Ind. Eng. Chem. Res. 1996,34, 2530-2535
2530
CORRELATIONS Boiling Point and Melting Point Prediction for Aliphatic, Non-Hydrogen-BondingCompounds Joseph F. Krzyzaniak, Paul B. Myrdal; Pahala Simamora, and Samuel H. Yakowsky* Department of Pharmaceutical Sciences, College of Pharmacy, University of Arizona, Tucson, Arizona 85721
Simple group contribution methods which incorporate nonadditive, nonconstitutive properties are proposed to predict normal boiling points and melting points for aliphatic, non-hydrogenbonding compounds. Boiling points and melting points are estimated from the ratio of the enthalpy of transition and the entropy of transition. The enthalpy of transition is assumed to be equal to the summation of group values. The entropy of boiling is estimated using a modification of Trouton’s rule, while the entropy of melting is estimated using a modification of Walden’s rule. The root mean square errors for the estimation of boiling points and melting points are 14.4 K and 34.3 K, respectively.
Introduction The boiling point and melting point are two of the most important fundamental physical properties of organic compounds. Transition temperatures are used for chemical identification as well as for the calculation of vapor pressure, aqueous solubility, and other physicochemical properties. Handbooks and research manuals contain either the boiling point or melting point but not both for most organic compounds. In the absence of experimental data, these properties must be estimated. There are a number of methods for estimating the boiling point or melting point from chemical structure (Abramowitz and Yalkowsky, 1990;Austin, 1930; Balaban et al., 1992;Beacall, 1928;Dearden and Rahman, 1988;Devotta and Pendyala, 1992;Holler, 1947; Stanton et al., 1992). There are few useful techniques that can be used to estimate both the boiling point and the melting point with a great deal of accuracy. Joback and Reid (1987) proposed a group contribution method to predict boiling points and melting points as well as many other physical properties. Recently, Simamora and Yalkowsky (1994)proposed an improved group contribution method which accounts for neighboring group effects for rigid aromatic compounds. They determined that boiling points can be accurately estimated from group contributions, which are additive constitutive properties, while melting point estimation requires the use of the nonadditive, nonconstitutive property, rotational symmetry, in addition t o additive constitutive properties. This study concentrates on the ongoing development of a complete group contribution method for estimating the boiling point and the melting point from chemical structure. The approach of Simamora and Yalkowsky is extended to predict these properties for aliphatic, nonhydrogen bond donating compounds. The boiling point is estimated from the ratio of the enthalpy of boiling and the entropy of boiling, and the melting point is
* Author t o whom correspondence should be addressed.
R e s e n t address: 3M Pharmaceuticals, 3M Center, Building 270-45-17, St. Paul, MN 55144-1000.
estimated from the ratio of the enthalpy of melting and the entropy of melting. The enthalpies of transition, which are considered additive and constitutive, are estimated from group contributions. The entropy of boiling and the entropy of melting must be estimated using nonadditive parameters.
