Table 4. Parameters of the Cox Equation. Tb Ao 103A1 106A2

tetradecane 526.691 3.13624 -2.063853 1.54151pentadecane 543.797 3.16774 -2.062348 1.48726hexadecane 559.978 3.18271 -2.002545 1.38448heptadecane 575.375 3.21826 -2.04 1.38octadecane 590.023 3.24741 -2.048039 1.36245nonadecane 603.989 3.27626 -2.06 1.35eicosane 617.415 3.31181 -1.02218 1.34878

Cox Equation

ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2)

Tm = 449 K sln

gHm/R intercept r2

tetradecane -6393.895 14.1610.01 0.9989

pentadecane -6787.973 14.5970.01 0.9994

hexadecane -7251.562 15.1900.01 0.9996

heptadecane -7612.665 15.5870.01 0.9996

octadecane -8014.871 16.0700.01 0.9996

nonadecane -8457.474 16.6400.01 0.9996

eicosane -8919.685 17.2570.01 0.9995

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

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?

ln(1/ta)

-13 -12 -11 -10 -9 -8 -7

ln(p

/p o)

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

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.

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.

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.

Suppose a mixture of the following n-alkanes were analyzed by gas chromatography:

Retention Times for C17 to C23

T/K 493.8 498.9 503.8 508.9 513.9 518.9 523.9t/min

methylene chloride1.721 1.747 1.746 1.765 1.779 1.792 1.816

heptadecane2.974 2.849 2.722 2.624 2.556 2.472 2.435

octadecane3.477 3.276 3.093 2.941 2.83 2.712 2.645

nonadecane4.182 3.88 3.61 3.375 3.202 3.035 2.926

eicosane5.144 4.685 4.295 3.952 3.695 3.459 3.294

heneicosane6.496 5.826 5.255 4.743 4.368 4.034 3.787

docosane8.37 7.392 6.56 5.811 5.275 4.799 4.44

tricosane10.923 9.498 8.295 7.232 6.468 5.798 5.288

C17 to C23.Tm = 508.8 K sln

gHm/R intercept r2

heptadecane -6108.278.2 12.1480.008 0.9992octadecane -6489.963.8 12.5840.006 0.9995nonadecane -6901.058.7 13.0770.006 0.9996eicosane -7270.060.5 13.4960.006 0.9996heneicosane -7670.965.3 13.9740.006 0.9996docosane -8064.571.6 14.4390.007 0.9996tricosane -8451.173.9 14.8970.008 0.9996

A plot of ln(1/ta) vs 1/T results in

C17 to C23

slngHm(508 K) l

gHm (298.15 K) lgHm (298.15 K)

(lit) (calc)heptadecane 50.8 86.5 86.42.octadecane 54.0 91.4 91.42.2nonadecane 57.4 96.4 96.72.3eicosane 60.4 101.8 101.62.4heneicosane 63.8 106.82.5docosane 67.0 111.92.7tricosane 70.3 117.02.8

lgHm (298.15 K) = (1.570.04) sln

gHm(Tm) – (6.660.30); r2 = 0.9985

Enthalpies of transfer from solution to the gas phase at T = Tm/kJ.mol-1

50 55 60 65 70 75 80 85

Exp

erim

enta

l vap

orza

tion

ent

halp

y at

T =

298

.15

K/ k

J. mol

-1

60

70

80

90

100

110

120

130

140

150

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).

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. Data 2004, 49, 77-85

Chickos, J. S.; Hanshaw, W. J. Chem. Eng. Data 2004, in press.

N, number of carbon atoms

0 5 10 15 20 25 30 35 40

lg Hm(2

98.1

5 K

)/ k

J. mo

l-1

0

20

40

60

80

100

120

140

160

180

200

220

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.

1/T/K

0.0016 0.0020 0.0024 0.0028 0.0032 0.0036

ln(p

/po)

-30

-25

-20

-15

-10

-5

0

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.

1/T/K

0.0016 0.0020 0.0024 0.0028 0.0032 0.0036

ln(p

/po)

-40

-35

-30

-25

-20

-15

-10

-5

0

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.

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

Compounds 10-8A 10-6B C Dheneicosane 1.9989 -2.9075 -98.135 6.6591docosane 2.1713 -3.1176 110.72 6.5353tricosane 2.3386 -3.3220 310.77 6.4198tetracosane 2.5072 -3.5286 530.15 6.2817pentacosane 2.6738 -3.7307 741.19 6.1496hexacosane 2.8244 -3.9193 910.53 6.0704heptacosane 3.0092 -4.1253 1198.8 5.8109octacosane 3.1389 -4.3120 1279.4 5.8835nonacosane 3.2871 -4.5043 1431.2 5.8413triacontane 3.4404 -4.6998 1601.6 5.7696

