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Molecular surface calculations on organic compounds
Journal of Molecular Structure (Theo&em), 254 (1992 1369-377 Elsevier Science Publishers B.V., Amsterdam
369
Molecular surface calculations on organic compounds. Molecular area-aqueous solubility relationships E. Silla*, I. Tufion, F. Villar Department of Physical Chemistry, Universidad Burjassot, Vakncia (Spain)
de Vakncia, Doctor Moliner 50,46100-
J.L. Pascual-Ahuir Department of Physiulogy and Biophysics, 10029 (USA)
Mount Sinai School of Medicine, New York, NY
(Received 14September 1990)
Abstract The molecular surface area was calculated for 82 hydrocarbons, esters, ethers, alcohols and ketones including linear, branched and cyclic ones. The relationship between the aqueous solubility and the molecular surface area was determined for each family of compounds and for all the families together. The results show that solubility is mainly determined by molecular surface area and that the influence of functional group is the same for all the oxygen containing compounds studied.
INTRODUCTION
The prediction of the influence of structural modifications on solution properties is of great importance in various physical, chemical and biological studies. It is a long-standing goal of physical organic chemistry to establish general structure-property relationships based on molecular calculations. Several reports [ 1 ] have been concerned with the consideration of the molecular surface area as a predictor of those properties. The concept of using the superficial area of a solute to determine its thermochemical activity was first introduced by Langmuir [ 21. Langmuir thought that the energy required to make a cavity in the bulk of a solvent was an important factor in relation to the solubility of the solute and proportional to the molecular surface area of the solute. Later, many studies were conducted on the correlation between the area and the solubility and hydrophobicity of many molecules [ 3-51. In addition, studies were made on models and methods for % whom correspondence should be addressed.
0166-1260/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved.
explaining and calculating the interaction of one molecule with its surroundings, making use of its molecular surface area and volume [ 6,7]. Methods of calculating the cavitation energy have been proposed by Pierotti [ 81, Sinagoglu and Halicioglu [9] and Huron and Claverie [lo]. Other energy terms such as the electrostatic and dispersion energies have also been related to the molecular surface area [ 11-171. In the present study we used the MSDOT computational method to calculate the molecular surface area of hydrocarbons, alcohols, ketones, ethers and esters and used these results to establish the relationship between the area and aqueous solubility. In the present work the assumptions of fixed solute geometry and spherical shaped solvent allowed us to obtain good results. A critical evaluation of these assumptions is given. MODELS AND METHODS
Solution energy terms
In an ideal solution the only term contributing to the free energy of mixing is the entropy of mixing (i.e. dG=RZ’ln X). The next step in solution theory is to admit an excess enthalpy to the process dG=RTlnX+Q
(1)
In a continuum model the solvation process comprises a cavitation step and an interaction step. The total change in the Gibbs free energy of solvation can be evaluated [ 111 as the sum of the cavitation, electrostatic and dispersionrepulsion contributions dG = dG,, + dG,i, + Gdis
(2)
It has been shown that the energy terms in eqn. (2) are functions of the solute’s surface area [ 11-171. Alternatively, Uhlig [ 121 and Eley [ 131 have proposed that for a spherical solute the free energy is linearly dependent on its surface area AG=4m2y+c
(3)
