 -1.019 -0.979
5.049 0.731 0.090 0.282 -1.563 0.365
-0.624 -2.037 -1.116 0.531 2.356 1.761
0.464 0.509 1.202 -0.307 -0.935 -1.605
-2.983 -2.255 -1.570 0.625 1.196 4.015
4
5 6
Ah -3.494 0.418 0.134 0.146 7.125 -0.562
Table 7. Comparison of Correlated Infinite Dilution Partition Coefficients S;-,~,,,,, of Organic Solutes i in 20 Organic SolventWater gystems at 298 K Using the Generalized LSER (LSER36) and the Individual LSER (LSER-ind) LSER36 LSER-ind organic solvent benzene toluene xylene chlorobenzene bromobenzene ethylbenzene nitrobenzene n-hexane n-heptane n-octane cyclohexane isobutanol n-pentanol l-octanol tetrachloromethane chloroform dichloroethane diethyl ether ethyl acetate butyl acetate total
nexp 50 36 34 20 15 16 14 43 39 22 56 16 14 263 46 50 22 37 15 18 826
dabs
0.16 0.14 0.16 0.11 0.11 0.20 0.35 0.18 0.21 0.12 0.24 0.23 0.13 0.13 0.19 0.15 0.17 0.16 0.18 0.17 0.16
nrs 2 1 0 1 0
1 1 1 1 0 4 0 1 1 2 0 3 0 0 0
19
dabs
nrs
0.14 0.09 0.14 0.05 0.10 0.08 0.07 0.14 0.19 0.07 0.20 0.07 0.09 0.13 0.17 0.12 0.07 0.15 0.09 0.11 0.13
2 0 0 0 0 0 0 1 1 0 3 0 1 1 1 0 2 0 0 0 12
All data were taken from the collection of Hansch and Leo (1979) and, for the partitioning of ethanol between alkanes and water, of Roddy and Coleman (1981) and are the same as those already applied to fit the LSER constants of the individual LSER equations for these 20 systems (Meyer and Maurer, 1993). Extending that method by including the extensive but scattered literature which has become available more recently is the object of future work. Table 6 gives the universal constants. In Table 7 the correlation is compared to the underlying experimental data. Furthermore Table 7 gives a comparison with the individual LSER equations of each system. For each system the number of experimental partition coefficients neq, the average absolute deviation d a b s (individual LSER and LSER36), and the number of cases nrs, where the calculated number of log Sros/w,298K has the wrong sign, are given. In the last case the model gives a wrong preference of a solute for one of the two phases, e.g., water or the organic solvent. The average absolute deviation over all available = 0.16 for the generalized experimental data is LSER equation and 0.13 for the individual equations. On the average, partition coefficients calculated by both methods deviate by less than 10%. With respect to the number of parameters needed in both methods (120 individual constants versus 36 universal constants), the loss of accuracy is surprisingly small. As LSER36 is a universal equation, it is now possible to estimate partition coefficients of organic solutes between water and an organic solvent for organic
Table 8. Comparisonbetween Predicted and Experimentally Determined Partition Coefficients for Four Different Cases Using LSER36 case 1 2 3 4 property params of estd known estd known organic solvent known estd estd organic solute known 55 99 308 nexp 69 14 24 10 !bYS 12 0.29 0.32 0.16 dabs 0.16 9 0 nrs 5 5
solventJwater systems for which no individual LSER equations are known. To test the reliability of the method, partition coefficients predicted with LSER36 were compared with experimental data. All predictions were made with the universal constants given in Table 6 and the substance-specific property parameters (for the organic solvents and the solutes) either given by Kamlet et al. (1988) with polarizability parameters corrected by Meyer and Maurer (1993) or estimated (cf. Table 3). Table 8 summarizes the results of that comparison. Four different categories are distinguished with regard to the source of the parameters for the solutes on the one side and for the organic solvent on the other side, which were either estimated (cf. Table 3) or known (all parameters given by Kamlet et al. (19881, except polarizability parameters which are given by Meyer and Maurer (1993)). In Table 8 the number of available experimental partition coefficients,neV, the number of solventlwater systems, nsys, the average absolute deviation, z a b s , in log Syodw,298K, and the number of cases in which a wrong preference for a phase is predicted, nm,are given. More detailed results are given as Tables XII-XV in the supplementary material. (See paragraph at end of paper regarding the availability of supplementary material.) The best prediction is observed when all parametersfor the organic solvent as well as for the solute-are known from direct experimental investigations (case 1). With an average absolute deviation d a b s = 0.16 the prediction is as reliable as the correlation of the 826 data points on which LSER36 is based (cf. Table 7). When one parameter set (either for the organic solvent or the solute) had to be estimated (cases 2 and 31, the average absolute deviation in log Syos,w,298K increased to about 0.3. On the other side, there is nearly no change when both parameter sets had to be estimated. This, at first glance, surprising result is due to the fact that nearly all experimental data follow homologous series of substances well represented in the data set of 826 partition coefficients used to determine the universal constants of the LSER36 method. Comparison with Other Models
