1. Adventures in Thermochemistry James S. Chickos * Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO 63121 E-mail: jsc@umsl.edujsc@umsl.edu 6 1867-72 Eads Bridge

2. Based on the behavior observed in the melting temperatures of homologous series, we wondered how boiling temperatures varied as a function of size?

3. The plot of the boiling temperatures of the n-alkanes as a function of the number of repeat units. Number of repeat units, n TBTB Question: How do the boiling temperatures of the n-alkanes vary as a function of the number of repeat units?

4. Modeling boiling temperature Exponential functions have previously been used to model the behavior observed for the n-alkanes. 1. Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem. 1961 65, 1050-1052. 2. Partington, J. An Advanced Treatise on Physical Chemistry, Vol II, Properties of Liquids, Longmans, Green Co.: N. Y., 1949, p 301. Is there any basis for expecting the boiling temperature of an infinite alkane to be finite? M = molecular weight; , b = constants 1 T B = 138 C 1/2 ; C = number of carbons 2

5. A plot of  l g H m (T B ) versus  l g S m (T B ) at T = T B for the following: n-alkanes (C 3 to C 20 ): circles, n-alkylcyclopentanes (C 7 to C 21 ): triangles, n-alkylcyclohexanes (C 8 to C 24 ): squares.  l g S m (T B ) / J mol -1 K -1  l g H m (T B ) / J mol -1

6. If the relationship between  l g H m (T B ) and  l g S m (T B ) can be expressed in the form of an equation of a straight line:  l g H m (T B ) = m  l g S m (T B ) + C (1) Since at the boiling temperature,  l g G m (T B ) = 0;  l g S m (T B ) =  l g H m (T B )/T B Therefore  l g H m (T B ) = m  l g H m (T B )/ T B +C Solving for T B : T B = m  l g H m (T B )/(  l g H m (T B ) - C) (2) This is an equation of a hyperbola As  l g H m (T B )   ; T B  m

7. The Correlation Equations Obtained by Plotting  l g H m (T B ) Versus  l g S m (T B ) n-alkanes  l g H m (T B ) = (3190.7  22.6)  l g S m (T B ) – (240583  350); r 2 = 0.9992 n 1-alkenes  l g H m (T B ) = (2469.3  109.7)  l g S m (T B ) – (169585  951); r 2 = 0.9806 n-alkylbenzenes  l g H m (T B ) = (3370.5  37.3)  l g S m (T B ) – (247175  296); r 2 = 0.9985 n-alkylcyclopentanes  l g H m (T B ) = (3028.8  97.4)  l g S m (T B ) – (220567  926); r 2 = 0.9877 n-alkylcyclohexanes  l g H m (T B ) = (3717.8  87.3)  l g S m (T B ) – (284890  999); r 2 = 0.9918 n-alkanethiols  l g H m (T B ) = (2268.7  162.6)  l g S m (T B ) – (161693  1728); r 2 = 0.9558 T B (  ) ~ 3000 K

8. If T B approaches 3000 K in an ascending hyperbolic fashion, then a plot of 1/[1 – T B /T B (  )] versus n, the number of repeat units, should result in a straight line.

9. squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes A plot of 1/[1- T B /T B (  )] versus the number of methylene groups using a value of T B (  ) = 3000 K.

10. Use of T B (  ) = 3000 K did not result in straight lines as expected. Therefore: T B (  ) was treated as a variable and allowed to vary in  5 K increments until the best straight line was obtained by using a non-linear least squares program resulting in the following.

11. squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes 1/[1- T B /T B (  )] = aN + b

12. The Results Obtained by Treating T B of a Series of Homologous Compounds as Function of the Number of Repeat Units, N, and Allowing T B (  ) to Vary; a Bm, b Bm : Values of a B and b B Obtained by Using the Mean Value of T B (  ) = 1217 K Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkanes 1076 0.06231 1.214 0.9 0.04694 1.1984 3.6 18 2-methyl-n-alkanes 1110 0.05675 1.3164 0.2 0.0461 1.2868 0.3 8 1-alkenes 1090 0.06025 1.265 0.4 0.04655 1.242 2.7 17 n-alkylcyclopentanes 1140 0.05601 1.4369 0.6 0.04732 1.4037 1.3 15 n-alkylcyclohexanes 1120 0.05921 1.5054 0.1 0.04723 1.4543 1.2 13 n-alkylbenzenes 1140 0.05534 1.5027 1.1 0.05684 1.5074 1.4 15 1-amino-n-alkanes 1185 0.04893 1.274 3.4 0.04607 1.267 3.4 15 1-chloro-n-alkanes 1125 0.05717 1.2831 0.3 0.04775 1.2628 1.6 13 1-bromo-n-alkanes 1125 0.05740 1.3264 1.0 0.0481 1.2993 1.5 12 1-fluoro-n-alkanes 1075 0.05833 1.2214 0.4 0.04495 1.1987 2.1 9 1-hydroxy-n-alkanes 1820 0.01806 1.220 0.8 0.03953 1.3559 3.6 12 2-hydroxy-n-alkanes 1055 0.05131 1.4923 1.8 0.03732 1.4031 1.8 7 n-alkanals 910 0.08139 1.4561 1.4 0.04277 1.3177 2.5 7 2-alkanones 1440 0.03071 1.2905 1.6 0.0430 1.3613 1.7 8 Using T B (  ) avg = 1217 K

13. Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkane-1-thiols1090 0.06170 1.3322 0.2 0.042 1.3635 2.8 14 n-dialkyl disulfides1190 0.08720 1.4739 0.4 0.08207 1.4608 0.6 9 n-alkylnitriles1855 0.01907 1.2294 2.6 0.04295 1.3869 3.4 11 n-alkanoic acids1185 0.0440 1.4964 1.3 0.04100 1.4790 1.3 16 methyl n-alkanoates1395 0.03158 1.3069 2.6 0.04200 1.3635 2.8 10 Mean Value of T B (  ) = (1217  246) K The results for T B (  ) for polyethylene are remarkably constant considering the use of data with finite values of n to evaluate T B (n) for n (  ). These results are also in good agreement with the values reported previously for the n-alkanes by Kreglewski and Zwolinski (T B (  ) = 1078 K), Somayajulu (T B (  ) = 1021 K), Stiel and Thodos ((T B (  ) = 1209) K. Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem. 1961 65, 1050-1052. Somayajulu, G. R. Internat. J. Thermophys. 1990, 11, 555-72. Stiel, L. T.; Thodos, G. AIChE. J. 1962, 8, 527-9.

14. A value of T B (  ) = (1217  246) K is considerably less than T B (  ) = 3000 K, the value obtained by assuming that  l g H m (T B )   as T B  . Why is T B (  ) = (1217  246) K, not ~3000 K? From the plot of  l g H m (T B ) vs  l g S m (T B ), shown earlier: T B = m  l g H m (T B )/(  l g H m (T B ) - C) Rearranging and solving for  l g H m (T B ) max using T B (  ) = 1217 results in:  l g H m (T B ) max = C (T B (  ))/(m - T B (  ))  l g H m (T B ) max = 154.5  18.5 kJ mol -1 A limiting value of 154.5  18.5 kJ mol -1 for  l g H m (T B ) max at T B is predicted where C and m are from plots of  l g H m (T B ) vs  l g H m (T B ) A limiting value for  l g H m (T B ) max suggests that this property may also be modeled effectively by a hyperbolic function

15. A plot of 1/[1-  l g H m (T B )/  l g H m (T B ) max ] against the number of repeat units, n 1-alkenes: circles n-alkylcyclohexanes: squares using a value of 154 kJ mol -1 for  l g H m (T B ) max.. Data from: Wilhoit, R. C.; Zwolinski B. J. Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds. TRC, Texas A&M Univ. College Station TX

16. Values of the Parameters of a H and b H Generated in Fitting  l g H m (T B ) of Several Homologous Series Using a Value of  l g H m (T B ) max = 154.5  18.5 kJ mol -1. a H b H  /kJ. mol -1 data points n-alkanes0.02960 1.12350.418 n-alkylbenzenes0.02741 1.2840.515 n-alkylcyclohexanes0.02697 1.27540.215 n-alkylcyclopentanes0.02821 1.24750.215 n-alk-1-enes0.02796 1.15540.417 n-alkane-1-thiols0.03172 1.18540.513

17. At this point it might be useful to ponder why vaporization enthalpies may approach a limiting value. Consider what vaporization enthalpies measure: intermolecular forces As the size of a flexible molecule increases, what trend would be expected in the ratio of intermolecular/intramolecular interactions? In the limiting case, for a flexible molecule the ratio between intermolecular/intramolecular interactions might be expected to go as the ratio of the surface area of a sphere to its volume: 4  r 2 /4/3  r 3 ~ 1/r

18. Why do all of the series related to polyethylene converge to a value for  l g H m (T B ) max = 154.5  18.5 kJ mol -1 ?

19. Ambroses’ Equation T C = T B + T B /[c + d(n+2)] where c and d are constants and n refers to the number of methylene groups. This equation suggests that T C  T B as n  . Ambrose, D. "NPL Report Chemistry 92" (National Physical Laboratory, Teddington, Middlesex UK, 1978). How do critical temperatures of homologous series vary with n?