Theoretical Background At the phase transition temperature, Tt,the free energy of transition is equal to zero. Thus, the phase transition temperature is related to the enthalpy of transition, AHt,, and entropy of transition, Utr,by
Enthalpy of Transition. The enthalpy of transition of a non-hydrogen-bonding molecule is assumed to be dependent upon the interactions between the molecular fragments and is equal to the summation of its constituent group values. The magnitude of this energy for any molecular fragment is related to its van der Waals forces and the change in the distance between the fragment and the fragments of its neighboring molecules that accompanies the phase transition. Group values are defined as the contribution of the constituent group to the enthalpy of transition for a compound. The enthalpy of boiling, A H b , and the enthalpy of melting, AHm, can be calculated by
A&) = &bi AHm = &mi
(3)
where ni is the number of times that group i appears in the compound, and bi and mi are the contributions of group i to the enthalpy of boiling and melting, respectively. Entropy of Boiling. The entropy of transition is a measure of the change in translational, rotational, and conformational freedom of a compound that accompanies a phase transition. The contribution of rotational and conformational freedom to the entropy of boiling is
0888-588519512634-2530~Q9.0010 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2531 small since compounds have a large degree of rotational and conformational freedom in both the liquid and the gas. On the other hand, the translational freedom increases greatly as a compound goes from a liquid to a gas. For this reason, the entropy of boiling is largely due to the change in translational freedom. For many organic molecules, the entropy of boiling, A&,, at the standard (1 atm) boiling point follows Trouton's rule, i.e., = 88 J/(degmol)
(4)
The success of Trouton's rule is due to the fact that the changes in the free volume of most liquids upon boiling are similar. In other words, the free volume is proportional to the translational freedom. Mishra and Yalkowsky (1990) found that a modification of Trouton's rule is necessary to accurately estimate the entropy of boiling for long-chain hydrocarbons. They found that the entropy of boiling can be determined by
&$ ! = 83.7
+ 0.67(n - 5 ) J/(degmol)
Ai$ = 86 + 0.4(2)+ 1421(HBN) J/(degmol) (6) where z is the effective number of torsional angles in a molecule and HBN, the hydrogen bond number, is an empirical parameter that assesses the effect of hydrogen bonding on the entropy of boiling. Since non-hydrogenbonding molecules are used in this study, eq 6 becomes b
= 86
+ 0.4(z)J/(degmol)
(7)
The effective number of torsional angles as described by Dannenfelser and Yalkowsky (1995) is a measure of the flexibility in a molecule and is empirically determined by t = (SP3
+ (0.5)SP2 + (0.5)RING) - 1
,!IS" = 56.5 - 19.2 log (T
+ 19.2 log q5 J/(degmol) (9)
where (T is the rotational symmetry number and 4 is the molecular flexibility number (note that 19.2 = 2.303 x R). The molecular flexibility number, 4, is the number of stable conformations that are possible for a molecule, and is calculated by
(5)
where n is the number of carbons in the aliphatic chain. This modification adjusts for the fact that the conformational freedom of flexible compounds is less in the liquid than in the gas. Recently, Myrdal et al. (1995) estimated the entropy of boiling for 851 functionally diverse compounds using a two-parameter model. They determined the entropy of boiling by
a
conformational freedom. The change in rotational freedom of a molecule is related to its rotational symmetry (Dannenfelser et al., 1994), while the change in conformational freedom of a molecule is related to the molecular flexibility. The rotational symmetry number, (T, is defined as the number of ways that a molecule can rotate to produce indistinguishable images. For example, trichloromethane receives a rotational symmetry number of 3. Recently, Dannenfelser and Yalkowsky (1995) showed that the molecular flexibility number and rotational symmetry number must be used to estimate the entropy of melting. Therefore, entropy of melting can be estimated by a modification of Walden's rule, i.e.,
(8)
where SP3 is the number of non-ring, nonterminal sp3 atoms (including NH, N, 0, and SI,SP2 is the number of non-ring nonterminal sp2 atoms, and RING is the number of monocyclic or fused ring systems in a molecule. Terminal groups are not included in z since those groups can be rotated without producing a conformationally different structure. Terminal groups include halogens, cyano and acetylene groups, carbonyl oxygens, hydrogens, and groups such as methyl, amino, and hydroxyl which contain hydrogen atoms that are assumed to be freely rotating. Since the stable conformations of a tert-butyl or a trihalomethyl group are identical, these groups are treated as terminal groups. Note that when eq 8 is negative, z is set equal to zero. Entropy of Melting. When a compound melts, there is a small expansion which allows the molecule to rotate more freely and to twist into more conformations than in a crystal. This expansion allows for only a small increase in translational freedom. For this reason, the entropy of melting is primarily due to rotational and
q5 = 3(r')