The results of the predictions by the LSER36 method can only be rated correctly by comparison with predictions from other methods. From several methods available, the UNIFAC group contribution method and Marcus’s recently published generalization of the LSER method are used here for comparison. Comparisons with some new developments, for example, space predictor or factor analysis method (Hait et al., 1993; Poe et al., 1993) are not possible as those methods have not yet been applied t o aqueous systems. Two versions of UNIFAC are applied: the original UNIFAC model (Fredenslund et al., 1975) with interaction parameters recommended for the presentation of liquid-liquid
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 379 Table 9. Comparison between log Sr& 298K Predicted by LSER30 (Property Parameters of the Solute are Known) and UNIFAC UNIFAC-LLE
LSER36
UNIFAC-Y"
I
9
cy
dodecane/water 0 = UNIFAC-LLE
LSER36
ncalc FsYs dabs nrs
102 21 1.06 15
16
42
21 0.31 9
0.99 10
8
0
0 = LSER36
~~
0
Table 10. Comparison between log S;odw298K Predicted by LSER36 (Property Parameters of the bolute are Estimated) and UNIFAC UNIFAC-LLE LSER36 UNIFAC-ym LSER36 240 30 30 ? ncaic 240 22 30 22 30 FsYs 0.26 0.51 0.14 dabs 1.48 7 0 0 nrs 24
phase equilibria (Magnussen et al., 1981)-here called UNIFAC-LLE-and the modification by Kikic et al. (1980) with interaction parameters as published by Bastos et al. (1988) as recommended for predicting activity coefficients a t infinite dilution-here called UNIFAC-y". With both UNIFAC methods the partition coefficients S$w,289K were determined and converted to Scodw,298K eq 6* At first a comparison is discussed for such combinations of substances where the property parameters of the organic solute are known (cases 1and 2 of Table 8). As for both UNIFAC methods only a limited number of groups is available, and also for some of those groups no interaction parameters are known, the comparison had to be restricted to 102 and 42 (UNIFAC-LLE and UNIFAC-y", respectively) data points in 21 and 8 organic water systems. As shown in Table 9, both UNIFAC versions yield much larger deviations (factor of 5-7 in log Sy0dw,29,K) than LSER36. The number of cases where a wrong preference for a phase is predicted is also considerably larger. As a typical example, Figure 3 shows the comparison between predicted and experimentally determined partition coefficients for UNIFAC-LLE (circles) and LSER36 (squares) for the system dodecane/water. The differences in the average absolute deviation in log Syo4,,298, (UNIFAC-LLE,a a b s = 1.23; LSER36, a a b s = 0.26) are obvious. When the comparison is extended to cases 3 and 4 of Table 8, i.e., cases where the properties of the organic solutes had to be estimated in an application of LSER36, similar results are obtained. For the same reasons as mentioned before, the comparisons had to be restricted t o 240 or 30 partition coefficients (UNIFAC-LLE or UNIFAC-y", respectively) in 30 or 22 systems (out of 363 data points in 34 systems). Table 10 gives some details of the comparison. Again the average absolute deviation resulting from the UNIFAC methods is considerably larger (by a factor of between about 3.6 and 5.7) than that resulting from the LSER36 method. To demonstrate the differences,predictions from UNIFACLLE and LSER36 for the system cyclohexane/water are compared to experimental data in Figure 4. Marcus (1991) modified the LSER and extended its application to 25 organic solventdwater systems. He introduced the cohesive energy density &p2 (square of Hildebrand's solubility parameter) and used it together with a volume parameter Vi (intrinsic volume divided by 100) to take into account all interactions resulting from size effects, van der Waals forces, polarity, and
0
0
42 8 0.17 0
/:
/ o f I
1
!
-4.0
-2.0
-3.0
-1.0
2.0
1.0
0.0
log Sf.xdPodrconr/*otrr Figure 3. Comparison of predicted and experimentally determined partition coefficients for the system dodecanelwater at 298 K.
4
/
cyclohexane/water
0 .
9
c) I
-3.0
I
-2.0
0
,
I
0.0
-1.0
I
1
1.0
2.0
I
I
3.0
4.0
.O
log Szclohrxonr/watrr Figure 4. Comparison of predicted and experimentally determined partition coefficients in the system cyclohexandwater at 298 K.
polarizability and used the solvatochromic parameters
p and a only to account for hydrogen bonding:
(11) @os
=Po, - P w
Aaos
= aos - %
(13)
Marcus reported constants Kv, Ka and Kp for 25 solvent/ water systems and developed a generalization which is based on the assumption that Kv, Ka, and Kp should not depend on the organic solvent. In the generalization procedure Marcus averaged the constants Kv, Kp, and Ka (weighted by the number of solutes of each solvent/water system) resulting in
log s ~ 0 d w , 2 9= 8 ~2 . 1 4 V i A 6 ~ -~7.67qAPOs ~ 4.62PiAaOs(14) With this equation the partition coefficient of solute i between water and an organic solvent os can be estimated from solute parameters Vi, ,!?, and a when the solvent parameters &p2,Bo*,and G~are known. Marcus applied his method to 21 systems with 547 partition
380 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
Nomenclature
R 0
k
= Marcus
L
tt oo b
:E:
