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CORRELATIONS Boiling Points and Melting Points of Chlorofluorocarbons James Wei† School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544-5263
The boiling points of the 15 chlorofluorocarbons based on methane are shown to be determined by the structural parameters of the number of chlorines, the number of fluorines, and the dipole moment. The melting points of these 15 compounds also depend on molecular symmetry and specifically by inclusion of the rotational entropy. The success of this structure-property relation would suggest that these molecules have close to free rotation in the liquid, despite their high dipole moments. Introduction There are fifteen chlorofluorocarbons (CFC) based on methane, with the formula CHnClmF4-n-m. The thermodynamic properties of these compounds are among the best investigated, because they include the most important refrigerants and blowing agents, as well as fuels, cleaning fluids, and anesthesia agents. These 15 compounds have been arranged in a triangle, with their boiling points, melting points, dipole moments, and symmetry numbers in Table 1. The boiling points and the melting points in Kelvin are taken from Lide and Milne;1 the dipole moments in Debye units are taken from Yaws;2 the symmetry numbers are calculated from group theory discussed in Eliel and Wilen.3 Both boiling points and melting points reach a maximum in the lower left-hand corner with CCl4 and decrease when moving up to CH4 or moving right to CF4. The dipole moments are zero in the three corners of the triangle but are at a maximum in the right center of the triangle at CH2F2. The symmetry numbers have the opposite tendency and are at a maximum in the corners but are at a minimum in the center of the triangle. The Boiling Points It is relatively easier to view and analyze data in a one-dimensional array instead of a two-dimensional array, and we have plotted the boiling points and melting points of the compounds around the edges of the triangle, from CCl4 on the lower left to CF4 on the lower right, to CH4 at the top, and back to CCl4 on the lower left. The left side of Figure 1 shows a linear increase of the boiling point from CF4 to CCl4, so that the group contribution method would work very well with the formula
Tb ) 145.1 + 76.2NCl † E-mail:
[email protected]. Telephone: 609/2582260. Fax: 609/258-6744.
The structure-property relation is quite satisfactory. Because chlorine has many more electrons than fluorine, the substitution of a chlorine atom for a fluorine atom would increase the van der Waals forces of attraction, which leads to a higher cohesive energy and boiling point. The middle part of Figure 1 shows a highly nonlinear decrease of boiling points from CCl4 to CH4, so that an additional force is at work. The right part of Figure 1 from CH4 to CF4 shows a very high maximum. Pauling pointed out4 that these nonlinearities are due to changes in the dipole moments when we substitute chlorine with hydrogen or hydrogen with fluorine, which increases the attraction forces between molecules and hence the boiling points. Figure 2 shows the plot of dipole moments of the same set of compounds, and it is seen that the substitution of chlorine by fluorine leads to a small change of the dipole moment of the order of 0.5, but the substitution of hydrogen by chlorine or fluorine leads to much greater dipole moment changes up to 1.8-2.0. The explanation of the structure-property relation of these experimental dipole moments requires more than molecular architecture and the electronegativity of the elements. Hydrogen has an electronegativity value of 2.1, chlorine has a value of 3.0, and fluorine has a value of 4.0, so that the difference between F and Cl is 1.0, which is much smaller than the difference between F and H at 1.9, but the difference between Cl and H is only 0.9, which is even smaller than the difference between F and Cl. Nevertheless, we can employ these experimental dipole moments together with the number of chlorine and fluorine atoms to obtain an estimation formula for all 15 CFC compounds:
Tb* ) 116.1 + 2.44NF + 55.98NCl + 44.56µ (1) This estimation has a standard deviation of 11.7 and an R2 of 0.977. It is also shown in Figure 3 as a comparison between the experimental Tb and the estimated Tb*. This estimation has the virtue of separating the contributions of the van der Waals forces of the atoms from the contributions of dipole moments. Because hydrogen is very different from fluorine, it raises
10.1021/ie9909439 CCC: $19.00 © 2000 American Chemical Society Published on Web 06/24/2000
Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 3117 Table 1. Fifteen CFC Based on Methanea CH4 111.6 90.7 0 12 CH3Cl 249.1 175.1 1.87 3 CH2Cl2 313.1 178.0 1.60 2
CH2ClF 264.0 140.1 1.82 1 CHCl2F 282.0 138.1 1.29 1
CHCl3 334.2 209.5 1.01 3 CCl4 349.9 250.1 0 12
CH3F 194.7 131.3 1.85 3
CCl3F 296.8 162.0 0.45 3
CH2F2 221.5 137.1 1.96 2 CHClF2 232.4 115.4 1.42 1
CCl2F2 243.3 115.1 0.51 2
CHF3 191.0 118.0 1.65 3 CClF3 191.7 92.1 0.51 3
CF4 145.1 89.6 0 12
a The first numbers are boiling points in K, the second numbers are melting points in K, the third numbers are dipole moments in Debye units, and the fourth numbers are symmetry numbers.
Figure 1. Experimental boiling points and meling points of 12 CFC on the outside of the triangle in Table 1.
the question of why the substitution effect, of 2.44, is so much smaller than the substitution effect of hydrogen by chlorine, of 55.98. The Melting Points When we turn our attention to the melting points on the left side of Figure 1, we find that, even for the simplest case of CF4 to CCl4, the linear assumption of group contribution method based on the number of chlorine atoms does not work. Pauling4 pointed out that the additional factor involved is molecular symmetry: the tetrahedral molecules CF4 and CCl4 have 12 rotation symmetries, the symmetrical top molecules CClF3 and CCl3F have 3 rotation symmetries, but the molecule CCl2F2 has a symmetry number of only 2. The
higher the symmetry of the molecule, the higher would be its melting point. His reasoning is that, at the equilibrium temperature between the solid and liquid, the number of molecules leaving the solid for the liquid must be equal to the number of molecules leaving the liquid for the solid. The former is dependent upon on the temperature and the average energy, but the latter is also dependent on the orientation of the liquid molecule as it approaches the crystal solid. A molecule with an unfavorable orientation would not adhere to the crystal, and a symmetrical molecule has a much higher probability of hitting upon a favorable orientation. A quantitative analysis based on statistical mechanics would show that the ratio of the entropy of rotation to the entropy of melting, or R ln(σ)/(Hm/Tm), is the
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Figure 2. Dipole moments and the symmetry numbers of 12 CFC.
The symmetry numbers σ of these 15 compounds are also given in Figure 2. The effect of symmetry to elevate melting points is shown in Figure 4, plotting melting points against boiling points. The molecules with σ ) 12 and 3 have melting points that lie above molecules with comparable boiling points but with σ ) 2 and 1. When we include the effects of symmetry, we obtain the estimation formula of melting points for all 15 compounds as
Tm* ) -9.9 - 1.25NF + 37.86NCl + 57.11µ + 4.84Sr (2)
Figure 3. Comparing the experimental and estimated boiling points for 15 CFC.
appropriate parameter.5 Because the heat of melting, Hm, is often not available, we can fall back on Sr ) R ln(σ) alone.
This estimation has a standard deviation of 8.4 and an R2 of 0.976. Figure 5 shows a satisfactory comparison between the experimental Tm and the estimated Tm*. When the symmetry effect is neglected, the standard deviation increases to 26.99 and the R2 decreases to 0.724. In fact, the estimation of Tm* with symmetry is slightly better than the estimation for Tb*, the boiling point. A summary of these results is provided in Table 2. Because the derivation of the quantitative treatment of melting points and their relation to the symmetry is based on free rotation in the liquid phase, the success
Table 2. Experimental and Estimated Boiling Points and Melting Points of the 15 CFC CH4 CH3F CH2F2 CHF3 CF4 CH3Cl CH2ClF CHClF2 CClF3 CH2Cl2 CHCl2F CCl2F2 CHCl3 CCl3F CCl4
Tb, K
Tm, K
sym
F
Cl
dipole
Sr
Tb*
% error Tb
Tm*
% error Tm
111.6 194.7 221.5 191.0 145.1 249.1 264.0 232.4 191.7 313.1 282.0 243.3 334.2 296.8 349.9
90.7 131.3 137.1 118.0 89.6 175.4 140.1 115.4 92.1 178.0 138.1 115.1 209.5 162.0 250.1
12 3 2 3 12 3 1 1 3 2 1 2 3 3 12
0 1 2 3 4 0 1 2 3 0 1 2 0 1 0
0 0 0 0 0 1 1 1 1 2 2 2 3 3 4
0 1.85 1.96 1.65 0 1.87 1.82 1.42 0.51 1.60 1.29 0.51 1.01 0.45 0
20.66 9.13 5.76 9.13 20.66 9.13 0.00 0.00 9.13 5.76 0.00 5.76 9.13 9.13 20.66
116.11 200.99 208.33 196.95 125.86 255.42 255.63 240.25 202.14 299.38 288.00 255.68 329.07 306.55 340.05
4.04 3.23 -5.95 3.12 -13.26 2.54 -3.17 3.38 5.44 -4.38 2.13 5.09 -1.54 3.29 -2.82
90.08 138.68 127.40 124.76 85.08 178.93 130.61 106.52 97.52 185.05 138.20 120.31 205.54 172.31 241.51
-0.69 5.62 -7.08 5.73 -5.05 2.02 -6.77 -7.70 5.88 3.96 0.07 4.52 -1.89 6.36 -3.43
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Figure 4. Measured boiling points and melting points of the CFC. The legend shows the symmetry numbers.
pounds based on methane, and the correlating parameters are the number of chlorine atoms, the number of fluorine atoms, the dipole moments, and the symmetry numbers. The success of these methods based on physics and chemistry would suggest that there is free rotation in the liquid phase for these compounds, despite their dipole moments. Nomenclature NF ) number of fluorine atoms in the molecule NCl ) number of chlorine atoms in the molecule Sr ) rotational entropy of the molecule, R ln(σ), J/K‚mol Tb ) boiling points, K Tb* ) estimated boiling points Tm ) melting points, K Tm* ) estimated melting points µ ) dipole moment of the molecule, Debye units σ ) symmetry number of the molecule
Literature Cited
Figure 5. Comparing the experiments and estimated melting points for 15 CFC.
of this estimation would suggest that molecular rotation is close to free rotation, despite the high values of the dipole moments. Summary Structure-property methods can be used to study the boiling points and melting points of the 15 CFC com-
(1) Lide, D. R.; Milne, G. W. A., Eds. Properties of Organic Compounds, Personal Edition; CRC Press Database: Boca Raton, FL, 1996. This is a CD-ROM with 27 500 organic compounds. (2) Yaws, C. L., Ed. Chemical Properties Handbook; McGrawHill: New York, 1999. (3) Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds; John Wiley & Sons: New York, 1994. (4) Pauling, L. General Chemistry; Dover Press: New York, 1970. (5) Wei, J. Molecular Symmetry, Rotational Entropy, and Elevated Melting Points. Ind. Eng. Chem. Res. 1999, 38, 50195027.
Received for review December 22, 1999 Revised manuscript received March 9, 2000 Accepted May 9, 2000 IE9909439
