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 5 Union Station STL

2. 1. Vaporization enthalpies at the boiling temperature are predicted to approach a limiting value 2.Boiling temperatures appear to converge to a finite limit. 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 1 atm as the number of repeat units  . 5. Enthalpies of transfer appear to show curvature with increasing size Can any more of this be experimentally verified? Previously we concluded the following:

3. Applications of Correlation Gas Chromatography Vapor Pressure Requirements: Vapor pressures of the standards preferably as a function of temperature over a range of temperatures

4. Retention Times as a Function of Temperature T/K354359364369374379384 Retention Times (t/min) methane0.5630.5640.5830.579 0.5800.585 octane1.5771.4241.3011.1961.1151.030.975 1-nonene2.6642.3192.0521.8271.6611.4841.367 decane5.3894.5123.8573.312.9212.5172.238 naphthalene18.13114.81512.30710.2698.7637.3846.32 dodecane21.77617.31914.03811.4529.5917.9126.631 tridecane44.43934.66827.45821.91417.92114.54611.94 Solvent: CH 2 Cl 2 t a = t i –t CH4 Applications of Correlation Gas Chromatography Vapor Pressure Using the following series of hydrocarbons as examples:

5. A plot of natural logarithm of the reciprocal adjusted retention times ln( t o /t a ) for (top to bottom): ,n- octane; , 1-nonene; , n-decane; , naphthalene; , n-dodecane; , n-tridecane as a function of 1/T; t o = 1 min. Plots of ln(t o /t a ) vs 1/ T

6. Equations resulting from a linear regression of ln(t o /t a ) versus (1/T)K -1 Compound ln(t o /t a )= -  sln g H m /RT + ln(A i ) n-octane ln(t o /t a )= (-32336/RT) + (11.064) r 2 =0.9995 1-nonene ln(t o /t a )= (-35108/RT) + (11.159) r 2 =0.9993 n-decane ln(t o /t a )= (-38973/RT) + (11.655) r 2 =0.9994 naphthalene ln(t o /t a )= (-41281/RT) + (11.176) r 2 =0.9997 n-dodecane ln(t o /t a )= (-46274/RT) + (12.685) r 2 =0.9996 n-tridecane ln(t o /t a )= (-50036/RT) + (13.232) r 2 =0.9997 t o = 1 min

7. A plot of experimental vapor pressures ln(p/p o ) against ln(t o /t a ) at T = 298.15 K; t o = 1 min; p o = 101 kPa A Plot of ln(p/p o ) exp vs ln(t o /t a ) octane decane dodecane tridecane

8.  sln g H m (368 K) ln (A) ln(t o /t a ) ln(p/p o ) ln(p/p o ) ln(p/p o ) lit a calc lit octane-32336 11.064-1.98 -3.99 -3.95 1-nonene-35108 11.159-3.00 -5.15 -4.96 b decane-38973 11.655-4.07 -6.32 -6.39 naphthalene-41281 11.176-5.48 -8.04 -7.98 c dodecane-46274 12.685-5.98 -8.63 -8.63 tridecane-50036 13.232-6.95 -9.79 -9.76 ln(p/p o ) = (1.182  0.015) ln(t o /t a ) -(1.53  0.059); r 2 = 0.9987 a Ruzicka, K.; Majer, V. J. Phys. Chem. Ref. Data 1994, 23, 1-39; b Physical Properties of Chemical Compounds II, Dreisbach, R. R. Advances in Chemistry Series 22, ACS, Washington: DC. c Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Steele, W. V. J. Chem. Thermodyn. 1993, 25, 1461-4. Results of Correlating ln(t o /t a ) with ln(p/p o ) at T = 298.15 K Vapor pressures for naphthalene are for the liquid

9. Provided vapor pressures of the standards are available as a function of temperature, this correlation can be repeated at other temperatures so that a vapor pressure temperature profile can be obtained. Applying this protocol as a function of temperature at T = 15 K intervals and fitting the data for 1-nonene and naphthalene to a third order polynomial results in: a predicted boiling temperature for nonene of : 421 K (420 K lit ) a predicted boiling temperature for naphthalene of: 507 K (493 K lit )

