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Table 4. Parameters of the Cox Equation. T b A o 10 3 A 1 10 6 A 2

Table 4. Parameters of the Cox Equation. T b A o 10 3 A 1 10 6 A 2 tetradecane 526.691 3.13624 -2.063853 1.54151 pentadecane 543.797 3.16774 -2.062348 1.48726 hexadecane 559.978 3.18271 -2.002545 1.38448 heptadecane 575.375 3.21826 -2.04 1.38

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Table 4. Parameters of the Cox Equation. T b A o 10 3 A 1 10 6 A 2

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  1. Table 4. Parameters of the Cox Equation. Tb Ao 103A1 106A2 tetradecane 526.691 3.13624 -2.063853 1.54151 pentadecane 543.797 3.16774 -2.062348 1.48726 hexadecane 559.978 3.18271 -2.002545 1.38448 heptadecane 575.375 3.21826 -2.04 1.38 octadecane 590.023 3.24741 -2.048039 1.36245 nonadecane 603.989 3.27626 -2.06 1.35 eicosane 617.415 3.31181 -1.02218 1.34878 Cox Equation ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2)

  2. ln(1/ta) = gslnHm(Tm)/R + intercept

  3. If the vaporization enthalpy correlates with the enthalpy of transfer from solution to vapor, will the vapor pressure correlate with the vapor pressure of the solute on the stationary phase of the column?

  4. The correlation observed between ln(1/ta) calculated by extrapolation to 298.15 K using the equations given in the previous table and ln(p/po) at 298.15 K calculated from the Cox equation for n-C14 to n-C20. The term po represents the vapor pressure (101.325 kPa) at the reference temperature, Tb, the normal boiling point of the n-alkane; the equation of the line obtained by a linear regression is given by ln(p/po) = (1.26  0.01)ln(1/ta) – (1.718  0.048); r2 = 0.9997.

  5. The selection of temperature is arbitrary, therefore this correlation should apply at any temperature. Can these correlations be used to evaluate vapor pressures and vaporization enthalpies of the larger n-alkanes for which data is not presently available? Until recently vaporization enthalpies and vapor pressures were available up to eicosane.

  6. Why is there any interest in knowing the vapor pressures and vaporization enthalpies of these higher alkanes? 1. n-Alkanes serve as excellent standards for the evaluation of vaporization enthalpies and vapor pressures of other hydrocarbons. 2. The properties of the n-alkanes are useful in predicting properties of crude oil and useful in the development of models for handling petroleum.

  7. Suppose a mixture of the following n-alkanes were analyzed by gas chromatography: Retention Times for C17 to C23 T/K 493.8 498.9 503.8 508.9 513.9 518.9 523.9 t/min methylene chloride 1.721 1.747 1.746 1.765 1.779 1.792 1.816 heptadecane 2.974 2.849 2.722 2.624 2.556 2.472 2.435 octadecane 3.477 3.276 3.093 2.941 2.83 2.712 2.645 nonadecane 4.182 3.88 3.61 3.375 3.202 3.035 2.926 eicosane 5.144 4.685 4.295 3.952 3.695 3.459 3.294 heneicosane 6.496 5.826 5.255 4.743 4.368 4.034 3.787 docosane 8.37 7.392 6.56 5.811 5.275 4.799 4.44 tricosane 10.923 9.498 8.295 7.232 6.468 5.798 5.288

  8. A plot of ln(1/ta) vs 1/T results in C17 to C23. Tm =508.8 K slngHm/R intercept r2 heptadecane -6108.278.2 12.1480.008 0.9992 octadecane -6489.963.8 12.5840.006 0.9995 nonadecane -6901.058.7 13.0770.006 0.9996 eicosane -7270.060.5 13.4960.006 0.9996 heneicosane -7670.965.3 13.9740.006 0.9996 docosane -8064.571.6 14.4390.007 0.9996 tricosane -8451.173.9 14.8970.008 0.9996