where y is the surface tension and e the interaction energy between solute and the solvent. This proposition may be extended to solutes of different geometries by replacing 47rr2by the surface area. Bearing in mind eqns. (2 ) and (3)) and noting that the enthalpic term (a) in eqn. (1) can be thought of as being surface-area dependent, the relationship AG=RTlnX+aS+b can be proposed where the last term includes interactions
(4)
not assumed in the model. In an equilibrium situation - RTln X= aS + b, and for compounds with
371
a low solubility X=sol M/1000 where sol is the molal solubility and M the molecular weight of the solvent. Then, if the stated hypotheses are acceptable, the following relationship must be fulfilled In sol=A S+B
(5)
Computational method
To calculate molecular surface areas adequate methods and a proper definition of the molecular surface are required. These surfaces have been described using simple geometrical models such as spheres [ 181, elipsoids [ 151 and cylinders [ 191. However, of the methods proposed most use van der Waals type geometrical models [1,14,16,20-221 which include all those molecular surfaces that make use of the van der Waals radius. There are three types of such surface: (a) the proper van der Waals surface (WMS), i.e. the external surface resulting from a set of spheres centred on the atoms or group of atoms forming a molecule; (b) the surface accessible to solvent (AMS), which is defined by Lee and Richards [ 231 as the surface generated by the centre of the solvent which is considered to be a rigid sphere which rolls around the van der Waals surface; and (c ) the molecular surface defined by Richards [ 241 (MS) which comprises the contact surface and the re-entrant surface. The contact surface is that part of the van der Waals surface of each atom which is accessible to a probe sphere of a given radius. The re-entrant surface is defined as the inward-facing part of the probe sphere when this is simultaneously in contact with more than one atom. In the present study we calculated the molecular surface area using the MSDOT method. This method is a numerical algorithm for calculating Richards’ molecular surface and has been amply described elsewhere [ 20,251. Essentially, in this method a probe sphere is placed at a tangent to each atom, each pair of neighbouring atoms and each triplet of neighbouring atoms. When the probe is free from collisions the points lying on the inward-facing surface of the probe sphere are chosen to become part of the molecular surface. The algorithm produces a set of surface points, the approximate area of the surface and the unit vectors to the surface at each point. In calculating the molecular surface area we used the following geometric parameters for all-trans conformations: H-O = 0.97 A, O-C = 1.43 A, C-C = 1.54 A, C-H= 1.09 A, C=O= 1.22 A, H-C-H= 109.47”, H-O-C= 105.00”, O=C0 = 125.27” and C-O-C = 109.47”. The given radii for the spheres centred on each atom were: RH = 1.2 A, RO= 1.4 A and Rc = 1.6 A. The chosen probe radius was 1.5 A. The graining parameter (density of points over surface, DEN ) used was DEN = 25. Calculations were made on a 3200 Microvax computer at the Department of Physical Chemistry of the University of Valencia.
372 TABLE 1 The calculated molecular surface area (k) and the Napierian logarithm of the observed molal aqueous solibility of the compounds studied Compound
Area
his01
Butanol Pentanol Hexanol Heptanol 0ctan01 Nonanol Decanol Dodecanol Tetradecanol Pentadecanol Hexadecanol 2-Butanol 2-Pentanol 2-Hexanol 2-Octanol 2-Nonanol 3-Pentanol 3-Hexanol 3-Heptanol 3-Nonanol 3-Methyl-2-butanol 2,4-Dimethyl-3pentanol 2-Ethylhexanol 2,2-Diethylpentanol 2-Methylbutanol 3,5,5-Trimethylhexanol Cyclohexanol 4-Methyl-P-pentanol 7-Methyloctanol 4-Methylpentanol 2-Methylpropanol 2-Pentanone 2-Hexanone P-Heptanone 3-Methyl-2-butanone 3-Methyl-2-pentanone I-Methyl-2pentanone 3-Pentanone 3-Hexanone 4-Methyl-3-pentanone 2,4-Dimethyl-3-pentanone