ln(p/po) = AT -3 + BT -2 + CT -1 + D

Compounds 10-8A 10-6B C Dhentriacontane 3.6037 -4.9002 1791.2 5.6790dotriacontane 3.7524 -5.0921 1947.2 5.6300tritriacontane 3.8983 -5.2809 2098.0 5.5850tetratriacontane 4.0435 -5.4679 2249.5 5.5370pentatriacontan 4.1746 -5.6480 2363.8 5.5436hexatriacontane 4.3320 -5.8432 2553.2 5.4470heptatriacontane 4.4890 -6.0370 2743.2 5.3470octatriacontane 4.6330 -6.2230 2891.9 5.3040

ln(p/po) = AT -3 + BT -2 + CT -1 + D

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. Data 1989, 34, 149-56;cMorgan, D. L.; Kobayashi, R. Fluid Phase Equil. 1994, 97, 211-242; d“conformal” fit to the Wagner equation; eexperimental values.

A Comparison of the Vapor Pressure and Vaporization Enthalpy of Octacosane Obtained by Correlation Gas Chromatography with Literature Values.

T/K ln(p/po) ln(p/po)b ln(p/po)c ln(p/po)d ln(p/po)e lgHm(T)a l

gHm(T) from ln(1/ta)a

docosane463 -5.6 -5.5 85.8 85.2c

docosane417.8 -8.1 -8.0 92.6 92.7e

docosane417.8 -8.1 -8.0 92.6 91.7d

tetracosane463 -6.5 -6.5 93.1 93.3c

tetracosane417.8 -9.2 -9.0 100.2 121.4e

tetracosane417.8 -9.2 -9.2 100.2 102.2d

hexacosane417.8 -10.3 -10.3 108.6 109.2e

octacosane417.8 -11.5 -11.4 116.7 114.3b

octacosane417.8 -11.5 -11.4 116.7 116.6c

octacosane417.8 -11.5 -11.5 116.7 128.9e

athis work; bChirico, R. D.; Nguyen, A.; Steele, W. V.; Strube, M. M. J. Chem. Eng. Data 1989, 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 Letters 1981, 14, 1335-1349.

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 l

gH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po)

TriacontaneMazee9 535.5 100.0 102.5 -2.5 -5.34 -5.39 0.0PERT212,c 535.5 103.3 102.5 0.8 -5.34 -5.39 0.05Francis and Wood8 549.7 102.6 100.9 1.7 -4.53 -4.80 0.27PERT212,c 549.7 101.0 100.9 -0.9 -4.75 -4.80 0.05Piacente et al.10 454 143.2 117.2 26.0 -9.6 -9.82 0.27PERT212,c 298.15 155.4 152.3 3.1 -28.9 -28.8 -0.10

HentriacontaneMazee9 535.7 105.0 105.9 -0.90 -5.69 -5.71 0.02PERT212,c 535.7 106.6 105.9 0.7 -5.65 -5.71 0.06Piacente et al.10 450 146.0 121.8 24.2 -10.4 -10.64 0.24PERT212,c 298.15 160.6 157.3 3.3 -30.0 -29.8 -0.20

DotriacontanePiacente et al.10 456 147.1 124.5 22.6 -10.2 -10.6 0.42PERT212,c 456 125.0 124.5 0.5 -10.58 -10.6 0.02PERT212,c 298.15 165.9 162.5 3.4 -31.1 -31.0 -0.10

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 l

gH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po)

TritriacontanePiacente et al.10 458 148.0 128.0 20.0 -10.6 -10.95 0.34PERT212,c 458 128.4 128.0 0.4 -10.89 -10.95 0.06PERT212.c 298.15 171.2 167.6 3.6 -32.2 -32.1 -0.1

TetratriacontaneMazee9 548.2 107.9 113.6 -5.7 -5.9 -6.1 0.16PERT212,c 548.2 114.3 113.6 0.7 -6.0 -6.1 0.1Francis and Wood8 584.4 140.2 107.6 32.6 -4.38 -4.31 -0.07PERT212,c 584.4 107.9 107.6 0.3 -4.5 -4.38 0.12Piacente et al.10 471 152.0 128.9 23.1 -10.1 -10.5 0.40PERT212,c 298.15 176.4 172.7 3.7 -33.3 -33.2 -0.1

PentatriacontaneMazee9 561.3 111.5 114.6 -3.1 -5.66 -5.81 0.15PERT212,c 561.3 115.2 114.6 0.6 -5.70 -5.81 0.11PERT212,c 298.15 181.7 178.0 3.7 -34.4 -34.3 -0.1

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 l

gH(Tm)blgH(Tm) ln(p/po)a ln(p/po)b ln(p/po)

HexatriacontaneMazee9 557.7 114.9 118.3 -3.4 -6.17 -6.26 0.091PERT212,c 557.7 119.0 118.3 0.7 -6.14 -6.26 0.12Piacente et al.10 484 157.0 133.4 23.6 -9.98 -10.4 -0.42PERT212,c 298.15 186.9 182.8 4.1 -35.4 -35.4 -0.1

