Adventures in Thermochemistry
James S. Chickos*
Department of Chemistry and Biochemistry
University of Missouri-St. Louis
Louis MO 63121
E-mail:
jsc@umsl.edu
6
Previously we concluded the following:
1. The sum of the vaporization enthalpy and the enthalpy of
interaction with the column at ~660 K show curvature
suggesting an approach to a limiting value.
2. Boiling temperatures obtained from vapor pressure
extrapolations obtained by correlation also appear to show
curvature and are modeled by a hyperbolic function
reasonably well.
What about vaporization enthalpies?
Evaluation of Vaporization Enthalpies
Basic Considerations in Using Gas Chromatography
In gas chromatography, the time a compound spends on the column (ta) is inversely
proportional to the compounds vapor pressure on the column. Therefore, the vapor
pressure p of a compound is proportional to 1/ta.
If 1/ta is proportional to vapor pressure, then for chromatograms run isothermally, a
plot of ln(to/ta) versus 1/T (K-1) over a 30 K temperature range, where to is the
reference time, 1 min, should result in a straight line with a negative slope equal to
the enthalpy of transfer from the stationary phase of the column to the gas phase
divided by the gas constant, slngHm(Tm)/R.
slngHm(Tm) = lgHm(Tm) + slnHm(Tm)
Provided suitable standards are available, enthalpies of transfer values
measured at Tm are also found empirically to correlate linearly with the
vaporization enthalpies of standards evaluated at any temperature,
including T = 298.15 K.
The vaporization enthalpies calculated by interpolation are reliable since
the standards provide reasonable temperature adjustments due to heat
capacity differences.
Vaporization enthalpies evaluated by extrapolation are not likely to be
as well compensated for temperature.
Evaluation of Vaporization Enthalpies: Previous Work
Peacock and Fuchs measured the enthalpies of transfer from the stationary phase of
the column to the gas phase on a packed silicone oil column and the measured the
enthalpy of solution in silcone oil (DC200). They found that:
slngHm(T)GC ≈ lgHm(Tm)OM + slnHm(Tm)sol where OM = other means
Several reasons are possible for the small differences between the two values
observed that include;
i. the approximate nature of their heat capacity adjustments
ii interaction of the analyte with the column not truly a solution property but more a
surface property
iii gas chromatographic results are not a true equilibrium property due to flow
lgHm(298.15)GC = 1.03 lgHm(298.15)OM - 0.864
r2 = 0.9999
Peacock, L. A.; Fuchs, R. Enthalpy of Vaporization Measurements by Gas Chromatography. J. Am.
Chem. Soc. 1977, 99, 5524-5.
A study of the effect of flow rate on the vaporization enthalpy and enthalpy of transfer
RTX-5 0.53 mm ID column; 30 m
DB-5 MS 0.25 mm ID column 30 m
The enthalpy of transfer appears to decrease slightly with decreasing flow. From the results of
Peacock and L. A.; Fuchs:
lgHm(298.15)GC = 1.03 lgHm(298.15)om - 0.864
lgHm(298.15)GC >lgHm(298.15)om when lgHm(298.15)om > 27.5 kJ·mol-1
The vaporization enthalpies of the compounds examined ranged from 41 to 80.3 kJ·mol-1
At zero flow rate the slope of 1.03 would probably been smaller since slngHm(T)GC would have
been slightly smaller.
Adjustments of Phase Change Enthalpies to T = 298.15 K
1.
Vapor pressure equations known to extrapolate well with temperature,
require no temperature adjustments..
2.
Vaporization enthalpy measured at elevated temperatures do require
adjustments for heat capacity differences between the liquid and gas
phases.
lgHm(298.15 K)/(kJ·mol-1) = lgHm (Tm)/kJ·mol-1 +
[(10.58 + 0.26·Cp(l)/(J·mol-1·K-1))( Tm/K - 298.15 K)]/1000
3.
Sublimation enthalpy adjustments
crgHm(298.15 K)/(kJ·mol-1) = crgHm (Tm)/kJ·mol-1 +
[(0.75 + 0.15·Cp(cr)/(J·mol-1·K-1))( Tm/K - 298.15 K)]/1000
4.
Fusion enthalpy adjustments
crlHm (298.15 K)/(kJ·mol-1) = crlHm (Tfus)/kJ·mol-1 +
[(0.15 Cp(cr)-0.26 Cp(l))/(J·mol-1·K-1) -9.83)] [Tfus/K-298.15]/1000
5. lgHm (298.15 K) = ∆crgHm (298.15 K) - ∆crlHm (298.15 K)
Heat Capacity Estimations
Cp(cr) and Cp(l) values were estimated by group additivity.
Carbon groups are identified by the the hybridization at carbon and the number
of H atoms attached: primary, 3; secondary, 2; tertiary 1; quaternary, 0.
Distinctions are made between aliphatic, and cyclic carbons and between
aromatic and cyclic unsaturated carbon atoms.
Groups values are available for a variety of functional groups.
A distinction is made for cyclic and acyclic functional groups
Acyclic
Groups
Retention Times (min) as a Function of
Temperature
T/K
354
359
364
369
374
379
384
Retention Times (t)
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
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
ln(to/ta)= - slngHm/RT + ln(Ai)
Compound
n-octane
1-nonene
n-decane
naphthalene
n-dodecane
n-tridecane
ln(to/ta)= (-32336/RT) + (11.064 ± 0.008)
ln(to/ta)= (-35108/RT) + (11.159 ± 0.010)
ln(to/ta)= (-38973/RT) + (11.655 ± 0.010)
ln(to/ta)= (-41281/RT) + (11.176 ± 0.008)
ln(to/ta)= (-46274/RT) + (12.685 ± 0.010)
ln(to/ta)= (-50036/RT) + (13.232 ± 0.010)
r2=0.9995
r2=0.9993
r2=0.9994
r2=0.9997
r2=0.9996
r2=0.9997
slngHm(Tm) = lgHm(Tm) + slnHm(Tm)
to = 1 min Tm = 368 K
Vaporization enthalpies (J.mol-1)
slngHm(368 K)
lgHm(298.15 K)
lit
lgHm(298.15 K)
Calcd
octane
32336
41560
41857 ± 1000
nonene
35108
45500
45667 ± 1000
decane
38973
51420
51310 ± 1100
naphthalene
41281
55650
54411 ± 1100
dodecane
46274
61520
61707 ± 1200
tridecane
50036
66680
67064 ± 1220
lgHm(298.15 K) = (1.416  0.0186)slngHm(368 K) – (4061 791); r2 = 0.9996
naphthalene lgHm(298.15 K) 54.4±1.1 + crlHm(298.15 K) 16.9±0.7
= crgHm(298.15 K) 71.3±1.3 kJ.mol-1 (recommended value 72.6±0.3)
Applications of the The Correlation-Gas Chromatographic Method
Objectives: To go where no one else has gone
1)
Evaluation of the vaporization enthalpies of large molecules
A: Determination of Vaporization Enthalpy
• Experimental retention times for n-C14 to C20:
T/K
434.3
439.3
444.2
449.1
454.1
459
463.8
t/min
methylene
chloride
tetradecane
1.251
1.215
1.246
1.216
1.222
1.228
1.249
3.039
2.695
2.485
2.29
2.145
2.022
1.942
pentadecane
hexadecane
4.107
5.827
3.558
4.933
3.205
4.344
2.887
3.807
2.643
3.409
2.451
3.084
2.288
2.805
heptadecane
octadecane
8.329
12.283
6.907
9.994
5.939
8.403
5.097
7.065
4.47
6.071
3.959
5.265
3.54
4.624
nonadecane
eicosane
18.549
28.345
14.836
22.305
12.2
17.935
10.075
14.57
8.487
12.04
7.219
10.076
6.211
8.522
Enthalpy of Transfer Determination for
Hexadecane
• ln(to/ta) = -gslnHm(Tm)/R*1/T + intercept
• slng(Tm) * 8.314 J mol-1 = 60.308 kJ mol-1
Hexadecane
0.4
ln (1/ta)
0.2
0.0
-0.2
-0.4
-0.6
0.00216 0.00218 0.00220 0.00222 0.00224 0.00226 0.00228 0.00230
1/T (K)
• 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) = -gslnHm(Tm)/R*1/T + intercept
• Vaporization enthalpies (in kJ mol-1) of the nalkanes (C14 to C20):
tetradecane
slngHm(449 K) lgHm (298.15 K) lgHm (298.15 K)
(lit)
(calc)
53.2
71.7
71.81.0
pentadecane
56.4
76.8
76.51.0
hexadecane
60.3
unknown
81.4
821.1
?
