Adventures in Thermochemistry
James S. Chickos*
Department of Chemistry and Biochemistry
University of Missouri-St. Louis
Louis MO 63121
E-mail: jsc@umsl.edu
5
Union Station STL
Previously we concluded the following:
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?
Applications of Correlation Gas Chromatography
Vapor Pressure
Requirements: Vapor pressures of the standards preferably as a
function of temperature over a range of temperatures
Applications of Correlation Gas Chromatography
Vapor Pressure
Using the following series of hydrocarbons as examples:
Retention Times as a Function of Temperature
T/K
354
359
364
369
374
379
384
Retention Times (t/min)
methane
0.563
0.564
0.583
0.579
0.579
0.580
0.585
octane
1.577
1.424
1.301
1.196
1.115
1.03
0.975
1-nonene
2.664
2.319
2.052
1.827
1.661
1.484
1.367
decane
5.389
4.512
3.857
3.31
2.921
2.517
2.238
naphthalene
18.131
14.815
12.307
10.269
8.763
7.384
6.32
dodecane
21.776
17.319
14.038
11.452
9.591
7.912
6.631
tridecane
44.439
34.668
27.458
21.914
17.921
14.546
11.94
Solvent: CH2Cl2
ta = ti –tCH4
Plots of ln(to/ta) vs 1/T
2
1
Ln(1/tc)
0
-1
-2
-3
-4
-5
0.00255
0.00260
0.00265
0.00270
0.00275
0.00280
0.00285
1/T, K-1
A plot of natural logarithm of the reciprocal adjusted retention times ln(to/ta) for
(top to bottom): ,n- octane;  , 1-nonene; , n-decane;  , naphthalene;
 , n-dodecane; , n-tridecane as a function of 1/T; to = 1 min.
Equations resulting from a linear regression
of ln(to/ta) versus (1/T)K-1
Compound
n-octane
1-nonene
n-decane
naphthalene
n-dodecane
n-tridecane
to = 1 min
ln(to/ta)= - slngHm/RT + ln(Ai)
ln(to/ta)= (-32336/RT) + (11.064)
ln(to/ta)= (-35108/RT) + (11.159)
ln(to/ta)= (-38973/RT) + (11.655)
ln(to/ta)= (-41281/RT) + (11.176)
ln(to/ta)= (-46274/RT) + (12.685)
ln(to/ta)= (-50036/RT) + (13.232)
r2=0.9995
r2=0.9993
r2=0.9994
r2=0.9997
r2=0.9996
r2=0.9997
A Plot of ln(p/po)exp vs ln(to/ta)
-3
octane
-4
ln(p/po) experimental
-5
-6
decane
-7
-8
dodecane
-9
tridecane
-10
-11
-8
-7
-6
-5
-4
-3
-2
-1
ln(to/ta), where to = 1 min
A plot of experimental vapor pressures ln(p/po) against ln(to/ta) at T =
298.15 K; to = 1 min; po= 101 kPa
Results of Correlating ln(to/ta) with ln(p/po) at T = 298.15 K
slngHm(368 K) ln (A)
octane
1-nonene
decane
naphthalene
dodecane
tridecane
-32336
-35108
-38973
-41281
-46274
-50036
11.064
11.159
11.655
11.176
12.685
13.232
ln(to/ta) ln(p/po)
lita
-1.98 -3.99
-3.00
-4.07 -6.32
-5.48
-5.98
-8.63
-6.95 -9.79
ln(p/po) ln(p/po)
calc
lit
-3.95
-5.15
-4.96b
-6.39
-8.04
-7.98c
-8.63
-9.76
ln(p/po) = (1.1820.015) ln(to/ta) -(1.53 0.059); r2 = 0.9987
Vapor pressures for naphthalene are for the liquid
aRuzicka,
K.; Majer, V. J. Phys. Chem. Ref. Data 1994, 23, 1-39;
bPhysical
Properties of Chemical Compounds II, Dreisbach, R. R. Advances in Chemistry
Series 22, ACS, Washington: DC.
cChirico,
1461-4.