20. A plot of experimental critical temperatures versus n, the number of methylene groups for (from top to bottom): alkanoic acids: hexagons, 2-alkanones: diamonds, 1-alkanols: solid circles, 1-alkenes: triangles, and n-alkanes: circles. Experimental Critical Temperatures

21. According to Ambroses’ equation and the previous plots, the critical temperatures of series related to polyethylene appear to behave in an ascending hyperbolic fashion. This suggests that a plot of 1/[1- T C /T C (  )] versus the number of methylene groups n should also be a linear function provided a suitable value of T C (  ) was used. Treating T C (  ) as a variable in ± 5 K increments, a non linear least squares fit the data resulted in the following:

22. Number of CH 2 groups 1/[1-T c /T c (  )]  carboxylic acids  2-alkanones  n-alkanes

23. Results Obtained for the Constants a C and b C by plotting 1/[1-T C (n)/ T C (  ) as a Function of the Number of Repeat Units, N, and Allowing T C (  ) to Vary; a Cm, b Cm : Values of a C and b C Obtained by Using the Mean Value of T C = 1217 K Polyethylene data Series T C (  )/K a C b C  /K T C (  )/K a Cm  b Cm  /K points n-alkanes 1050 0.1292 1.4225 1.7 1217 0.07445 1.4029 9.8 16 n-alkanals 1070 0.1171 1.7753 1.0 1217 0.07756 1.6355 1.8 8 alkanoic acids 1105 0.0961 2.1137 3.4 1217 0.06456 1.9329 3.9 31 1-alkanols 1045 0.1157 1.8362 3.6 1217 0.06773 1.6639 4.7 11 2-alkanones 1105 0.10063 1.8371 1.3 1217 0.07193 1.718 1.9 11 3-alkanones 1185 0.07827 1.8168 1.3 1217 0.07158 1.7811 1.3 10 1-alkenes 1035 0.1327 1.5496 0.3 1217 0.08278 1.4518 3.1 8 2-methylalkanes 950 0.16282 1.7767 0.6 1217 0.07862 1.5329 1.7 5

24. A plot of experimental critical temperatures versus n, the number of methylene groups for (from top to bottom): alkanoic acids: hexagons, 2-alkanones: diamonds, 1-alkanols: solid circles, 1-alkenes: triangles, and n-alkanes: circles. The lines were calculated using T C (  ) = 1217 K. Critical Temperatures vs n

25. What are the consequences if T B (  ) = T C (  )?

26. At T C,  l g H m (T C ) = 0 This explains why  l g H m (T B ) fails to continue to increase but may infact decrease as the size of the molecule get larger. What does  l g H m (T B ) measure? If vaporization enthalpies are a measure of intermolecular interactions, as the size of the molecule get larger, the ratio of intermolecular/intramolecular interactions  0 as n  .

27. Are there any additional consequences if T B (  ) = T C (  )? Since T B is the normal boiling temperature, If T C (  ) = T B (  ), then in the limit, P C (  ) = P B (  ) = 101.325 kPa; 0.1 MPa. The critical pressure should decrease with increasing n asympotically approaching 0.1MPa as n  . Therefore a plot of 1/[1- P C (  )/P C (n)] versus n using P C (  ) = 0.1 MPa should result in a straight line.

28. n, number of CH 2 groups 1/[1-P c /P c (  )] A Plot of 1/[1-P c (  ) /P c ] vs n for carboxylic acids 1/[1-Pc (  ) /Pc] vs n

29. .A plot of the critical pressure versus the number of repeat units for the 1-alkanols: triangles, n-alkanes: circles, 2-methylalkanes: squares Critical Pressures vs n

30. What about other series?

31. How about the fluorocarbons?

32. n, number of CF 2 groups T B /K symbols: experimental T B / K lines: calculated T B / K circles: prefluoroalkanes squares: perfluorocarboxylic acids Boiling Temperatures Versus the Number of CF 2 Groups

33. Table 7. Values of the Parameters of a B and b B Generated in Fitting T B of Several Homologous Perfluorinated Series Using Equation 3 and Allowing T B (  ) to Vary in 5 K Increments; a Bm, b Bm : Values of a B and b B Using an Average Value of T B (  ) = 915 K T B = T B (  )[1-1/(1-a B N + b B )] (3) T B (  )/Ka B b B  /K T B (  )/K a Bm b Bm  /KN n-perfluoroalkanes 880 0.07679 1.2905 2.1 915 0.06965 1.2816 2.2 13 n-perfluoroalkanoic acids 950 0.06313 1.5765 1.2 915 0.07053 1.6085 1.3 8 methyl n-perfluoroalkanoates 915 0.06637 1.5000 1.6 4 1-iodo-n-perfluoroalkanes 915 0.07409 1.3751 1.8 5

34. n, number of CF 2 groups T C /K symbols: experimental T C / K lines: calculated T C / K using T C = 915 K for the n- perfluoroalkanoic acids Critical Temperatures Versus the Number of CF 2 Groups

35. A plot of the critical pressure versus the number of repeat units using P C (  ) = 0.101 (MPa) n, number of CF 2 groups Perfluoroalkanes P C (MPa)

36. Conclusions: 1. Boiling temperatures appear to converge to a finite limit. 2.Vaporization enthalpies are predicted to approach a limiting value and then decrease as the size of the homologous series increases. 3.Critical temperature and boiling temperatures appear to converge as a function of the number of repeat units. 4.Critical pressures appear to converge to some finite pressure (~1 atm) as the number of repeat units  . Can any of this be experimentally verified?