Solubility of Nonelectrolytes in Polar Solvents
2239
Solubility of Nonelectrolytes in Polar Solvents. V. Estimation of the Solubility of Aliphatic Monofunctional Compounds in Water Using a Molecular Surface Area Approach G. L. Amldon,+l S. H. Yalkowsky, S. T. Anlk, and S. C. Valvanl Center for Health Sciences, School of Pharmacy, University of Wisconsin, Madlson, Wisconsin 63706 and The Upjohn Company, Kalamazoo, Michigan 4900 1 (Received April 11, 1975) Publication costs assisted by The Upjohn Company
The molecular surface areas for 158 aliphatic hydrocarbons, olefins, alcohols, ethers, ketones, aldehydes, esters, and fatty acids have been computed and correlated with their aqueous solubilities. The hydrocarbon and functional group contributions to the free energy of solution are compared and discussed with particular regard to the chosen standard state. The results indicate that the functional group contributions to the free energy of solution in water are nearly equivalent from the pure liquid standard state while being significantly different when the gas phase (1 mmHg) standard state is chosen. The interpretation of the differing hydrocarbon surface area slopes is shown to be complicated by mutual miscibility considerations (water solubility in the pure liquid) and by the presence of curvature for the longer chain length (greater than (210) compounds. The curvature in the alcohol and fatty acid data is shown to become very evident when correction is made to the pure (supercooled) liquid standard state for the solid compounds. Finally the surface area method is shown to hold considerable promise in its extension to the solubility estimation of complex organic molecules with limited aqueous solubilities.
Introduction Recently, increasing attention has been directed to the use of a cavity or interfacial tension model and corresponding molecular surface areas for the calculation of the transfer (solvent) free energy contributions to ~ o l u b i l i t y , par~-~ titi0ning,~?5complexation,5-9 and solution conformational equilibria6J0 processes. Historically, Langmuirll was the first to suggest the use of the molecular surface area in the estimation of solution free energies and it has subsequently been employed or discussed by numerous investigators in a variety of c o n t e x t ~ . ~In - l ~this report we extend the surface area method of estimating aqueous solubilities, previously shown to be successful in estimating the solubilities of alcoh o l ~and ~ hydrocarbon^.^,^ The following additional aliphatic (cyclic and acyclic) monofunctional compounds are considered: ethers, ketones, aldehydes, carboxylic acids, esters, and olefins. The objective of this investigation is to assess the following: (i) the degree to which molecular surface area is a useful parameter in the estimation of aqueous solubilities; (ii) is the hydrocarbon contribution the same for all functional groups; (iii) the relative functional group contributions to the solubility process; (iv) the evidence for curvature in the log (solubility) vs. surface area (or chain length) graphs above (210; and (v) how the choice of standard state, i.e., pure (supercooled) liquid, effects the interpretation of the results. Method The surface area approach to solubility is suggested by considering the following three steps in the transfer of a solute from pure liquid to aqueous solution to be proportional to the molecular surface area:3 (i) removal of solute from its pure liquid; (ii) creation of a cavity in water; and (iii) placement of solute into the cavity. Adding on the entropy of mixing (cratic contribution) gives the following result: AG = 0-TSA + RT In x where TSA is total molecular surface area. At equilibrium -RT In X, = 0-TSA where X, is
the mole fraction solubility of the pure liquid in watera3For monofunctional aliphatic compounds the total surface area (TSA) can be further divided into hydrocarbon (HYSA) and functional group (FGSA) contributions TSA=HYSA FGSA Assuming that the hydrocarbon and functional group portions contribute independently suggests the following generalized equation for use in solubility correlations log S = B,.HYSA B,.FGSA -I- h',.IFG @a (1) where S is the aqueous solubility in molal concentration units, 00 the intercept, HYSA and FGSA are the hydrocarbon and functional groups surface areas, respectively, and IFG is the functional group index, being zero for hydrocarbons and one for a monofunctional compound. Molecular surface areas were calculated by the method reported by Hermann* including a solvent radius of 1.5 A. The pure liquid form of the solute is chosen as the standard state with the appropriate correction (to the supercooled liquid) being made for the few solids in the s t ~ d y . The ~J~ parameters in eq 1 were determined by regression analysis using the experimental solubilities and the computed molecular surface area. The data set for each group of monofunctional compounds included the solubilities of 17 hydrocarbon~~' to allow determination of the IFG coefficient for that functional group. Solubilities were taken from ref 17-25 and multiple determinations were included.26
+
+
+
Results The results of the regression analysis using eq 1 are presented in Table I. The overall statistics are excellent with an average standard error of 0.167 and an average correlation coefficient of 0.991. Two features of Table I are particularly interesting. The first is the very similar values of the IFG term for all functional groups except olefins and the second is the negative value of the FGSA term. The simiThe Journal of Physical Chemistry, Voi. 79, No. 21, 1975
Amidon et al.