114.55 134.50 153.16 172.28 190.93 210.05 230.29 266.39 304.17 321.62 338.69 111.06 130.33 149.23 187.39 207.45 127.28 146.55 165.45 203.61 124.19 155.31 178.20 189.59 125.00 181.61 135.70 142.96 203.71 145.88 108.82 121.76 140.81 160.38 118.26 131.35 137.30 124.30 144.09 138.44 149.82
-1.35 - 2.72 -4.07 -5.40 -6.91 - 8.22 - 10.68 - 12.77 - 13.80 - 14.60 0.07 -0.63 -2.00 -4.76 -6.32 -0.49 -1.83 -3.19 -6.12 - 0.40 -2.80 - 4.99 -5.57 -1.06 - 5.77 -0.96 - 1.81 -5.74 - 2.28 0.02 -0.39 - 1.80 -3.28 -0.29 -1.55 - 1.63 -0.53 -1.90 - 1.87 -2.99
0.09
Compound
Area
In Sol
I-Heptanone 5-Nonanone Methyl acetate Ethyl acetate Propyl acetate Isopropyl acetate Isobutyl acetate Methyl butyrate Ethyl butyrate Propyl butyrate Ethyl hexanoate Ethyl heptanoate Ethyl octanoate Ethyl nonanoate ethyl decanoate Diethyl ether Methyl butyl ether Methyl isobutyl ether Methyl-t-butyl ether Methyl-s-butyl ether Methylpropyl ether Methylisopropyl ether Ethylpropyl ether Ethylisopropyl ether Dipropyl ether Propylisopropyl ether Butane Pentane Hexane Heptane Octane Methylcyclohexane Cyclohexane Isobutane 2-Methylbutane 2,2,4-Trimethylpentane 2,2,5_Trimethylhexane Neopentane 2,2-Dimethylbutane 2,4-Dimethylpentane 3-Methylpentane
165.07 201.11 96.24 116.56 135.37 130.22 150.24 134.44 154.75 173.57 195.04 212.53 231.61 249.81 268.89 117.83 132.17 130.00 122.29 125.43 115.21 109.48 136.73 130.46 156.52 150.25 102.79 123.78 140.74 160.31 175.21 145.81 130.06 101.60 116.01 156.33 166.09 115.35 126.71 148.74 132.59
-3.32 - 5.93 1.19 -0.09 - 1.69 - 1.20 - 2.85 - 1.79 -2.94 -4.39 - 5.43 - 6.32 -7.80 - 8.74 -9.43 -0.15 -2.28 -2.07 -0.48 - 1.69 -0.86 -0.06 - 1.53 - 1.28 -3.03 -3.07 -6.06 -7.53 -9.11 - 10.44 - 12.06 - 8.87 - 7.32 -5.87 -7.32 - 10.26 - 11.03 - 7.20 - 8.45 -9.52 - 8.22
373 RESULTS AND DISCUSSION
The molecular surface area of 82 different hydrocarbons, esters, ethers, alcohols and ketones, including linear, branched and cyclic ones, was calculated (see Table 1) . The molal solubilities [ 26-281 used in the correlations are referred to the pure supercooled liquid at 25’ C. The linear relationships between the Napierian logarithm of the molal solubility and the molecular surface area are shown in Table 2. The data in Table 2 show that the assumptions made about molecular geometry are acceptable and we can conclude that deviations from the assumed geometry are small. Hermann [3] has used exact conformations or weighted averages, when several conformations were possible, for his hydrocarbon surface area calculations. However, Hermann’s results are no better than those obtained in the present study because the greatest source of error is in the method employed to compute the surface area and in the kind of area used to describe the molecular behaviour in solution. The influence of branching, isomerism and cyclization on solubility can also be estimated using the molecular surface area. Thus linear compounds are less soluble in water than the corresponding branched ones; the linear compounds TABLE 2 The slope (A), intercept (B ), coefficient of correlation (T) and standard deviation (SD) for all compounds studied’ Compounds
AxlO*
B
r
SD
Alcohols Ketones Esters Ethers Hydrocarbons
-
7.687 7.760 6.782 7.231 5.718
0.996 0.990 0.997 0.907 0.982
0.395 0.236 0.285 0.470 0.350
6.757 6.845 6.208 6.734 7.865
“Calculatedusinghrsol=AS+B. TABLE 3 The solubility of alcohols, ketones, esters and ethers as a function of the molecular surface area [ 11, and the solubility of all the compounds studied as a function of the molecular surface area and the number of functional groups (N) [ 2 ] Equation
AxlO*
B
c
r
SD
In sol=AS+B In sol=AS+BN+C
- 6.551 - 6.602
7.280 6.992
0.371
0.994 0.994
0.392 0.402
r, Correlation coefficient; SD, standard deviation.
l
00
0
0 0
0 0 0
t 100
I
150
I
200
t
250
I
300
#
350
400
AREA
Fig. 1. The Napierian logarithm of the observed molal solubility plotted versus the molecular surface area (A2) for hydrocarbons (0) and other compounds ( + ) .