  9. C17 to C23 slngHm(508 K) lgHm (298.15 K) lgHm (298.15 K) (lit) (calc) heptadecane 50.8 86.5 86.42. octadecane 54.0 91.4 91.42.2 nonadecane 57.4 96.4 96.72.3 eicosane 60.4 101.8 101.62.4 heneicosane 63.8 106.82.5 docosane 67.0 111.92.7 tricosane 70.3 117.02.8 lgHm (298.15 K) = (1.570.04)slngHm(Tm) – (6.660.30); r2 = 0.9985

  10. Figure. The correlations obtained by plotting vaporization enthalpy at T =298.15 K against the enthalpy of transfer measured at the mean temperature indicated; triangles: n-C14 to C20 (449 K); solid triangles: n-C17 to C23(508.8 K); hexagons: n-C19 to C25(538.7 K); squares: n-C21 to C27(523.8 K); circles: n-C23 to C30(544 K).

  11. In this manner, vaporization enthalpies and vapor pressures were calculated from T = 570 to 298.15 K for C21 to C38. All of the compounds are solids at T = 298.15 K so the vapor pressures and vaporization enthalpies are hypothetical properties. Chickos, J. S.; Hanshaw, W. J. Chem. Eng. Data2004, 49, 77-85 Chickos, J. S.; Hanshaw, W. J. Chem. Eng. Data2004, in press.

  12. Figure. The vaporization enthalpies of the n-alkanes at T = 298.15 K . The circles represent recommended vaporization enthalpies from the literature; the squares represent the vaporization enthalpies previously evaluated by correlation-gas chromatography;4 the triangles are the results of this study.

  13. Figure. A plot of ln (p/po) versus 1/T for the n-alkanes; from top to bottom: : n-heneicosane; : docosane; : n-tricosane; : tetracosane; : pentacosane; : hexacosane; : heptacosane; : octacossane; : nonacosane; : triacontane; po is a reference pressure.

  14. Figure. A plot of ln (p/po) versus 1/T for the n-alkanes from T = 298.15 K to T = 570 K (from top to bottom). , hentriacontane; , dotriacontane; , tritriacontane; , tetratriacontane; , pentatriacontane; , hexatriacontane; , heptatriacontane; , octatriacontane.

  15. Since the values were all obtained by extrapolation, are they any good?

  16. ln(p/po) = AT -3 + BT -2 + CT -1 + D Compounds 10-8A 10-6B C D heneicosane 1.9989 -2.9075 -98.135 6.6591 docosane 2.1713 -3.1176 110.72 6.5353 tricosane 2.3386 -3.3220 310.77 6.4198 tetracosane 2.5072 -3.5286 530.15 6.2817 pentacosane 2.6738 -3.7307 741.19 6.1496 hexacosane 2.8244 -3.9193 910.53 6.0704 heptacosane 3.0092 -4.1253 1198.8 5.8109 octacosane 3.1389 -4.3120 1279.4 5.8835 nonacosane 3.2871 -4.5043 1431.2 5.8413 triacontane 3.4404 -4.6998 1601.6 5.7696

  17. ln(p/po) = AT -3 + BT -2 + CT -1 + D Compounds 10-8A 10-6B C D hentriacontane 3.6037 -4.9002 1791.2 5.6790 dotriacontane 3.7524 -5.0921 1947.2 5.6300 tritriacontane 3.8983 -5.2809 2098.0 5.5850 tetratriacontane 4.0435 -5.4679 2249.5 5.5370 pentatriacontan 4.1746 -5.6480 2363.8 5.5436 hexatriacontane 4.3320 -5.8432 2553.2 5.4470 heptatriacontane 4.4890 -6.0370 2743.2 5.3470 octatriacontane 4.6330 -6.2230 2891.9 5.3040

  18. A Comparison of the Vapor Pressure and Vaporization Enthalpy of Octacosane Obtained by Correlation Gas Chromatography with Literature Values. Temp ln(p/po) ln(p/po)b ln(p/po)c K from ln(1/ta)a 298.15 -26.49 -25.88 -26.52d 453.15 -8.92 -8.88 -8.91d 463.15 -8.30 -8.27 -8.28d 483.1 -7.16 -7.14 -7.12e 518.1 -5.45 -5.43e 553.1 -4.04 -4.01e 588.1 -2.86 -2.83 e lgHm(468.15 K)/kJ.mol-1 106.7a 105.6b 107.2d athis work;bChirico, R. D.; Nguyen, A.; Steele, W. V.; Strube, M. M. J. Chem. Eng. Data1989, 34, 149-56;cMorgan, D. L.; Kobayashi, R. Fluid Phase Equil. 1994, 97, 211-242; d“conformal” fit to the Wagner equation; eexperimental values.