(10)
where z is the same as above. The entropy of melting can be written in terms of the rotational symmetry number and the effective number of torsional angles by simplifying eq 9, i.e.,
AS, = 56.5 - 19.2 log 0
+ 9.2(z) J/(degmol)
(11)
Since the phase transition temperature can be determined by the ratio of the enthalpy of transition and entropy of transition, the boiling point, Tb, can be estimated by substituting eqs 2 and 7 into eq 1,i.e., Tb
= Mi,/ub= &ibi/(86
+ 0.4(~))
(12)
Similarly, the melting point, Tm,can be estimated by substituting eqs 3 and 11 into equation 1,i.e.,
T, = Mm/AS,= &mi/(56.5
- 19.2 log 0
+ 9.2(t)) (13)
Methodology Aliphatic, non-hydrogen-bonding organic molecules were studied in this paper. This includes compounds consisting of halogen, ester, ketone, ether, aldehyde, cyano, sulfide, disulfide, nitro, thiocyanate, isothiocyanate, and aliphatic carbon groups. All available compounds, ranging in molecular weights from 26 to 557 daltons, were selected from common handbooks and research manuals. Transition temperatures which were experimentally determined at reduced pressures were not used in this study. Additionally, compounds that decomposed before their transition temperatures were not used. Molecular Descriptors. The molecular descriptors used in this study consist of molecular fragments along with their neighboring group designations and correction factors. The fragmentation scheme is representative of the functional groups contained in the data set and is similar to the scheme developed by Myrdal et al. (1993). Correction factors are developed to take into account steric and electronic effects which are not considered in simple group contribution methods. The molecular fragments used in this study are given in the first column of Table 1. Each fragment is
2532 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Table 1. Group Values for the Enthalpy of Transition (J/mol)
molecular fragments -CHx -CH& > CH>C< =CH2 -CH= >C=
=C= &H -C=
-F -c1 -Br -I -0-CH=O -C(=O)-COO-
-S-
-ss-NO2 -C=N -N=C=S -S-C=N
b, values
10183 2389 -5958 -14374 9977 2318 -6416 2128 9540 2762 9014 12352 14839 17628 2120 15416 6611 6748 6655 11001 17302 15080 19422b 22412b
m, values" X V 1449 1953 1806 2347 (-600) (387) -1155 (129) 1456 2448 2448 1603 1603 1355b 2892 1938 1938 1777 2227 2488 4478 3512 5285 6789 4950b (2921Ib 3527 707Bb 7968 5332b 7352 7254 4507 8271 6827 10547b 963gb
5067b
Values in parentheses determined to be statistically insignificant ( a > 0.05). bBased on fewer than 10 occurrences.
Table 2. Correction Factors for the Enthalpy of Transition (J/mol) correction fractors
bi values
GEM VIC RING3 RING4 RING5 RING6+ CHbridge Cbridge
-1094 -135 5792 3803 3189 2565 7706
mi valuesa -1106 -230 (67) (-22) -817 -689 2125 6432
a Values in parentheses determined to be statistically insignificant ( a > 0.05).
identified according to the hybrid state of the atoms to which it is bonded. Two types of "neighboring" groups are considered, X and V, which are used as prefmes for sp3 atoms and either sp2 or sp atoms, respectively. For example, the methyl groups in ethane are designated as XCH3 while the those of propene and propyne are both designated as VCH3. Similarly, the CH2 group in 1-butyne is designated as VCH2. Correction factors consist of geminal, vicinal, ring, and fused ring parameters as shown in the first column of Table 2. The geminal parameter, GEM, is defined as the number of painvise interactions among terminal electron-withdrawing groups on a single carbon atom, while the vicinal parameter, VIC, is the number of painvise interactions among terminal electron-withdrawing groups on adjacent atoms. The terminal electron-withdrawing groups used in this study consist of halogens, cyano, nitro, thiocyanate, and isothiocyanate groups. For example, perchloroethane will have six geminal interactions and nine vicinal interactions. The RING3, RING4, RING5, and RINGG+ parameters designate the number of atoms in a three, four, five, and greater than five member ring, respectively. In fused ring systems, bridgehead carbons are designated by either CHbridge or Cbridge. The ring parameters correct for the fact that an atom in a ring will interact
differently than an atom in a chain. A total of 31 molecular descriptors are used for estimating the boiling point and 43 molecular descriptors are used for estimating the melting point. Statistical Analysis. The database was created on an IBM-compatible personal computer utilizing dbase IV software. The statistical analysis was performed on the University of Arizona's VAX, Model 4000-300, utilizing the Statistical Analysis System software (1985). The correlation coefficient and standard deviation are used to measure the accuracy of the correlation for the molecular descriptors. The root mean square error, RMSE, is used to determine the degree of accuracy of the models used in predicting the normal boiling points and the melting points. Cross-Validation. In order to evaluate the strength of the proposed method, a 10-fold cross-validation experiment was performed for both boiling point and melting point estimations. Ten test sets were randomly selected with each compound included in only one test set. Each test set consisted of 10% of the original compounds. The remaining 90% of the compounds for each test set were used as the training set.