have a lower molecularsurfacearea. We also includedin our studythree cyclic compounds (cyclohexane,methylcyclohexaneand cyclohexanol) which do not show any specialdifferencefrom the other compounds. The cyclic compounds are well describedby the generalequation without the addition of any special parameter.Thus it seems that our model (fixed geometry and molecularsurface as defined by Richards,and the computingmethod) works well. For molecules with a surface area largerthan 300 A2, a tendency to greaterdeviation in the resultswas observed.This can be explainedon the basis that it is energetically favourable for these molecules to be more folded and to present a minimalmolecularsurfacearea. As the slopes and intercepts of the different families of oxygen containing organiccorners (alcohols,ketones,estersand ethers) were similar,we tried to describe all these compounds together.The values are presentedin Table 3 in which we have included all the oxygen containing compounds in one equation. Let us emphasize that for these families (alcohols, ketones, esters and
375
9 t % -c
O-
-5 -
-lO-
-15-
.04&LC___ -20
-15
-10
-I
-5
0
5
Insol Fig. 2. The calculated molal solubility using the second equation in Table 3 plotted versus the observed molal solubility (Napierian logarithm).
ethers) the solubility is determined mainly by the molecular surface area, the influence of the functional group being nearly the same for all of them. As expected, inclusion of all the molecules (hydrocarbon and oxygen containing compounds) does not give rise to a single general equation unless a new parameter (N) is taken into account. This parameter can be thought of as the number of functional groups in the compounds (N=l for alcohols, ketones, ethers and esters and N= 0 for hydrocarbons) and can be used to describe all the compounds by only one equation, avoiding the different interaction of hydrocarbons and the other families with the solvent. Hall and Smith [5] used the entropy effects involved in the free energy change on solvation to explain the differences in solubility between alkanes and alcohols and ethers. For these authors, as the structure of the water layers around a solute differs depending on whether or not the solute contains highly charged atoms, the alkanes must have different entropy terms from the other molecules. The influence of the functional group is thus reflected by the intercept (see Fig. 1) and is the cause of the different solubilities of these two kinds of compound.
376
From the equation In sol = AS + BN+ C (Table 3) it can be concluded that the influence of molecular surface area is approximately the same for all the compounds studied here. We could extrapolate this result and assume that the surface area generally determines the solubility of different organic families in the same way. In Fig. 2 the solubility calculated with the above equation (Table 3) is plotted versus the observed solubility (Naperian logarithm). Figure 2 shows that there is a close relationship between solubility and surface area, and this dependence is the same for all the compounds studied in this work. In conclusion, the computing method used is appropriate enough to obtain good molecular surface area results and these results can be used to predict different molecular properties. Although no great difference exists between the results obtained here and those obtained using the van der Waals surface area, it must be taken into account that, as molecules become bigger the deviation from linear geometry (here assumed) is more important and thus the differences between the molecular and van der Waals surface areas are more important. Therefore in such studies it is important to use a good method of calculating the molecular surface area. ACKNOWLEDGEMENTS
This work and its presentation in XIX CICTPEL at Rome (Italy) was supported in part by Action Concertada de Investigation (N. 545.4). I.T. acknowledges a doctoral fellowship from the Miisterio de Education y Ciencia (Spain). The authors are grateful to the S.E.U.I. (Spain), project OP90-0042.
REFERENCES 1 A.Y. Meyer, Chem. Sot. Rev., 15 (1986) 449. 2 I. Langmuir, Third Coiioid Symposium Monograph, Chemical Catalog Co., New York, 1925, p. 3. 3 R.B. Hermann, J. Phys. Chem., 76 (1972) 2754. 4 G.L. Amidon, S.C. VaIvani and S.H. YaIkowsky, J. Phys. Chem., 86 (1976) 829. 5 G.G. Hall and C.M. Smith, J. Mol. Struct. (Theochem), 179 (1988) 293. 6 S. Miertus, E. Scrocco and J. Tomasi, Chem. Phys., 55 (1981) 117. 7 F. FIoris and J. Tomasi, J. Comput. Chem., 10 (1989) 616. 8 R.A. Pierotti, J. Phys. Chem., 67 (1963) 1840. 9 0. Sinagogiu and 0. Hahcioglu, Ann. New York Acad. Sci., 158 (1969) 308. 10 M.J. Huron and P. CIaverie, J. Phys. Chem., 76 (1972) 2123; 78 (1974) 1853, 78 (1974) 1862. 11 S. Miertus, V. Frecer and M. Majekova, J. Mol. Struct. (Theochem), 173 (1988) 353. 12 H.H. Uhhg, J. Phys. Chem., 41 (1937) 1215. 13 D. Eley, Trans. Faraday Sot., 35 (1939) 1421. 14 J.L. Pascuai-Ahuir, E. Siiia, J. Tomasi and R. Bonacorsi, J. Comput. Chem., 8 (1987) 778. 15 B.J. Costa CabraI,D. RinaIdi and J.L. RivaiI, C.R. Acad. Sci. (Paris), 298 (1984) 675.