  19. T/K ln(p/po) ln(p/po)b ln(p/po)c ln(p/po)d ln(p/po)elgHm(T)algHm(T) from ln(1/ta)a docosane 463 -5.6 -5.5 85.8 85.2c docosane 417.8 -8.1 -8.0 92.6 92.7e docosane 417.8 -8.1 -8.0 92.6 91.7d tetracosane 463 -6.5 -6.5 93.1 93.3c tetracosane 417.8 -9.2 -9.0 100.2 121.4e tetracosane 417.8 -9.2 -9.2 100.2 102.2d hexacosane 417.8 -10.3 -10.3 108.6 109.2e octacosane 417.8 -11.5 -11.4 116.7 114.3b octacosane 417.8 -11.5 -11.4 116.7 116.6c octacosane 417.8 -11.5 -11.5 116.7 128.9e athis work;bChirico, R. D.; Nguyen, A.; Steele, W. V.; Strube, M. M. J. Chem. Eng. Data1989, 34, 149-56;c “conformal” fit to the Wagner equation;Morgan, D. L.; Kobayashi, R. Fluid Phase Equil. 1994, 97, 211-242; d Sasse, K.; Jose, J.; Merlin, J.-C., Fluid phase Equil.1988, 42, 287-304;eGrenier-Loustalot, M. F.; Potin-Gautier, M.; Grenier, P., Analytical Letters1981, 14, 1335-1349.

  20. Table. Literature and Calculated Values of lgH(Tm) and ln(p/po) at T =Tm; Enthalpies in kJ.mol-1 Tm/K lgH(Tm)a lgH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po) Triacontane Mazee9 535.5 100.0 102.5 -2.5 -5.34 -5.39 0.0 PERT212,c 535.5 103.3 102.5 0.8 -5.34 -5.39 0.05 Francis and Wood8 549.7 102.6 100.9 1.7 -4.53 -4.80 0.27 PERT212,c 549.7 101.0 100.9 -0.9 -4.75 -4.80 0.05 Piacente et al.10 454 143.2 117.2 26.0 -9.6 -9.82 0.27 PERT212,c 298.15 155.4 152.3 3.1 -28.9 -28.8 -0.10 Hentriacontane Mazee9 535.7 105.0 105.9 -0.90 -5.69 -5.71 0.02 PERT212,c 535.7 106.6 105.9 0.7 -5.65 -5.71 0.06 Piacente et al.10 450 146.0 121.8 24.2 -10.4 -10.64 0.24 PERT212,c 298.15 160.6 157.3 3.3 -30.0 -29.8 -0.20 Dotriacontane Piacente et al.10 456 147.1 124.5 22.6 -10.2 -10.6 0.42 PERT212,c 456 125.0 124.5 0.5 -10.58 -10.6 0.02 PERT212,c 298.15 165.9 162.5 3.4 -31.1 -31.0 -0.10

  21. Table. Literature and Calculated Values of lgH(Tm) and ln(p/po) at T =Tm; Enthalpies in kJ.mol-1 Tm/K lgH(Tm)a lgH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po) Tritriacontane Piacente et al.10 458 148.0 128.0 20.0 -10.6 -10.95 0.34 PERT212,c 458 128.4 128.0 0.4 -10.89 -10.95 0.06 PERT212.c 298.15 171.2 167.6 3.6 -32.2 -32.1 -0.1 Tetratriacontane Mazee9 548.2 107.9 113.6 -5.7 -5.9 -6.1 0.16 PERT212,c 548.2 114.3 113.6 0.7 -6.0 -6.1 0.1 Francis and Wood8 584.4 140.2 107.6 32.6 -4.38 -4.31 -0.07 PERT212,c 584.4 107.9 107.6 0.3 -4.5 -4.38 0.12 Piacente et al.10 471 152.0 128.9 23.1 -10.1 -10.5 0.40 PERT212,c 298.15 176.4 172.7 3.7 -33.3 -33.2 -0.1 Pentatriacontane Mazee9 561.3 111.5 114.6 -3.1 -5.66 -5.81 0.15 PERT212,c561.3 115.2 114.6 0.6 -5.70 -5.81 0.11 PERT212,c298.15 181.7 178.0 3.7 -34.4 -34.3 -0.1