Results The group values for the enthalpy of boiling, bi, and the enthalpy of melting, mi, are given in Tables 1 and 2. The summation of these values is used to calculate the total enthalpy for each compound. Group parameters and correction factors that have a confidence level, a, greater than 0.05 are enclosed in parentheses and are considered statistically insignificant. The boiling points for the compounds used in this study were successfully correlated using eq 12, i.e.,
n = 870
RMSE = 14.4
r2 = 0.999
The melting points for the compounds used in this study were successfully correlated using eq 13, i.e.,
n = 596
RMSE = 34.3
r2 = 0.977
The observed and predicted boiling points and melting points are summarized in Figures 1and 2, respectively. They are also supplied in supporting information along with the rotational symmetry number and the effective number of torsional angles for each compound. Examples for estimating the boiling point and melting point using this method are given in the Appendix. The data in Figure 1 show a slight curvature which indicates a systematic error. Recent work by Myrdal et al. (1995) indicates that the entropy of boiling is not a linear function of flexibility. This nonlinearity was also observed by Screttas and Mecha-Screttas (1991). Since eqs 7 and 11 do not take this curvature into account, they are not appropriate for predicting the boiling points and melting points for long chain compounds. For this reason, this study is limited to compounds with a flexibility of no greater than that of tridecane, i.e., z = 10. The remaining compounds were used in developing eqs 12 and 13 for estimating boiling points and melting points, respectively. No outliers were eliminated from this study.
Ind. Eng. Chem. Res., Vol. 34,No. 7,1995 2533 700
-./-/
600
E
Cb.400
m
-8 300
ux)
/
100
0
0
100
ux)
300
400
500
600
700
O b d B P (K)
/
--
.. 0 0
100
200
300
400
O b d M p
500
600
700
6)
Figure 2. Predicted melting points versus observed melting points for 596 aliphatic, non-hydrogen-bonding organic compounds. Table 3. Regression Analysis for the Proposed Method boiling point melting point elementalcomposition C, H C, H,F, C1, Br, I C, H,0 C,H,N,O,S,F,Cl,Br,I
n 486 206 95 83
RMSE 11.4 16.9 14.0 21.6
n 241 242 71 42
RMSE 31.2 37.3 25.2 28.2
total data set
870
14.4
596
34.3
a
set
n 783 783 783 783 783 783 783 783 783 783
RMSE 14.4 14.7 14.1 15.0 14.7 14.4 14.8 14.6 14.4 14.8
test set
n 87 87 87 87 87 87 87 87 87 87
RMSE 17.4 14.8 20.0 10.8 15.9 18.1 13.3 15.7 17.6 13.1
Discussion
Figure 1. Predicted boiling points versus observed boiling points for 870 aliphatic, non-hydrogen-bonding organic compounds.
500
~~
training set
1 2 3 4 5 6 7 8 9 10
500
j
Table 4. Cross-ValidationResults Using the Proposed Method for Estimating Boiling Points
Each compound was only used in one set.
Table 3 gives a summary of how eqs 12 and 13 perform on different classes of compounds. "he n corresponds to the number of compounds used in each class. It is clear that for each class of compounds the RMSE for boiling is less than that for melting. Additionally, the RMSE for the various classes are comparable t o the overall data set as well as to one another for both boiling point and melting point methods.