10. Vapor Pressures by Gas Chromatography Vapor pressure of an analyte off a column is inversely proportion to it adjusted retention, 1/t a. Why is 1/t a proportional to the vapor pressure of the pure material when the enthalpy of transfer is a measure of both the vaporization enthalpy and the interaction on the column?  sln g H m (T m ) =  l g H m (T m ) +  sln H m (T m ) Raoult’s Law: : the vapor pressure of component a is equal to the product of vapor pressure of pure a (p a o ) times its mole fraction, χ a p a(obs) = p a o · χ a Since the stationary phase is a polymer, χ a ≈ 1 Returning to the n-alkanes Daltons Law of Partial Pressures p T = p analyte + p stationary phase = p analyte The effects of  sln H m (T m ) are small and compensated by the standards.

11. Vapor Pressures of the Standards literature vapor pressure evaluated using the Cox equation a ln (p/p o ) = (1-T b /T)exp(A o +A 1 T +A 2 T 2 ) a Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal data Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C5-C20. J. Phys. Chem. Ref. Data 1994, 23, 1-39. p o = 101.325 kPa

12. Equations for the temperature dependence of ln(t o /t a ) for C 14 to C 20 where t o = 1 min: ln(t o /t a ) = -  sln H m (T m )/R*1/T + intercept

13. Vapor pressures of n-alkanes (C 14 to C 20 ) at T = 298.15 K: ln(p/p o ) = (1.27  0.01) ln(t o /t a ) - (1.693  0.048); r 2 = 0.9997 -13.3 ? unknown p o = 101.325 kPa

14. Correlation between ln(1/t a ) calculated by extrapolation to T = 298.15 K versus ln(p/p o ) calculated from the Cox equation for C 14 to C 20 (p o = 101.325 kPa) ln(p/p o ) = (1.27  0.01) ln(t o /t a ) - (1.693  0.048); r 2 = 0.9997

15. Vapor pressure -temperature dependence for hexadecane; line: vapor pressure calculated from the Cox equations for C 14, circles; vapor pressures calculated by correlation treating hexadecane as an unknown and correlating ln(t o /t a ) with ln(p/p o ) for C 14, C 15, C 17 -C 20 as a function of temperature from T = (298.15 to 500) K. Normal boiling temperature: 560.2 (expt); 559.9 (calcd) Correlations of Vapor Pressures of Hexadecane from T/K = (298.15 to 500) K 500 K

16. By a process of extrapolation, vapor pressures of C 17 to C 20 were used to evaluate C 21 to C 23 ; C 19 to C 23 were used to evaluate C 24 and C 25,... By such a process of extrapolation, vapor pressure equations were obtained for C 21 through to C 38 using commercially available samples from T = (298.15 to 540) K at 30 K intervals and the resulting vapor pressures were fit to the following third order equation which has been found to extrapolate well with temperature: ln(p/po) = A (T/K) -3 + B(T/K) -2 + C(T/K) -1 + D; Using this equation the boiling temperatures of C 21 to C 38 could be predicted

17. a Literature value. b This work. c Mazee, W. M., “Some properties of hydrocarbons having more than twenty carbon atoms,” Recueil trav. chim 1948, 67, 197-213. Francis, F.; Wood, N. E., The boiling points of some higher aliphatic n-hydrocarbons, J. Chem. Soc. 1926, 129, 1420. Some Available Comparisons With Direct Measurements

18. Experimental vapor pressures for the n-alkanes larger than C 38 are not available. What are available are estimated values. a,b The values are available in the form of a program called PERT2 that runs in Windows a Morgan, D. L.; Kobayashi, R. Extension of Pitzer CSP models for vapor pressures and heats of vaporization to long chain hydrocarbons.Fluid Phase Equilib. 1994, 94, 51–87. PERT2 is a FORTRAN program written by D. L. Morgan in 1996 which includes parameters for n-alkanes from C 1 to C 100 and heat of vaporization and vapor pressure correlations. The parameters for C 51 to C 100 are unpublished based on the critical property (Tc, Pc) correlations of Twu and the Kudchadker & Zwolinski extrapolation of n-alkane NBPs presented in Zwolinski & Wilhoit (1971). Using vapor pressures calculated from C 24 through to C 38, values for C 40 through to C 76 were evaluated. b Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C 21 to C 100. J. Chem. Eng. Data 1966, 11, 253.