311 16 17 18 19 20 21 22 23 24 25 26 27 28
M.L.J. D rummond, J. Chem. Phys., 88 (1988) 5014; 88 (1988) 5021. P. Claverie, J.P. Daudey, J. Langlet, B. Pullman, D. Piazzola and M.J. Huron, J. Phys. Chem., 82 (1978) 405. B. Linder, Adv. Chem. Phya., 12 (1967) 225. A. Horta and I. Fermindez-Pierola, Macromolecules, 14 (1981) 1519. M.L. Connolly, J. Appl. CrystalIogr., 16 (1983) 548. M.L. Connolly, Molecular Surface Program, QCPE 429,198l. H.R. Karfunkel and V. Eyraud, J. Comput. Chem., 10 (1989) 628. B. Lee and F.M. Richards, J. Mol. Biol., 55 (1971) 379. F.M. Richards, Ann. Rev. Biophys. Bioeng., 6 (1977) 151. M.L. Connolly, Science, 221 (1983) 709. G.L. Amidon, S.H. Yalkowsky and S. Leung, J. Pharm. Sci., 6 (1974) 1858. C. Hansch, J.E. Quinlan and G.L. Lawrence, J. Org. Chem., 33 (1968) 347. J.M. Sorensen and W. Arlt, in D. Behrens and R. Eckermann (Eds.), Liquid-Liquid Equilibrium, Chemistry Data Series, Vol. 5, Part 1, Dechema, Frankfurt, 1979.
369
Molecular surface calculations on organic compounds. Molecular area-aqueous solubility relationships E. Silla*, I. Tufion, F. Villar Department of Physical Chemistry, Universidad Burjassot, Vakncia (Spain)
de Vakncia, Doctor Moliner 50,46100-
J.L. Pascual-Ahuir Department of Physiulogy and Biophysics, 10029 (USA)
Mount Sinai School of Medicine, New York, NY
(Received 14September 1990)
Abstract The molecular surface area was calculated for 82 hydrocarbons, esters, ethers, alcohols and ketones including linear, branched and cyclic ones. The relationship between the aqueous solubility and the molecular surface area was determined for each family of compounds and for all the families together. The results show that solubility is mainly determined by molecular surface area and that the influence of functional group is the same for all the oxygen containing compounds studied.
INTRODUCTION
The prediction of the influence of structural modifications on solution properties is of great importance in various physical, chemical and biological studies. It is a long-standing goal of physical organic chemistry to establish general structure-property relationships based on molecular calculations. Several reports [ 1 ] have been concerned with the consideration of the molecular surface area as a predictor of those properties. The concept of using the superficial area of a solute to determine its thermochemical activity was first introduced by Langmuir [ 21. Langmuir thought that the energy required to make a cavity in the bulk of a solvent was an important factor in relation to the solubility of the solute and proportional to the molecular surface area of the solute. Later, many studies were conducted on the correlation between the area and the solubility and hydrophobicity of many molecules [ 3-51. In addition, studies were made on models and methods for % whom correspondence should be addressed.
0166-1260/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved.