The group values for the enthalpy of boiling, bi, for each molecular fragment were found to be relatively independent of neighboring group effects. Since the X and V group parameters are not statistically different, they were combined into a single group parameter. Unlike the enthalpy of boiling, the group values for the enthalpy of melting, Xmi and Vmi,were found t o be different from one another. It is also observed that most mi values are lower than the corresponding bi values. This is consistent with the findings of Simamora and Yalkowsky (1994)and can be explained by the fact that the van der Waals interactions are inversely related to a high power of the intermolecular distance. It follows that the bi values would be larger than the mi values since the intermolecular distance changes only slightly upon melting while increasing tremendously upon boiling. In general, the molecular fragments with larger dipole moments tend to have a greater contribution to the enthalpy of transition. For example, the Xmi value is approximately 68% higher than the Vmi value for each of the halogens. This seems t o be attributed to the greater electronegativity of the unsaturated carbon; e.g., chloroethane and chloroethene have dipole moments of 2.05 and 1.44,respectively. When comparing the halogens in series for both bi and mi values, there is another interesting trend. Even though the halogens have about the same dipole moment, there is an increase in the heat of transition in going from fluorine t o iodine. This can be explained by the greater polarizability of the larger atoms. The greater polarizability of an atom the easier a dipole can be induced. This in turn increases the enthalpy of transition. In Table 2, the group values for the geminal and vicinal correction factors indicate that the heat of transition decreases for each painvise interaction. Also, the geminal group has a greater effect than the vicinal group. This is attributed to the fact that when a carbon atom contains multiple electron-withdrawing groups, the net group dipole moment is reduced which decreases intermolecular attractions and the heat of transition. When electron-withdrawing groups are vicinal, the repulsion can be minimized by rotating to a more stable conformation. Although correction factors such as GEM and VIC increase the predictive ability of this method, a group contribution approaoh is currently not able to distinguish between geometric isomers. Cross-Validation. In the cross-validation, the resulting group values for each training set were used t o estimate the transition temperature of the corresponding test set. Tables 4 and 5 give the number of compounds and the root mean square errors for both
2534 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Table 5. Cross-ValidationResults Using the Proposed Method for Estimating Melting Point test set
training set set
1
2 3 4 5 6 7 8 9 10
n
RMSE
n
537 536 537 536 536 536 536 536 537 537
34.1 34.0 34.1 34.7 34.4 34.7 34.1 34.1 33.2 35.1
59 60 59 60 60 60 60 60 59 59
RMSE 37.3 38.6 37.7 32.3 35.1 32.3 39.9 42.4 44.8 27.4
the training and test sets in all 10 trials for boiling point and melting point, respectively. In Table 4, the average RMSE for the 10 training sets is 14.6 f 0.26 while the average RMSE for the 10 ten test sets is 15.7 f 2.75. These numbers are comparable to the overall root mean square error of 14.4 for the entire boiling point data set. In Table 5, the average RMSE for the 10 training sets is 34.3 & 0.52 while the average RMSE for the 10 test sets is 36.8 f 5.17. These numbers are also comparable to the overall root mean square error of 34.3 for the entire melting point data set. The cross-validation indicates that there is a small increase in the standard deviation in the test sets when compared to the training sets. This fact is not surprising due to the fact that no outliers were eliminated from either the boiling point or melting point data set. The favorable results from the cross-validation test strongly support the predictive ability of this method. Comparison of Methods. A comparison of the proposed group contribution method for estimating boiling points and melting points with the method of Joback and Reid (1987) was performed. The observed and calculated transition temperatures along with the corresponding error is given for both the proposed method and the method by Joback and Reid in the supporting information. The two boiling point methods were compared using the 87 compounds described in set 8 of the cross-validationexperiment. For estimating the melting point methods, the 59 compounds defined in set 3 of the