heptadecane
63.3
86.5
86.31.2
octadecane
66.6
91.4
91.11.3
nonadecane
70.3
96.4
96.41.4
eicosane
74.2
101.8
101.91.4
lgHm (298.15 K) = (1.4240.019) slngHm(Tm) – (3.980.35); r 2= 0.9991
Experimental vaporisation enthalpy, kJ /mol (T = 298.15 kJ/mol)
Correlations between vaporization enthalpy at T = 298.15 K
against the enthalpy of transfer
105
100
95
90
85
80
75
70
50
55
60
65
70
75
Enthalpies of transfer from solution to the gas phase, kJ/mol (T = Tm)
80
Some Details Concerning the Advantages and Limitations of
Correlation-Gas Chromatography
1. The method works well on hydrocarbons and hydrocarbon
derivatives regardless of the hydrocarbon structure
2. With hydrocarbon derivatives, standards need to be chosen with the
same number and type of functional group as the compound(s) to be
evaluated unless demonstrated otherwise
3. Measurements can be made on small sample sizes and purity is not
generally an issue
4. Correlation of the standards needs to be documented experimentally
5. The results are only as good as the quality of the standard data
6. Vaporization enthalpies and liquid vapor pressures are obtained for
materials that are solid at room temperature
7. Correlations of enthalpies of transfer with vaporization enthalpies
at T = 298.15 K is arbitrary. The correlation can be with vaporization
enthalpies at any temperature.
Applications of correlation gas chromatography for the evaluation of the vaporization
enthalpies of large n-alkanes.
• Reliable vaporization enthalpies are available up to eicosane
• Using the available data from heptadecane to eicosane, vaporization enthalpies
were evaluated for C21,C22, C23. These values in turn were used to evaluate the
larger n-alkanes in a stepwise process up to C38, most of which are commercially
available.
• Additionally, a few other larger n-alkanes, C40, C42, C48, C50, and C60 are likewise
commercially available. These were used in conjunction with polywax as
identification standards
• Comparisons of a few of the results with literature values was possible, most
comparisons were with estimations by PERT2a and estimated Antoine Constantsb
aPERT2
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. Morgan, D. L.; Kobayashi, R.
“Extension of Pitzer CSP models for vapor pressures and heats of vaporization to long chain hydrocarbons,”
Fluid Phase Equilibrium 1994, 94, 51-87.
bKudchadker, A.
P.; Zwolinski, B. J. “Vapor Pressures and Boiling Points of Normal Alkanes, C 21 to C100,” J.
Chem. Eng. Data 1966, 11, 253-55.
9000
An Partial Isothermal Chromatogram of Polywax 1000
8000
Intensity
7000
6000
C60
5000
4000
3000
10
20
30
Time / min
A partial isothermal GC trace of a mixture of Polywax 1000
spiked with n-alkanes C42, C50 and C60 run at T = 648 K
Since these vaporization enthalpies were
obtained by extrapolation, it is likely that
the actual curvature is greater as
evaluated by PERT2
400
300
200
g
l Hm (298.15 K) / kJ mol
-1
500
curvature
100
0
0
20
40
60
80
100
N
The vaporization enthalpies at T = 298.15 for C5 to C92. N represents the
number of carbon atoms. The solid line was derived using the recommended
vaporization enthalpies of C5 to C20 The empty circles are values calculated
values using the program PERT2 The solid circles are values evaluated from
correlations of slngHm(Tm) with lgHm(298.15K).