HeptatriacontanePiacente et al.10 491 155.0 135.2 19.8 -9.88 -10.3 -0.42PERT212,c 491 136.0 135.2 0.8 -10.2 -10.3 0.1PERT212,c 298.15 192.1 187.5 4.6 -36.5 -36.4 -0.1

OctatriacontanePiacente et al.10 491 160.0 138.8 21.2 -10.3 -10.7 -0.4PERT212,c 491 139.6 138.8 0.8 10.58 -10.7 0.12PERT212,c 298.15 197.3 192.6 4.7 -37.6 -37.5 -0.1aLiterature value. bThis work. cCalculated using PERT2.

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

Table. Vaporization, Solid-Liquid Phase Change, and Sublimation Enthalpies at T = 298.15 K.l

gHm tpceHm cTfus tpceHm cr

gHm

(298.15 K) Kc (298.15 K)d (298.15 K)e

heneicosane 106.82.5a 63.42.1 313.2 61.92.1 168.73.3docosane 111.92.7a 77.12.1 316.8 75.22.2 187.63.5tricosane 1172.8a 75.53.9 320.4 73.14.0 190.14.9tetracosane 121.92.8a 86.13.6 323.6 83.33.7 205.24.6pentacosane 126.82.9a 84.43.0 326.3 81.23.2 208.04.3hexacosane 131.73.2a 93.94.4 329.2 90.24.5 221.95.6heptacosane 135.63.3a 89.57.1 331.7 85.47.2 221.07.9octacosane 141.94.9a 100.33.8 334.2 95.74.0 237.66.4nonacosane 147.15.1a 97.93.3 336.2 92.93.6 240.66.3triacontane 152.35.3a 105.16.7 338.2 99.66.9 251.98.7hentriacontane 157.31.2b 109.9 341.1 103.9 261.1dotriacontane 162.51.4b 117.74.8 342.5 111.35.2 273.75.4tritriacontane 167.61.4b 113.58.8 344.3 106.69.0 274.29.1tetratriacontane 172.76b 127.46.3 345.6 120.16.7 292.89.0pentatriacontane 178.19.2b 129.04.3 347.7 121.24.9 299.210.4hexatriacontane 182.99.4b 128.89.6 348.9 120.69.9 303.513.7heptatriacontane 187.69.6b 137 349.8 128.4 316.0octatriacontane 192.79.8b 136.7 351.7 127.6 320.3

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.

Can the vapor pressure of the n-alkanes be used to evaluate vapor pressures of PAHs?Retention Times for Some n-Alkanes and PAHsT/K 398.2 403.2 408.2 413.2 418.2 423.2 428.2

t/minCH2Cl2 2.83 2.839 2.851 2.862 2.874 2.886 2.9decane 4.217 4.033 3.884 3.76 3.66 3.575 3.514dodecane 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 4.955biphenyl 16.115 13.9 12.111 10.68 9.622 8.542 7.80tetradecane

17.402 14.716 12.594 10.928 9.622 8.542 7.711pentadecane

28.148 23.196 19.334 16.336 13.993 12.089 10.644

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, biphenyldecane -4651.538 11.360.01 0.9996naphthalene -4862.041 10.640.01 0.9996dodecane -5439.539 12.130.01 0.9974biphenyl -5659.152 11.630.01 0.9958tetradecane -6306.249 13.170.01 0.9996pentadecane -6744.150 13.720.01 0.9997

Table. Vaporization Enthalpies of Some PAHs in kJ.mol-1

slnvHm(413.2 K) l

gHm (298.15 K) lgHm (298.15 K)

(lit) (calc)decane 38.67 51.4 52.52.4dodecane 45.22 61.5 61.72.8naphthalene 40.42 54.92.5biphenyl 47.05 64.32.9tetradecane 52.43 71.7 72.03.3pentadecane 56.07 76.8 77.13.5

lgHm (298.15 K) = (1.4190.062) sln

gHm(Tm) – (2.420.93); r2 = 0.9925

lgHm(298.15 K)(lit)a l

gHm(298.15 K)

Naphthalene Summary 55.71.0 54.91.6b

biphenylSummary 65.52.2 64.32.9b

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 Acta 1999, 331, 93-204; bthis work.

NaphthaleneWagner Equationln(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/kPa A 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

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 -6.30naphthalene -5.66 -8.07dodecane -6.11 -8.63 -8.63biphenyl -7.35 -10.17tetradecane -7.98 -10.94 -10.96pentadecane -8.90 -12.08 -12.11

ln(p/po)calc = (1.2460.020) ln(1/ta)) – 1.0130.078; r2 = 0.9990

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

C12H10 biphenyl -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.