19. a Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.

20. The vapor pressures were fit to the following third order polynomial: ln(p/p o ) = A(T/K) -3 + B(T/K) -2 +C(T/K) + D

21. 10 -8 A T 3 10 -6 B T 2 CTCTD heneicosane1.9989-2.9075-98.1356.6591 docosane2.1713-3.1176110.726.5353 tricosane2.3386-3.322310.776.4198 tetracosane2.5072-3.5286530.156.282 pentacosane2.6738-3.7307741.196.150 hexacosane2.8244-3.9193910.536.070 heptacosane3.0092-4.12531198.85.811 octacosane3.1389-4.31201279.45.884 nonacosane3.2871-4.50431431.25.841 triacontane3.4404-4.69981601.65.770 hentriacontane3.6037-4.90021791.25.679 dotriacontane3.7524-5.09211947.25.630 tritriacontane3.8983-5.28092098.05.585 tetratriacontane4.0435-5.46792249.55.537 pentatriacontane4.1746-5.64802363.85.544 hexatriacontane4.3320-5.84322553.25.447 heptatriacontane4.4890-6.03702743.25.347 octatriacontane4.6330-6.22302891.95.304 tetracontane4.9289-6.60653183.35.270 dotetracontane5.1471-6.92243348.95.291 tetratetracontane5.5011-7.34673778.65.117 hexatetracontane5.6451-7.59923810.65.224 octatetracontane5.8908-7.93264039.65.187 10 -8 A T 3 10 -6 B T 2 CTCTD pentacontane6.1330-8.26024268.35.143 dopentacontane4.8707-7.40871564.87.455 tetrapentacontane5.0959-7.71671772.47.410 hexapentacontane5.3213-8.01921997.27.326 octapentacontane5.5446-8.32032215.77.251 hexacontane7.3061-9.84485365.44.957 dohexacontane6.1197-9.02982863.77.000 tetrahexacontane6.2051-9.22152812.17.149 hexahexacontane6.2905-9.41262761.77.295 octahexacontane6.3771-9.59642731.57.398 heptacontane6.4622-9.78332688.67.527 doheptacontane6.5473-9.96772650.77.646 tetraheptacontane6.6325-10.14912619.67.750 hexaheptacontane6.7165-10.33202580.87.870 octaheptacontane6.9185-10.63522862.67.718 octacontane7.0339-10.84502927.07.731 dooctacontane7.1142-11.01002862.87.852 tetraoctacontane7.2562-11.25453066.07.726 hexaoctacontane7.3278-11.41842970.37.897 octaoctacontane7.4656-11.65953147.17.810 nonacontane7.5587-11.82873121.07.885 dononacontane7.7815-12.18304010.66.856

22. N = the number of carbon atoms. The solid symbols represent the experimental and the others the calculated boiling temperatures of C 3 to C 92. The dotted line was calculated for the n-alkanes using a limiting boiling temperature of T B (∞) = 1076 K. The solid line was obtained by using a by fitting the experimental data to the hyperbolic function previously described and a value of T B (∞) = (1217 ± 246) K Using the constants of the previous slide, the normal boiling temperatures were predicted by extrapolation. A plot of the normal boiling temperatures of the n-alkanes as a function of the number of methylene groups resulted in the following:

23. Conclusions: Based on the data available, it appears that boiling temperature appear consistent with the prediction that boiling temperatures would approach a limiting value. The agreement with average value of 1217 obtained previously is probably fortuitous

24. Rachael Maxwell, Boy friend, Richard Heinze Dmitry Lipkind Darrel Hasty