explaining and calculating the interaction of one molecule with its surroundings, making use of its molecular surface area and volume [ 6,7]. Methods of calculating the cavitation energy have been proposed by Pierotti [ 81, Sinagoglu and Halicioglu [9] and Huron and Claverie [lo]. Other energy terms such as the electrostatic and dispersion energies have also been related to the molecular surface area [ 11-171. In the present study we used the MSDOT computational method to calculate the molecular surface area of hydrocarbons, alcohols, ketones, ethers and esters and used these results to establish the relationship between the area and aqueous solubility. In the present work the assumptions of fixed solute geometry and spherical shaped solvent allowed us to obtain good results. A critical evaluation of these assumptions is given. MODELS AND METHODS
Solution energy terms
In an ideal solution the only term contributing to the free energy of mixing is the entropy of mixing (i.e. dG=RZ’ln X). The next step in solution theory is to admit an excess enthalpy to the process dG=RTlnX+Q
(1)
In a continuum model the solvation process comprises a cavitation step and an interaction step. The total change in the Gibbs free energy of solvation can be evaluated [ 111 as the sum of the cavitation, electrostatic and dispersionrepulsion contributions dG = dG,, + dG,i, + Gdis
(2)
It has been shown that the energy terms in eqn. (2) are functions of the solute’s surface area [ 11-171. Alternatively, Uhlig [ 121 and Eley [ 131 have proposed that for a spherical solute the free energy is linearly dependent on its surface area AG=4m2y+c
(3)
where y is the surface tension and e the interaction energy between solute and the solvent. This proposition may be extended to solutes of different geometries by replacing 47rr2by the surface area. Bearing in mind eqns. (2 ) and (3)) and noting that the enthalpic term (a) in eqn. (1) can be thought of as being surface-area dependent, the relationship AG=RTlnX+aS+b can be proposed where the last term includes interactions
(4)
not assumed in the model. In an equilibrium situation - RTln X= aS + b, and for compounds with
371
a low solubility X=sol M/1000 where sol is the molal solubility and M the molecular weight of the solvent. Then, if the stated hypotheses are acceptable, the following relationship must be fulfilled In sol=A S+B
(5)
Computational method
To calculate molecular surface areas adequate methods and a proper definition of the molecular surface are required. These surfaces have been described using simple geometrical models such as spheres [ 181, elipsoids [ 151 and cylinders [ 191. However, of the methods proposed most use van der Waals type geometrical models [1,14,16,20-221 which include all those molecular surfaces that make use of the van der Waals radius. There are three types of such surface: (a) the proper van der Waals surface (WMS), i.e. the external surface resulting from a set of spheres centred on the atoms or group of atoms forming a molecule; (b) the surface accessible to solvent (AMS), which is defined by Lee and Richards [ 231 as the surface generated by the centre of the solvent which is considered to be a rigid sphere which rolls around the van der Waals surface; and (c ) the molecular surface defined by Richards [ 241 (MS) which comprises the contact surface and the re-entrant surface. The contact surface is that part of the van der Waals surface of each atom which is accessible to a probe sphere of a given radius. The re-entrant surface is defined as the inward-facing part of the probe sphere when this is simultaneously in contact with more than one atom. In the present study we calculated the molecular surface area using the MSDOT method. This method is a numerical algorithm for calculating Richards’ molecular surface and has been amply described elsewhere [ 20,251. Essentially, in this method a probe sphere is placed at a tangent to each atom, each pair of neighbouring atoms and each triplet of neighbouring atoms. When the probe is free from collisions the points lying on the inward-facing surface of the probe sphere are chosen to become part of the molecular surface. The algorithm produces a set of surface points, the approximate area of the surface and the unit vectors to the surface at each point. In calculating the molecular surface area we used the following geometric parameters for all-trans conformations: H-O = 0.97 A, O-C = 1.43 A, C-C = 1.54 A, C-H= 1.09 A, C=O= 1.22 A, H-C-H= 109.47”, H-O-C= 105.00”, O=C0 = 125.27” and C-O-C = 109.47”. The given radii for the spheres centred on each atom were: RH = 1.2 A, RO= 1.4 A and Rc = 1.6 A. The chosen probe radius was 1.5 A. The graining parameter (density of points over surface, DEN ) used was DEN = 25. Calculations were made on a 3200 Microvax computer at the Department of Physical Chemistry of the University of Valencia.