Vapor pressures and Vaporization Enthalpies of the n Alkanes from C78 to C92 at T = 298.15 K by
Correlation–Gas Chromatography, Chickos, J. S.; Lipkind, D. J. Chem.Eng. Data 2008, 53, 2432–2440.
220
200
sln Hm (Tm) / kJ mol
-1
400
300
g
200
g
l Hm (298.15 K) / kJ mol
-1
500
180
160
140
100
120
0
0
20
40
60
80
N
Vaporization Enthalpies at T/K = 298.15
100
100
40
50
60
70
80
90
N
Enthalpies of transfer at T/K = 676
A comparison of the curvature observed in vaporization enthalpy vs the enthalpy
of transfer
More curvature is observed with vaporization enthalpy than with enthalpy of
transfer
100
The Vaporization Enthalpies of the n-Alkanes at T = 298.15 K As A Function
of the Number of Carbon Atoms, N
N
lgHm(298.15 K)
kJ mol-1
N
lgHm(298.15 K)
kJ mol-1
N
lgHm(298.15 K)
kJ mol-1
N
lgHm(298.15 K)
kJ mol-1
5
26.42
21
106.8±2.6
36
182.8±5.5
64
315.4±2.9
6
31.52
22
111.9±2.7
37
187.5±5.6
66
324.0±3.0
7
36.57
23
117.0±2.8
38
192.5±5.7 b
68
331.9±3.0
8
41.56
24
121.9±2.8
40
203.5±2.9
70
340.3±3.1
9
46.55
25
126.8±2.9
42
213.5±2.1
72
348.4±3.2
10
51.42
26
131.7±3.3
44
223.7±2.3
74
356.2±3.3
11
56.58
27
135.6±3.3
46
233.3±2.3
76
364.3±3.3
12
61.52
28
141.9±5.1
48
243.0±2.4
78
372.1±1.4
13
66.68
29
147.1±5.3
50
252.5±2.5
80
379.6±2.2
14
71.73
30
152.3±5.3
52
261.8±3.6
82
387.2±2.4
15
76.77
31
157.2±1.4 b
54
271.0±3.7
84
394.0±3.2
16
81.35
32
162.5±1.4
56
279.7±3.8
86
402.2±2.6
17
86.47
33
167.6±1.4
58
288.5±3.9
88
409.3±3.9
18
91.44
34
172.7±1.5
60
299.9±3.0
90
416.5±4.3
19
96.44
35
178.1±5.4 b
62
306.8±2.8
92
424.5±4.5
How is it possible to measure a vaporization enthalpy greater
that a C-C bond strength (~335 kJmol-1)?
Vapor pressures and vaporization enthalpies for C14 to C20 are known over a large
temperature range. glHm(Tm) and ΔslngHm(Tm) correlate at any temperature
Values of at ΔslngHm(449 K) and ΔlgHm(449 K) on an SPB-5 Column
Tm = 449 K
-slope/T
intercept
ΔslngHm(449 K)
kJmol-1
ΔlgHm(449 K)
kJmol-1
lit1
tetradecane
pentadecane
hexadecane
heptadecane
octadecane
nonadecane
eicosane
6393.8±95
6787.9±73
7251.5±62
7612.6±65
8014.8±71
8457.4±74
8919.6±85
14.161±0.01
14.597±0.01
15.190±0.01
15.587±0.01
16.070±0.01
16.640±0.01
17.257±0.01
53.2±0.8
56.4±0.6
60.3±0.5
63.3±0.5
66.6±0.6
70.3±0.6
74.2±0.7
56.92
60.71
64.50
68.19
72.11
76.01
79.81
glHm(449 K)/kJmol-1 = (1.0980.0133) slngHm(449 K) - (1.390.25)
calcd (eq 1)
57.0±0.8
60.6±0.8
64.8±0.9
68.1±0.9
71.8±1.0
75.8±1.0
80.1±1.1
r2 = 0.9993
(1)
slngHm(Tm) = lgHm(Tm) + slnHm(Tm)
slnHm(Tm) must be of opposite sign to lgHm(Tm)
1Ruzicka,
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.