cross-validation experiment were used. These sets were chosen because their root mean square errors were similar t o the average root mean square errors of the test sets used in the cross-validation experiment. The transition temperatures for the compounds used in each test set were calculated using the b, and m, values given in Tables 1 and 2 which were determined from the entire boiling point and melting point data set. The results of the boiling point and melting point comparison which are given in the supporting information show that the proposed method is more accurate than the method of Joback and Reid (1987). The proposed boiling point method has a RMSE of 14.5 for the 87 compounds tested while the method by Joback and Reid has a RMSE of 21.0. Additionally, the proposed melting point method has a RMSE of 34.4 while the method by Joback and Reid has a RMSE of 51.5 for the 59 compounds tested. One of the reasons for the increase in accuracy is that the proposed method considers the effect that hybridization of the adjacent group has on the molecular fragment, whereas the method by Joback and Reid does not. This method also corrects for repulsive interaction of
proximal electron-withdrawing groups which are not usually considered in most group contribution methods. Additionally, the proposed method takes into consideration the fact that the entropy of boiling is not merely a constant for aliphatic organic compounds and is dependent upon molecular flexibility. Similarly, the entropy of melting must account for both rotational symmetry and molecular flexibility. From the above, it is clear that the use of rotational symmetry and molecular flexibility increases the accuracy of both boiling point and melting point prediction. However, melting point is not estimated as accurately as the boiling point, as indicated by the larger dispersion of the melting point predictions than the boiling point predictions in Figures 1 and 2. This is believed t o be due to the fact that the melting point is dependent upon a number of factors that we cannot presently quantitate. Among the most important of these factors are packing efficiency, solvation, and polymorphism. The greater accuracy of boiling point prediction is also due to the fact that the boiling point is not affected by these factors.
Conclusion The proposed group contribution method enables a simple and accurate prediction of the boiling point and the melting point from chemical structure. This is accomplished by using additive constitutive properties to estimate the enthalpy of transition and nonadditive nonconstitutive properties to estimate the entropy of transition.
Acknowledgment This work was supported through a grant from the Environmental Protection Agency (R-817475-01). The contents of this paper do not necessarily reflect the views and policies of the EPA.
Nomenclature
T,,= transition temperature, K AHt, = enthalpy of transition, J/mol ASt, = entropy of transition, J/(degmol) Tm= temperature of melting, K AHm = enthalpy of melting, Jlmol ASm = entropy of melting, J/(degmol) T b = temperature of boiling, K A H b = enthalpy of boiling, J/mol ASb = entropy of boiling; J/(degmol) b, = contribution of the molecular descriptor i to the enthalpy of boiling m, = contribution of the molecular descriptor i to the enthalpy of melting n, = number of times the molecular descriptor i appears in the compound
Greek Symbols
a = confidence level 0 = external rotational symmetry number 4 = molecular flexibility number 5 = an empirical measure of the effective number of torsional angles
Ind. Eng. Chem. Res., Vol. 34,No. 7, 1995 2535
Appendix Calculation of Boiling Point: 1,1,2,3,3-Pentafluoro-1,2,3-trichloropropane. observed boiling point = 347 K
F rotational symmetry: u = 1
F CI
molecular flexibility:
F
Literature Cited
7 =2
AH,, =xnibi
+
+ +
+ +
+
= 3(C) 5(F) 3(C1) 7(GEM) 12(VIC) = 3(-14374) 5(9014) 3(12352) 7(-1094) 12(-135) = 29726 J/mol
ASb = 86 = 86
+ +
+ 0.42
+ 0.4(2)
= 86.8 J/(degmol)
Tb = AHdASb = 29726186.8 = 342 K Calculation of Melting Point: trune-l,2-Dichlorocyclohexane. CI 1
€1
observed melting point = 267 K
: rotational symmetry: u = 2
molecular flexibility: r = 0
AH,
= Cnim,
+ 2(XCH) + 2(XC1) + 1(VIC) + 6(RING6+) = 4(2347) + 2(387) + 2(4478) + 1(-230) + = 4(XCH2)
6(-689) = 14754 J/mol
AS, =66.5 - 19.2 log o + 9.22 = 56.5 - 19.2 log 2 = 50.7 J/(degmol)
T, = “/AS,
transition temperatures, the estimation of the proposed method, and the estimation for the transition temperatures by the method of Joback and Reid. All compounds are sorted by the molecular weight (36 pages). Ordering information is given on any current masthead page.
