Table 4. Parameters of the Cox Equation. T b A o 10 3 A 1 10 6 A 2 tetradecane526.691 3.13624-2.063853 1.54151 pentadecane543.797 3.16774-2.0623481.48726 hexadecane559.978 3.18271-2.0025451.38448 heptadecane575.375 3.21826-2.041.38 - PowerPoint PPT Presentation
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Table 4. Parameters of the Cox Equation. Tb Ao 103A1 106A2
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:
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?
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
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
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.
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.