R. D.; Knipmeyer, S. E.; Nguyen, A. Steele, W. V. J. Chem. Thermodyn. 1993, 25,
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)
Vapor Pressures by Gas Chromatography
Vapor pressure of an analyte off a column is inversely proportion to it
adjusted retention, 1/ta.
Why is 1/ta 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?
slngHm(Tm) = lgHm(Tm) + slnHm(Tm)
Daltons Law of Partial Pressures pT = panalyte + pstationary phase = panalyte
Raoult’s Law:: the vapor pressure of component a is equal to the
product of vapor pressure of pure a (pao) times its mole fraction, χ a
pa(obs) = pao·χ a
Since the stationary phase is a polymer, χ a ≈ 1
The effects of slnHm(Tm) are small and compensated by the standards.
Returning to the n-alkanes
Vapor Pressures of the Standards
• literature vapor pressure evaluated using the Cox equationa
• ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2)
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
705
3.41304
-1.8894
1.04575
octacosaneb
po = 101.325 kPa
aRuzicka,
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.
Equations for the temperature dependence of
ln(to/ta) for C14 to C20 where to = 1 min:
Tm = 449 K
slngHm/R
intercept
r2
tetradecane
-6393.895
14.1610.01
0.9989
pentadecane
-6787.973
14.5970.01
0.9994
hexadecane
-7251.562
15.1900.01
0.9996
heptadecane
-7612.665
15.5870.01
0.9996
octadecane
-8014.871
16.0700.01
0.9996
nonadecane
-8457.474
16.6400.01
0.9996
eicosane
-8919.685
17.2570.01
0.9995
ln(to/ta) = -slnHm(Tm)/R*1/T + intercept
Vapor pressures of n-alkanes (C14 to C20) at T = 298.15 K:
ln(to/ta) at
298.15 K
tetradecane
-7.3
ln (p/po) at
298.15 K from
Cox eq.
-10.9
ln (p/po) at
298.15 K from
correlation eq.
-10.9
pentadecane
-8.2
-12.1
-12.1
hexadecane
-9.2
unknown
-13.3
heptadecane
-10.0
-14.3
-14.3
octadecane
-10.8
-15.4
-15.4
nonadecane
-11.8
-16.6
-16.6
eicosane
-12.7
-17.8
-17.8
-13.3
?
ln(p/po) = (1.27  0.01) ln(to/ta) - (1.693  0.048); r 2 = 0.9997
po = 101.325 kPa
Correlation between ln(1/ta) calculated by extrapolation
to T = 298.15 K versus ln(p/po) calculated from the Cox
equation for C14 to C20 (po = 101.325 kPa)
-10
-11
-12
ln(p/po)
-13
-14
-15
-16
-17
-18
-19
-13
-12
-11
-10
ln(1/ta)
-9
-8
-7
ln(p/po) = (1.27  0.01) ln(to/ta) - (1.693  0.048); r 2 = 0.9997
Correlations of Vapor Pressures of Hexadecane from T/K = (298.15 to 500) K
0
-2
ln(p/po)
-4
-6
500 K
-8
-10
-12
-14
0.0018 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036
1/T, K-1
Vapor pressure -temperature dependence for hexadecane;
line: vapor pressure calculated from the Cox equations for C14,
circles; vapor pressures calculated by correlation treating hexadecane as an
unknown and correlating ln(to/ta) with ln(p/po) for C14, C15, C17-C20 as a function
of temperature from T = (298.15 to 500) K.
Normal boiling temperature: 560.2 (expt); 559.9 (calcd)
By a process of extrapolation, vapor pressures of C17 to C20 were used to
evaluate C21 to C23; C19 to C23 were used to evaluate C24 and C25, ...
By such a process of extrapolation, vapor pressure equations were
obtained for C21 through to C38 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 C21 to C38 could be
predicted
Some Available Comparisons With Direct Measurements
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.
a Literature
Experimental vapor pressures for the n-alkanes larger than C38 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
Using vapor pressures calculated from C24 through to C38, values for
C40 through to C76 were evaluated.