Values of at ΔslngHm(509K) and ΔlgHm(509 K) on an SPB-5 Column
-slope T
intercept
ΔslngHm(509 K)
kJ⋅mol-1
heptadecane
octadecane
nonadecane
eicosane
heneicosane
docosane
tricosane
6108.2±78.2
6489.9±63.8
6901.0±58.7
7270.0±60.5
7670.9±65.3
8064.5±71.6
8451.1±73.9
12.148±0.008
12.584±0.006
13.077±0.006
13.496±0.006
13.974±0.006
14.439±0.007
14.897±0.008
50.8±0.7
54.0±0.5
57.4±0.5
60.4±0.5
63.8±0.5
67.1±0.6
70.3±0.7
ΔlgHm(509 K)
kJ⋅mol-1
lit1,2
calcd
62.831
66.341
69.741
73.071
76.662
80.132
83.542
lgHm(509 K)/kJmol-1 = (1.0620.004) slngHm(509 K) + (8.94.020.07)
62.9±0.3
66.2±0.3
69.8±0.3
73.1±0.3
76.6±0.3
80.1±0.4
83.5±0.4
r2 = 0.9999
1Ruzicka,
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, 139.
2Chickos,
J. S.; Hanshaw, W. Vapor pressures and vaporization enthalpies of the n-alkanes from C21-C30 at
T = 298.15 K by correlation–gas chromatography, J. Chem. Eng Data 2004, 49, 77-85.
Enthalpies of Condensation: -slngHm(T), - lgHm(T) and slnHm(T) as a Function of
Temperature
-ΔslngHm(449 K)
tetradecane
pentadecane
hexadecane
heptadecane
octadecane
nonadecane
eicosane
-53.2±0.8
-56.4±0.6
-60.3±0.5
-63.3±0.5
-66.6±0.6
-70.3±0.6
-74.2±0.7
-ΔslngHm(509 K)
heptadecane
octadecane
nonadecane
eicosane
heneicosane
docosane
tricosane
-50.8±0.7
-54.0±0.5
-57.4±0.5
-60.4±0.5
-63.8±0.5
-67.1±0.6
-70.3±0.7
-ΔlgHm(449 K) (lit)
kJ⋅mol-1
-56.92
-60.71
-64.5
-68.19
-72.11
-76.01
-79.81
-ΔlgHm(509 K) (lit)
kJ⋅mol-1
-62.83
-66.34
-69.82
-73.07
-76.66
-80.13
-83.54
ΔslnHm(449 K)
3.7±0.8
4.3±0.6
4.2±0.5
4.9±0.5
5.5±0.6
5.7±0.6
5.6±0.7
ΔslnHm(509 K)
12.0±0.7
12.3±0.5
12.4±0.5
12.7±0.5
12.9±0.5
13.0±0.6
13.2±0.7
gslnHm(Tm) = lgHm(Tm) + slnHm(Tm)
18
16
slnHm(Tm) / kJ mol
-1
14
12
10
8
6
4
2
0
300
350
400
450
500
550
600
T/K
Figure. The effect of temperature, 450, 509, 539 K, on the magnitude of
slnHm(T/ K). ■, eicosane; ●, nonadecane.
Conclusions:
1. The enthalpy of interaction of analyte with the column is
endothermic and a function of temperature; this allows access
to the measurement of large vaporization enthalpies
2. The overall enthalpy of condensation on the column is still
highly exothermic, just less so then might have been imagined
Graduate Students
William Hanshaw
Patamaporn Umnahanant
Hui Zhao
Dmitry Lipkind
Visiting Graduate Students
Manuel Temprado, Instituto de Química Física “Rocasolano”, Madrid 28006, Spain
Visiting Faculty and Collaborators
Maria Victoria Roux, On leave from the Instituto de Química Física “Rocasolano”,
Madrid 28006, Spain
Sergey Verevkin, University of Rostock, Rostock Germany
Brad Hart
Jack Uang Don Hesse
Sid Kamath Sarah Hosseini