+ 9.2(0)
= 14754/50.7
= 291 K
Supporting Information Available: Tabulated data listing the observed boiling points and melting points used in this study along with calculated values for boiling point and melting point using eq 12 and eq 13, respectively. The rotational symmetry number, u, and the effective number of torsional angles, z, are also supplied. Additionally,the data for the compounds used in the test sets are included along with the observed
Abramowitz, R.; Yalkowsky, S. H. Melting Point, Boiling Point, and Symmetry. Pharm. Res. 1990,7,942-947. Austin, J. B. A Relation between the Molecular Weight and Melting Points of Organic Compounds. J. Am. Chem. Soc. 1930, 52,1049-1053. Balaban. A. T.: Kier. L. B.: Joshi. N. Correlations between Chemical Structure and Normal Boiling Points of Acyclic Ethers, Peroxides, Acetals, and Their Sulfur Analogues. J. Chem. ZnE Comput. Sci. 1992,32,237-244. Beacall, T. The Melting-Points of Benzene Derivatives. Red. Trav. Chim. Pays-Bas. 1928,47,37-44. Dannenfelser, R. M.; Yalkowsky, S. H. Predicting the Total Entropy of Melting from Molecular Structure. Submitted for publication in Znd. Eng. Chem. Res. 1995. Dannenfelser, R. M.; Surendren, N.; Yalkowsky, S. H. Molecular Symmetry and Related Properties. SAR QSAR Environ. Res. 1994,1,273-292. Dearden, J. C.;Rahman, M. H. QSAR Approach to the Prediction of Melting Points of Substituted Anilines. Math. Comput. Model. 1988,11,843-846. Devotta, S.; Pendyala, V. R. Modified Joback Group Contribution Method for Normal Boiling Point of Aliphatic Halogenated Compounds. Znd. Eng. Chem. Res. 1992,31,2042-2046. Holler, A. An Observation on the Relation between the Melting Points of the Disubstitution Isomers of Benzene and Their Chemical Constitution. J . Org. Chem. 1947,13,70-74. Joback, K.G.;Reid, R. C. Estimation of Pure-Component Properties from Group- Contributions. Chem. Eng. Commun. 1987, 57,233-243. Mishra, D.; Yalkowsky, S. Estimation of Entropy of Vaporization: Effect of Chain Length. Chemosphere 1990,21,111-117. Myrdal, P.; Krzyzaniak, J.; Yalkowsky, S. Modified Trouton’s Rule for Predicting the Entropy of Boiling. Submitted for publication in Znd. Eng. Chem. Res. 1995. Myrdal, P.; Ward, G. H.; Simamora, P.; Yalkowsky, S. AQUAFAC: Aqueous Functional Group Activity Coefficients. SAR QSAR Environ. Res. 1993,1, 53-61. SAS User’s Guide: Statistics, Version 5 Edition; SAS Institute: C a y , NC, 1985. Screttas, C.; Mecha-Screttas, M. Some Properties and Trends of Enthalpies of Vaporization and of Trouton’s Ratios of Organic Compounds. Correlation of Enthalpies of Vaporization and of Enthalpies of Formation with Normal Boiling Points. J . Org. Chem. 1991,56,1615-1623. Simamora, P.; Yalkowsky, S. H. Group Contribution methods for Predicting the Melting Point and Boiling Point of Aromatic Compounds. Znd. Eng.Chem. Res. 1994,33,1405-1409. Stanton, D. T.;Egolf, L. M.; Jurs, P. C. Computer-Assisted Prediction of Normal Boiling Points for Pyrans and Pyrroles. J. Chem. Znf. Comput. Sci. 1992,32,306-316.
Received for review December 1, 1994 Revised manuscript received March 29, 1995 Accepted April 20, 1995@ IE940708K Abstract published in Advance ACS Abstracts, J u n e 1, 1995. @