PERT2 is a FORTRAN program written by D. L. Morgan in 1996 which includes
parameters for n-alkanes from C1 to C100 and heat of vaporization and vapor
pressure correlations. The parameters for C51 to C100 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).
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.
b
Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of
Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.
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.
The vapor pressures were fit to the following third order
polynomial:
ln(p/po) = A(T/K)-3 + B(T/K)-2 +C(T/K) + D
10-8A
T3
10-6 B
T2
C
T
pentacontane
6.1330
-8.2602
4268.3
5.143
6.5353
dopentacontane
4.8707
-7.4087
1564.8
7.455
310.77
6.4198
tetrapentacontane
5.0959
-7.7167
1772.4
7.410
-3.5286
530.15
6.282
hexapentacontane
5.3213
-8.0192
1997.2
7.326
2.6738
-3.7307
741.19
6.150
octapentacontane
5.5446
-8.3203
2215.7
7.251
hexacosane
2.8244
-3.9193
910.53
6.070
hexacontane
7.3061
-9.8448
5365.4
4.957
heptacosane
3.0092
-4.1253
1198.8
5.811
dohexacontane
6.1197
-9.0298
2863.7
7.000
octacosane
3.1389
-4.3120
1279.4
5.884
tetrahexacontane
6.2051
-9.2215
2812.1
7.149
nonacosane
3.2871
-4.5043
1431.2
5.841
hexahexacontane
6.2905
-9.4126
2761.7
7.295
triacontane
3.4404
-4.6998
1601.6
5.770
octahexacontane
6.3771
-9.5964
2731.5
7.398
hentriacontane
3.6037
-4.9002
1791.2
5.679
heptacontane
6.4622
-9.7833
2688.6
7.527
dotriacontane
3.7524
-5.0921
1947.2
5.630
doheptacontane
6.5473
-9.9677
2650.7
7.646
tritriacontane
3.8983
-5.2809
2098.0
5.585
tetraheptacontane
6.6325
-10.1491
2619.6
7.750
tetratriacontane
4.0435
-5.4679
2249.5
5.537
hexaheptacontane
6.7165
-10.3320
2580.8
7.870
pentatriacontane
4.1746
-5.6480
2363.8
5.544
octaheptacontane
6.9185
-10.6352
2862.6
7.718
hexatriacontane
4.3320
-5.8432
2553.2
5.447
octacontane
7.0339
-10.8450
2927.0
7.731
heptatriacontane
4.4890
-6.0370
2743.2
5.347
dooctacontane
7.1142
-11.0100
2862.8
7.852
octatriacontane
4.6330
-6.2230
2891.9
5.304
tetraoctacontane
7.2562
-11.2545
3066.0
7.726
tetracontane
4.9289
-6.6065
3183.3
5.270
hexaoctacontane
7.3278
-11.4184
2970.3
7.897
dotetracontane
5.1471
-6.9224
3348.9
5.291
octaoctacontane
7.4656
-11.6595
3147.1
7.810
tetratetracontane
5.5011
-7.3467
3778.6
5.117
nonacontane
7.5587
-11.8287
3121.0
7.885
hexatetracontane
5.6451
-7.5992
3810.6
5.224
dononacontane
7.7815
-12.1830
4010.6
6.856
octatetracontane
5.8908
-7.9326
4039.6
5.187
10-8A
T3
10-6 B
T2
C
T
heneicosane
1.9989
-2.9075
-98.135
6.6591
docosane
2.1713
-3.1176
110.72
tricosane
2.3386
-3.322
tetracosane
2.5072
pentacosane
D
D
BT / 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:
1200
1000
800
600
400
200
0
0
20
40
60
80
100
N-2
N = the number of carbon atoms. The solid symbols represent the
experimental and the others the calculated boiling temperatures of C3 to
C92. The dotted line was calculated for the n-alkanes using a limiting
boiling temperature of TB(∞) = 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 TB(∞) = (1217 ± 246) K
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
Rachael Maxwell, Boy friend, Richard Heinze Dmitry Lipkind Darrel Hasty