372 TABLE 1 The calculated molecular surface area (k) and the Napierian logarithm of the observed molal aqueous solibility of the compounds studied Compound
Area
his01
Butanol Pentanol Hexanol Heptanol 0ctan01 Nonanol Decanol Dodecanol Tetradecanol Pentadecanol Hexadecanol 2-Butanol 2-Pentanol 2-Hexanol 2-Octanol 2-Nonanol 3-Pentanol 3-Hexanol 3-Heptanol 3-Nonanol 3-Methyl-2-butanol 2,4-Dimethyl-3pentanol 2-Ethylhexanol 2,2-Diethylpentanol 2-Methylbutanol 3,5,5-Trimethylhexanol Cyclohexanol 4-Methyl-P-pentanol 7-Methyloctanol 4-Methylpentanol 2-Methylpropanol 2-Pentanone 2-Hexanone P-Heptanone 3-Methyl-2-butanone 3-Methyl-2-pentanone I-Methyl-2pentanone 3-Pentanone 3-Hexanone 4-Methyl-3-pentanone 2,4-Dimethyl-3-pentanone
114.55 134.50 153.16 172.28 190.93 210.05 230.29 266.39 304.17 321.62 338.69 111.06 130.33 149.23 187.39 207.45 127.28 146.55 165.45 203.61 124.19 155.31 178.20 189.59 125.00 181.61 135.70 142.96 203.71 145.88 108.82 121.76 140.81 160.38 118.26 131.35 137.30 124.30 144.09 138.44 149.82
-1.35 - 2.72 -4.07 -5.40 -6.91 - 8.22 - 10.68 - 12.77 - 13.80 - 14.60 0.07 -0.63 -2.00 -4.76 -6.32 -0.49 -1.83 -3.19 -6.12 - 0.40 -2.80 - 4.99 -5.57 -1.06 - 5.77 -0.96 - 1.81 -5.74 - 2.28 0.02 -0.39 - 1.80 -3.28 -0.29 -1.55 - 1.63 -0.53 -1.90 - 1.87 -2.99
0.09
Compound
Area
In Sol
I-Heptanone 5-Nonanone Methyl acetate Ethyl acetate Propyl acetate Isopropyl acetate Isobutyl acetate Methyl butyrate Ethyl butyrate Propyl butyrate Ethyl hexanoate Ethyl heptanoate Ethyl octanoate Ethyl nonanoate ethyl decanoate Diethyl ether Methyl butyl ether Methyl isobutyl ether Methyl-t-butyl ether Methyl-s-butyl ether Methylpropyl ether Methylisopropyl ether Ethylpropyl ether Ethylisopropyl ether Dipropyl ether Propylisopropyl ether Butane Pentane Hexane Heptane Octane Methylcyclohexane Cyclohexane Isobutane 2-Methylbutane 2,2,4-Trimethylpentane 2,2,5_Trimethylhexane Neopentane 2,2-Dimethylbutane 2,4-Dimethylpentane 3-Methylpentane
165.07 201.11 96.24 116.56 135.37 130.22 150.24 134.44 154.75 173.57 195.04 212.53 231.61 249.81 268.89 117.83 132.17 130.00 122.29 125.43 115.21 109.48 136.73 130.46 156.52 150.25 102.79 123.78 140.74 160.31 175.21 145.81 130.06 101.60 116.01 156.33 166.09 115.35 126.71 148.74 132.59
-3.32 - 5.93 1.19 -0.09 - 1.69 - 1.20 - 2.85 - 1.79 -2.94 -4.39 - 5.43 - 6.32 -7.80 - 8.74 -9.43 -0.15 -2.28 -2.07 -0.48 - 1.69 -0.86 -0.06 - 1.53 - 1.28 -3.03 -3.07 -6.06 -7.53 -9.11 - 10.44 - 12.06 - 8.87 - 7.32 -5.87 -7.32 - 10.26 - 11.03 - 7.20 - 8.45 -9.52 - 8.22
373 RESULTS AND DISCUSSION
The molecular surface area of 82 different hydrocarbons, esters, ethers, alcohols and ketones, including linear, branched and cyclic ones, was calculated (see Table 1) . The molal solubilities [ 26-281 used in the correlations are referred to the pure supercooled liquid at 25’ C. The linear relationships between the Napierian logarithm of the molal solubility and the molecular surface area are shown in Table 2. The data in Table 2 show that the assumptions made about molecular geometry are acceptable and we can conclude that deviations from the assumed geometry are small. Hermann [3] has used exact conformations or weighted averages, when several conformations were possible, for his hydrocarbon surface area calculations. However, Hermann’s results are no better than those obtained in the present study because the greatest source of error is in the method employed to compute the surface area and in the kind of area used to describe the molecular behaviour in solution. The influence of branching, isomerism and cyclization on solubility can also be estimated using the molecular surface area. Thus linear compounds are less soluble in water than the corresponding branched ones; the linear compounds TABLE 2 The slope (A), intercept (B ), coefficient of correlation (T) and standard deviation (SD) for all compounds studied’ Compounds
AxlO*
B
r
SD
Alcohols Ketones Esters Ethers Hydrocarbons
-
7.687 7.760 6.782 7.231 5.718
0.996 0.990 0.997 0.907 0.982
0.395 0.236 0.285 0.470 0.350
6.757 6.845 6.208 6.734 7.865
“Calculatedusinghrsol=AS+B. TABLE 3 The solubility of alcohols, ketones, esters and ethers as a function of the molecular surface area [ 11, and the solubility of all the compounds studied as a function of the molecular surface area and the number of functional groups (N) [ 2 ] Equation
AxlO*
B
c
r
SD
In sol=AS+B In sol=AS+BN+C
- 6.551 - 6.602
7.280 6.992
0.371
0.994 0.994
0.392 0.402
r, Correlation coefficient; SD, standard deviation.