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TABLE I: Results of Regression Analysis on the Solubility of Monofunctional Aliphatic Compoundsa Compd
4
63
$2
60
Y
S
n
Hydrocarbons -0 .O 195(0 .OO 1) 2.21 0.977 0.165 18 Alcohols -0.184(0.003) 3.37(0.10) -0.023 (0 .OO 2) 1.84 0.993 0.180 91 Ethers -0.0201(0.0006) 3.46(0.09) -0.060(0.008) 2.38 0.997 0.130 45 Ketones / -0.0186(0.0005) 3.61( 0.11) -0.034(0.003) 1.93 0.996 0.158 53 aldehydes Esters -0.0166(0.0004) 3.66(0.14) -0.030( 0.003) 1.30 0.992 0.190 76 Carboxylic -0.0175(0.004) 3.66(0.51) -0.024(0.007) 1.59 0.995 0.193 34 acids Olefins -0.0200( 0.0007) 0.4 7( 0.19) -0 -018( 0.006) 2,35 0.987 0.155 30 a The model is log (sol) = 6’1-HYSA + 6’2-IFG + &.FGSA + BO (the values in parentheses are standard errors),The significance level of the overall regression equation in each case was greater than 99.99%. larity of the HYSA and FGSA coefficients suggest the use of the simpler equation log (S) =BI’*TSA
+ B,’.IFG + Bo‘
(2)
The results using this model are presented in Table 11. The average standard error and correlation coefficient are only slightly poorer for this more restricted model and the IFG terms are again very similar except for the olefins. The results in Table I1 suggest that, excluding the olefins, an equation including only TSA and a constant may give a reasonable correlation. The result is
+
log (sol) = -0.016STSA 4.44 (3) (0.002) with (r = 0.988, s = 0.216, n = 227). This is a surprisingly good correlation considering its simplicity and the variety of compounds covered. Hydrocarbons Surface Area Coefficients. The coefficients for the HYSA term in eq 1 can be compared either on an energyhnit area or a energy/CH2 group b a s k 3 For the hydrocarbons these values are 18.5erg/cm2 and 846 cal/ CH2 group (using 31.8 Az as the area/CH2 group), respectively. The value of 18.5 erg/cm2 may be compared with the value of about 50 erg/cm2 for a bulk hydrocarbon-water int e r f a ~ e Part . ~ ~ of this difference is due to the definition of surface area, having included a solvent radius ( R = 1.5 A) in this study. The incremental increase in surface area per -CH2- group with solvent radius 1.5 A is 31.8 A2 while that with solvent radius zero is 22.7 A2. Allowing for this difference the slope becomes 26 erg/cm2. The factor of two that remains is well within the range of what is expected for a curvature correction, undoubtedly important at a molecular i n t e r f a ~ e .For ~ ~ the ~ ~ seven , ~ ~ groups of compounds included in this study the general trend is for the more polar compounds to show smaller (in absolute value) slopes and intercepts (Table I and 11). This suggests a smaller methylene group hydrophobic effect for the polar compounds. This may be due to the differing effect of a methylene unit on solute-solvent interactions in the aqueous phase or solute-solute, solute-solvent interactions in the “solute” phase (vide infra). IFG Coefficient. The IFG coefficient can be interpreted as the logarithmic solubility increase of the (mono) substituted compound over that of its hydrocarbon homomorph.30 For example, 1-butanol is 1.9 X lo3 times more soluble than n-pentane, while 103.37= 2.34 X lo3 is the average solubility increase for all alcohols studied. Excluding the olefins, the IFG coefficients are not significantly different, though the esters and carboxylic acids have the largest The Journal of Physical Chemistry, Vol. 79,No. 2 I, 1975
numerical values. The average IFG coefficient is 3.55 (excluding olefins) and corresponds to a -4.84 kcal/mol contribution of the functional group to the free energy of transfer (compared to its hydrocarbon homomorph). The olefinic group contributes -641 cal/mol to the free energy of transfer. The fact that the IFG coefficients are not significantly different suggests that a considerable amount of compensation must be occurring. That is, while some of the groups can interact more strongly with water than others, they also interact with themselves more strongly, with the net difference being nearly the same for all functional groups (except olefins) considered (vide infra). F G S A Coefficient. The FGSA coefficient indicates the effect of the surface area variation of the functional group (through structural isomerization) on solubility. This, for example, is one of the terms which distinguishes between primary, secondary, and tertiary alcohol^.^ In all cases it is negative indicating that reducing the functional group surface area increases the solubility of the compound. Aside from possible electronic effects which are presumed to be small3 three factors determine the magnitude of this term: (1) the surface area dependence of the ability of the functional group to interact with water, (2) the cavity size in water, and (3) the surface area dependence of the ability of the functional group to interact with itself in the pure liquid phase. While factor 1would be expected to give a positive contribution to the FGSA coefficient factors 2 and 3 would make negative contributions, and on the basis of these results must be larger in magnitude than factor 1. If factor 3 was important it should be observable in some of the properties of the pure liquids. This has been shown to be true in the case of the alcohols where a reduction in the hydroxyl group surface area decreases its boiling point (increases vapor pressure) leading to an increase in ~olubility.