  22. Table. Literature and Calculated Values of lgH(Tm) and ln(p/po) at T =Tm; Enthalpies in kJ.mol-1 Tm/K lgH(Tm)a lgH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po) Hexatriacontane Mazee9 557.7 114.9 118.3 -3.4 -6.17 -6.26 0.091 PERT212,c 557.7 119.0 118.3 0.7 -6.14 -6.26 0.12 Piacente et al.10 484 157.0 133.4 23.6 -9.98 -10.4 -0.42 PERT212,c 298.15 186.9 182.8 4.1 -35.4 -35.4 -0.1 Heptatriacontane Piacente et al.10 491 155.0 135.2 19.8 -9.88 -10.3 -0.42 PERT212,c 491 136.0 135.2 0.8 -10.2 -10.3 0.1 PERT212,c298.15 192.1 187.5 4.6 -36.5 -36.4 -0.1 Octatriacontane Piacente et al.10 491 160.0 138.8 21.2 -10.3 -10.7 -0.4 PERT212,c 491 139.6 138.8 0.8 10.58 -10.7 0.12 PERT212,c298.15 197.3 192.6 4.7 -37.6 -37.5 -0.1 aLiterature value. bThis work. cCalculated using PERT2.

  23. Any other uses for subcooled liquid vapor pressures and vaporization enthalpies?

  24. Table. Vaporization, Solid-Liquid Phase Change, and Sublimation Enthalpies at T = 298.15 K. lgHmtpceHm cTfus tpceHmcrgHm (298.15 K) Kc (298.15 K)d(298.15 K)e heneicosane 106.82.5a 63.42.1 313.2 61.92.1 168.73.3 docosane 111.92.7a 77.12.1 316.8 75.22.2 187.63.5 tricosane 1172.8a 75.53.9 320.4 73.14.0 190.14.9 tetracosane 121.92.8a 86.13.6 323.6 83.33.7 205.24.6 pentacosane 126.82.9a 84.43.0 326.3 81.23.2 208.04.3 hexacosane 131.73.2a 93.94.4 329.2 90.24.5 221.95.6 heptacosane 135.63.3a 89.57.1 331.7 85.47.2 221.07.9 octacosane 141.94.9a 100.33.8 334.2 95.74.0 237.66.4 nonacosane 147.15.1a 97.93.3 336.2 92.93.6 240.66.3 triacontane 152.35.3a 105.16.7 338.2 99.66.9 251.98.7hentriacontane 157.31.2b 109.9 341.1 103.9 261.1 dotriacontane 162.51.4b 117.74.8 342.5 111.35.2 273.75.4 tritriacontane 167.61.4b 113.58.8 344.3 106.69.0 274.29.1 tetratriacontane 172.76b 127.46.3 345.6 120.16.7 292.89.0 pentatriacontane 178.19.2b 129.04.3 347.7 121.24.9 299.210.4 hexatriacontane 182.99.4b 128.89.6 348.9 120.69.9 303.513.7 heptatriacontane 187.69.6b 137 349.8 128.4 316.0 octatriacontane 192.79.8b 136.7 351.7 127.6 320.3

  25. Many substances are released into the environment by a variety of natural and man promoted events. Combustion of fossil fuel for example leads to the production of a variety of polyaromatic hydrocarbons. Many of these material are large, non-volatile molecules and present in very small amounts. On account of their dispersal, they may be crystalline solids when pure but in the environment, they are present adsorbed onto particulates and their distribution in an west to east direction is governed by the prevailing winds. However, long-lived non-volatile materials tend to accumulate in the polar regions where their vapor pressure is the lowest. Their rate of dispersal in a northerly or southerly direction depends on their vapor pressure. It has been found that this is best approximated by the compounds sub-cooled vapor pressure.