l
00
0
0 0
0 0 0
t 100
I
150
I
200
t
250
I
300
#
350
400
AREA
Fig. 1. The Napierian logarithm of the observed molal solubility plotted versus the molecular surface area (A2) for hydrocarbons (0) and other compounds ( + ) .
have a lower molecularsurfacearea. We also includedin our studythree cyclic compounds (cyclohexane,methylcyclohexaneand cyclohexanol) which do not show any specialdifferencefrom the other compounds. The cyclic compounds are well describedby the generalequation without the addition of any special parameter.Thus it seems that our model (fixed geometry and molecularsurface as defined by Richards,and the computingmethod) works well. For molecules with a surface area largerthan 300 A2, a tendency to greaterdeviation in the resultswas observed.This can be explainedon the basis that it is energetically favourable for these molecules to be more folded and to present a minimalmolecularsurfacearea. As the slopes and intercepts of the different families of oxygen containing organiccorners (alcohols,ketones,estersand ethers) were similar,we tried to describe all these compounds together.The values are presentedin Table 3 in which we have included all the oxygen containing compounds in one equation. Let us emphasize that for these families (alcohols, ketones, esters and
375
9 t % -c
O-
-5 -
-lO-
-15-
.04&LC___ -20
-15
-10
-I
-5
0
5
Insol Fig. 2. The calculated molal solubility using the second equation in Table 3 plotted versus the observed molal solubility (Napierian logarithm).
ethers) the solubility is determined mainly by the molecular surface area, the influence of the functional group being nearly the same for all of them. As expected, inclusion of all the molecules (hydrocarbon and oxygen containing compounds) does not give rise to a single general equation unless a new parameter (N) is taken into account. This parameter can be thought of as the number of functional groups in the compounds (N=l for alcohols, ketones, ethers and esters and N= 0 for hydrocarbons) and can be used to describe all the compounds by only one equation, avoiding the different interaction of hydrocarbons and the other families with the solvent. Hall and Smith [5] used the entropy effects involved in the free energy change on solvation to explain the differences in solubility between alkanes and alcohols and ethers. For these authors, as the structure of the water layers around a solute differs depending on whether or not the solute contains highly charged atoms, the alkanes must have different entropy terms from the other molecules. The influence of the functional group is thus reflected by the intercept (see Fig. 1) and is the cause of the different solubilities of these two kinds of compound.
376
From the equation In sol = AS + BN+ C (Table 3) it can be concluded that the influence of molecular surface area is approximately the same for all the compounds studied here. We could extrapolate this result and assume that the surface area generally determines the solubility of different organic families in the same way. In Fig. 2 the solubility calculated with the above equation (Table 3) is plotted versus the observed solubility (Naperian logarithm). Figure 2 shows that there is a close relationship between solubility and surface area, and this dependence is the same for all the compounds studied in this work. In conclusion, the computing method used is appropriate enough to obtain good molecular surface area results and these results can be used to predict different molecular properties. Although no great difference exists between the results obtained here and those obtained using the van der Waals surface area, it must be taken into account that, as molecules become bigger the deviation from linear geometry (here assumed) is more important and thus the differences between the molecular and van der Waals surface areas are more important. Therefore in such studies it is important to use a good method of calculating the molecular surface area. ACKNOWLEDGEMENTS
This work and its presentation in XIX CICTPEL at Rome (Italy) was supported in part by Action Concertada de Investigation (N. 545.4). I.T. acknowledges a doctoral fellowship from the Miisterio de Education y Ciencia (Spain). The authors are grateful to the S.E.U.I. (Spain), project OP90-0042.
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