Adventures in Thermochemistry
James S. Chickos*
Department of Chemistry and Biochemistry
University of Missouri-St. Louis
Louis MO 63121
E-mail: jsc@umsl.edu
4
Gateway to the West
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 some small finite
pressure (~1 atm) as the
number of repeat units  .
Can any of this be
experimentally verified?
If vaporization enthalpies at the boiling point attain some
maximum value, then vaporization enthalpies of homologous
series as a function of temperature should show some
curvature as the size increases.
How do known vaporization enthalpies of the n-alkanes at T =
298.15 K behave as a function of the number of carbons?
Literature Vaporization Enthalpies of the n Alkanes
C5 to C20 at T = 298.15 K
100
.
-1
l Hm(298.15 K) kJ mol
120
80
g
60
40
20
4
6
8
10
12
14
16
18
20
22
N, Number of Carbons
lgHm(Tm) = (5.01±0.007)N + (1.487±0.1)
r2 = 0.99997
Ruzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related
Thermodynamic Properties Between the Triple Point and Normal Boiling Temperatures
for n-Alkanes C5-C20. J. Phys. Chem. Ref. Data 1994, 23, 1.
Applications of gas chromatography
The measurement of vaporization enthalpies
A. Calorimetric
B. Vapor pressure dependency on temperature
The measurement of vapor pressure
A. Various static method
B. Effusion methods
C. Transpiration methods
both properties depend on pure samples, moderate quantities (> mg)
Our group has been interested in developing a method that could
circumvent the requirement of sample purity and quantity and
could be applicable in the sub-pascal region
250
Signal Intensity
200
150
100
50
0
0
100
200
300
Time (sec)
400
500
A series of isothermal runs. The compounds are n-alkanes
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.
The amount of time a compound spends on the column, ta, (the adjusted retention
time) is obtained by subtracting the retention time of an non-retained reference (often
the solvent) from the retention time of each analyte.
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)
Both terms are predicted to have the same dependence on size. Coiling of the nalkane decreasing intermolecular interactions will lead to an attenuation of both
slngHm(Tm) and lgHm(Tm).
A plot of ln(to/ta) versus 1/T (K-1)
2
From top to bottom:
docosane
tetracosane
hexacosane
nonacosane
dotriacontane
tetratriacontane
hexatriacontane
octatriacontane
ln(to/ta) where to = 1 min
1
0
-1
-2
-3
-4
-5
0.00188
0.00192
0.00196
0.00200
1/T / K
to = 1 min
ln(to/ta) = -slngHm(Tm)/RT +C
Enthalpies of transfer measured at Tm = 520 K vs the number of carbon atoms
from C21 to C38
1.1e+5
1.0e+5
9.0e+4
8.0e+4
g
sln Hm(520 K) / kJ mol
-1
1.2e+5
7.0e+4
6.0e+4
20
22
24
26
28
30
32
34
36
38
40
N, number of carbon atoms
slngHm(520 K) = (3005±13.1)N+(3054±287);
slngHm(Tm) = lgHm(Tm)+ slnHm(Tm)
r2 = 0.9997
Individual n- alkanes are available commercially for most even
n-alkanes up to C60. In addition, alkanes derived from oligomers
of polyethylene are available up to ~C100
Even Alkanes from Polywax1000
C60
C86
dotetracontane
tetratetracontane
hexatetracontane
octatetracontane
pentacontane
dopentacontane
tetrapentacontane
hexapentacontane
octapentacontane
hexacontane
dohexacontane
tetrahexacontane
hexahexacontane
octahexacontane
heptacontane
doheptacontane
tetraheptacontane
hexaheptacontane
Slope
Intercept
-11790
-12378
-12965
-13532
-14106
-14651
-15197
-15734
-16260
-16782
-17288
-17804
-18324
-18769
-19259
-19736
-20187
-20656
19.069
19.708
20.347
20.955
21.577
22.155
22.736
23.304
23.857
24.403
24.93
25.472
26.02
26.457
26.963
27.451
27.899
28.377
slngHm(653 K) N
kJ mol-1
98.02
102.91
107.79
112.50
117.27
121.80
126.34
130.81
135.18
139.52
143.73
148.02
152.34
156.04
160.11
164.08
167.83
171.73
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
A plot of slngHm(T) against the number of carbon atoms, N for N = 42 to 76.
1.8e+5
2.8e+5
2.6e+5
1.6e+5
-1
sln Hm (653 K) /J mol
1.4e+5
1.2e+5
g
g
sln Hm (653 K) /J mol
-1
2.4e+5
1.0e+5
2.2e+5
2.0e+5
1.8e+5
1.6e+5
1.4e+5
1.2e+5
1.0e+5
8.0e+4
40
45
50
55
60
65
70
75
80
8.0e+4
20
N
The equation of the linear fit:
slngHm(653 K) = (299913)N + (3039286);
r2 = 0.9997.
40
60
80
100
120
140
160
180
N
The equation of the line fit by a second order
polynomial is given by:
slngHm(653 K) (-8.775)N2 +3200.8N - 20915;
r2 = 0.9999.
220
Enthalpies of transfer
kJ/mol as a function of the
number of carbon atoms
from C50 to C92
g
sln Hm (Tm) / kJ mol
-1
200
180
160
140
120
to a third order polynomial
100
40
50
60
70
80
90
100
N
triangles: slngHm(653 K) = (2.12±0.02)N + (16.18±0.73);
r2 = 0.9989
triangles: slngHm(653 K) = -(8.37±0.96)10-3N 2+(3.45±0.14)N –(29.6±5.3); r2 = 0.9998
circles: slngHm(676 K) = (2.12±0.016)N + (12.43±0.92);
0.9909
circles: slngHm(676 K) = -(5.64±0.56)10-3N 2+(2.93±0.08)N –(15.1±2.8);
squares: slngHm(676 K)= (2.12±0.018)N + (11.42±0.78);
squares: slngHm(676 K)= -(7.47±0.42)10-3N 2+(3.24±0.06)N –(29.8±2.3);
r2 =
r2 = 0.9998
r2 = 0.9989
r2 = 0.9999
Conclusions:
Based on the data available, it appears that enthalpies of
transfer at temperatures below the boiling temperature do
show some curvature as a function of carbon number.
Whether this is due to changes in lgHm(Tm) or slnHm(Tm)
or both is not known from these results.
Richard Heinze
Hui Zhao
Tom Murphy
William Hanshaw
Hui Zhao
William Hanshaw
Patamaporn Umnahanant (T)
T