~ This seems to be generally true for the compounds included in this study. Thus the increase in solubility due to branching is due in part to the effect of branching on the properties of the pure liquid (vide infra). Intercept. Three factors influence the value of the intercept of eq 1. (i) the solubility units employed (molal in this study), (ii) the definition of surface area31 (includes a 1.5-A solvent radius in this study, and (iii) the solubility of water in the “solute” phase (vide infra). The consideration? leading to eq 1 suggest that on a mole fraction and a natural log scale basis the intercept should be zero. Converting this to log and a molality concentration scale gives an expected intercept of 1.74. The solvent radius effect, as noted by Reynolds et a1.: results from the fact that with a solvent radius, a solute
Solubility of Nonelectrolytes in Polar Solvents
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TABLE 11: Results of Regression Analysis Using the Model log (sol) = 81.TSA
4
Compd
02
+ O2.IFG + Boa 00
Y
S
Hydrocarbons -0 .O 195( 0 .OO 1) 2.21 0.977 0.165 Alcohols -0.0185(0.0003) 3 .16( 0 .O 5) 1.90 0.992 0.184 Ethers -0.0184(0.0007) 3 .OO(O .05) 1.87 0.995 0.168 Ketones/aldehydes -0 .O 17 7( 0 .OO 06) 3.06(0.06) 1.64 0.993 0.196 Esters -0 .0152(0 .0004) 3.00(0.06) 0.882 0.989 0.219 Carboxylic acids -0.0173( 0.0004) 3.16(0.07) 1.52 0.995 0.193 Olefins -0.0200(0.0008) 0.52 O( 0.06) 2.35 0.987 0.153 a Values in parentheses are standard errors. The significance level of the overall regression equation in every case was greater than 99.99%. with zero radius (“no particle”) would have a nonzero surface area dependant on the solvent radius used in the computations. Using a solvent radius of 1.5 8, results in a surface area of 28.3 A2 for this particle of zero radius. This, however, is not the appropriate area to use for the intercept considerations in this study. The reason for this is evident from Figure 1, which is a graph of surface area with zero solvent radius vs. surface area with a 1.5-8, solvent radius for normal hydrocarbons methane through decane as well as some arbitrary point particles of radius 0.5, 1.0, and 1.5 8, (the surface area of methane is equivalent to that of a point particle radius of 1.98 A). The graph is nonlinear, however, since all compounds in this study are larger than methane the nonlinearity can be neglected. Hence the solvent radius effect on the intercept should be taken from the extrapolated intercept of the linear segment. For the normal hydrocarbon^^^ the equation of the line is
+
TSA (1.5) = 1.41TSA(O) 91.8 where TSA(a) is the total surface with solvent radius a. The slope of 1.41 is just the ratio of methylene unit increments to the TSA with and without a solvent radius (31.8/ 22.6). The solubility model is log (sol) = B,*TSA(1.5) Bo Assuming that a molecular surface area with zero solvent radius is a more “natural” choice33and using the results in Table I for hydrocarbons we obtain log ( ~ 0 1 = ) -0.0195.TSA(L5) 221 = -0.0275.TSA(O) 0.42 Thus the observed intercept is smaller than the expected intercept of 1.74 on a molal scale. The intercept on this basis for the monofunctional compounds would be appropriately smaller. This result for the intercept indicates that, for example, from the results for hydrocarbons, a “h drocarbon” molecule with a surface area of about 105 (including solvent radius) would have a 1 m solubility (methane has a surface area of 152 A2). This result is quite consistent with, for example, graphs of log (sol) vs. chain lengths, which extrapolate to a 1 m solubility for n E 0.5. This indicates that, solvent radius considerations aside, the extrapolation from large (four carbons and above) surface area molecules to smaller molecules (e.g., inert gases) is not pla~sible.~,~~
+
+ +
I2
Discussion The conventional standard state chosen in solubility studies, the pure (supercooled) liquid, while convenient in many respects,16 complicates the interpretation of the structural effects on the solution process in three ways. The first is that the effect of the structural change on the properties of the pure liquid must be considered, the second is
Figure 1. Relationship between surface area with zero solvent radius and that with a 1.5-A solvent radius for the C1-Cl0 hydrocarbons and several point particles of radii 0, 0.5, 1.0, and 1.5 A.
the solubility of water in the pure solute and the consequent lowering of the solute activity, and the third is that if in the course of studying a homologous series, at some point the compounds become solids at the temperature of interest a correction must be made to the pure supercooled liquid using thermal dataa3J5 Vapor Phase Standard State. Hildebrand35 has suggested that the use of a vapor phase standard state, e.g., solubility at 1 mmHg, would facilitate the analysis of solutesolvent interactions since solute-solute interactions can generally be neglected. This standard state is the usual one for gases. The solubility of a liquid based on the pure liquid standard state can be converted to the gas-phase standard state by assuming that Henry’s law holds for the solute and dividing the solubility by the vapor pressure of the pure liqid.^^ Since the solubilities in this study are less than about 1A4 (