  26. Can the vapor pressure of the n-alkanes be used to evaluate vapor pressures of PAHs? Retention Times for Some n-Alkanes and PAHs T/K 398.2 403.2 408.2 413.2 418.2 423.2 428.2 t/min CH2Cl2 2.83 2.839 2.851 2.862 2.874 2.886 2.9 decane 4.217 4.033 3.884 3.76 3.66 3.575 3.514 dodecane 7.47 6.731 6.135 5.654 5.264 4.938 4.685 naphthalene 7.656 6.96 6.388 5.92 5.538 5.21 4.955 biphenyl 16.115 13.9 12.111 10.68 9.622 8.542 7.80 tetradecane 17.402 14.716 12.594 10.928 9.622 8.542 7.711 pentadecane 28.148 23.196 19.334 16.336 13.993 12.089 10.644

  27. Table 9. Equations for the Temperature Dependence of ln(1/ta) of Some n-Alkanes and PAHsa Tm = 413.2 K slnvHm/R intercept r2 naphthalene, biphenyl decane -4651.538 11.360.01 0.9996 naphthalene -4862.041 10.640.01 0.9996 dodecane -5439.539 12.130.01 0.9974 biphenyl -5659.152 11.630.01 0.9958 tetradecane -6306.249 13.170.01 0.9996 pentadecane -6744.150 13.720.01 0.9997

  28. Table. Vaporization Enthalpies of Some PAHs in kJ.mol-1 slnvHm(413.2 K) lgHm (298.15 K) lgHm (298.15 K) (lit) (calc) decane 38.67 51.4 52.52.4 dodecane 45.22 61.5 61.72.8 naphthalene 40.42 54.92.5 biphenyl 47.05 64.32.9 tetradecane 52.43 71.7 72.03.3 pentadecane 56.07 76.8 77.13.5 lgHm (298.15 K) = (1.4190.062)slngHm(Tm) – (2.420.93); r2 = 0.9925

  29. lgHm(298.15 K)(lit)a lgHm(298.15 K) Naphthalene Summary 55.71.0 54.91.6b biphenyl Summary 65.52.2 64.32.9b Sabbah, R.; Xu-wu, A. Chickos, J. S.; Planas Leitao, M. L.; Roux, M. V.; Torres, L. A. "Reference materials for calorimetry and differential scanning calorimetry," Thermochimica Acta1999, 331, 93-204; bthis work.

  30. Naphthalene Wagner Equation ln(p/pc)=1/T/Tc [A(1-T/Tc)+B(1- T/Tc)1.5+C(1- T/Tc)2.5+D(1-T/Tc)5] Tc/K pc/kPaA B C D 748.4 4105 -7.79639 2.25115 -2.7033 -3.2266 Biphenyl Cox Equation ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2) Tb/K Ao 103A1 106A2 528.422 2.93082 -1.44703 1.00381

  31. Table. Correlation of ln(1/ta) with Experimental Vapor Pressures at 298.15 K. ln(1/ta) ln(p/po)expt ln(p/po)calc decane -4.24 -6.32 -6.30 naphthalene -5.66 -8.07 dodecane -6.11 -8.63 -8.63 biphenyl -7.35 -10.17 tetradecane -7.98 -10.94 -10.96 pentadecane -8.90 -12.08 -12.11 ln(p/po)calc = (1.2460.020) ln(1/ta)) – 1.0130.078; r2 = 0.9990

  32. Table 14. A Comparison of Subcooled Liquid Vapor Pressures with Literature Values at T = 298.15 K. ln(p/po)calca ln(p/po)lit C10H8 naphthalene -8.07-7.98c, -7.91b C12H10biphenyl-10.17-10.28d, -10.2b aThis work. bLei, Y. D.; Chankalal, R.; Chan, A. Wania, F. “Supercooled liquid vapor pressures of the polycyclic aromatic hydrocarbons,” J. Chem. Eng. Data 2002, 47, 801 – 806; cChirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V. “The thermodynamic properties to the temperature 700 K of naphthalene and of 2,7-dimethylnaphthalene,” J. Chem. Thermodyn.1993, 25, 1461-94; dChirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V.“The thermodynamic properties of biphenyl,” J. Chem. Thermodyn.1989, 21, 1307-1331.

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