Adventures in Thermochemistry
James S. Chickos*
Department of Chemistry and Biochemistry
University of Missouri-St. Louis
Louis MO 63121
E-mail: jsc@umsl.edu
Eads Bridge
1867-72
6
Based on the behavior observed in the melting
temperatures of homologous series, we wondered how
boiling temperatures varied as a function of size?
Question: How do the
boiling temperatures
of the n-alkanes vary
as a function of the
number of repeat
units?
800
700
600
TB
500
The plot of the
boiling temperatures
of the n-alkanes as a
function of the
number of repeat
units.
400
300
200
0
5
10
15
Number of repeat units, n
20
25
Modeling boiling temperature
Exponential functions have previously been used to model the
behavior observed for the n-alkanes.
TB (M )  TB ()  α * e
bM 2 / 3
1
M = molecular weight; , b = constants
TB = 138 C1/2;
C = number of carbons
2
Is there any basis for expecting the boiling temperature of
an infinite alkane to be finite?
1. Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem. 1961 65, 1050-1052.
2. Partington, J. An Advanced Treatise on Physical Chemistry, Vol II,
Properties of Liquids, Longmans, Green Co.: N. Y., 1949, p 301.
70000
A plot of lgHm(TB)
versus lgSm(TB) at T
= TB for the following:

lgHm(TB) / J mol-1
60000
50000
n-alkanes
(C3 to C20): circles,
40000
n-alkylcyclopentanes
(C7 to C21): triangles,
30000
n-alkylcyclohexanes
(C8 to C24): squares.
20000
10000
80
82
84
86
lgSm(TB)
88
90

/ J mol-1 K-1
92
94
If the relationship between lgHm(TB) and lgSm(TB) can
be expressed in the form of an equation of a straight line:
lgHm(TB) = m lgSm(TB) + C
(1)
Since at the boiling temperature, lgGm(TB) = 0;
lgSm(TB) = lgHm(TB)/TB
Therefore lgHm(TB) = m lgHm(TB)/ TB +C
Solving for TB:
TB = m lgHm(TB)/( lgHm(TB) - C)
This is an equation of a hyperbola
As lgHm(TB)  ;
TB  m
(2)
The Correlation Equations Obtained by Plotting lgHm(TB) Versus lgSm(TB)
n-alkanes
lgHm(TB) = (3190.722.6) lgSm(TB) – (240583350);
r2 = 0.9992
n 1-alkenes
lgHm(TB) = (2469.3109.7) lgSm(TB) – (169585951);
r2 = 0.9806
n-alkylbenzenes
lgHm(TB) = (3370.537.3) lgSm(TB) – (247175296);
r2 = 0.9985
n-alkylcyclopentanes
lgHm(TB) = (3028.897.4) lgSm(TB) – (220567926);
r2 = 0.9877
n-alkylcyclohexanes
lgHm(TB) = (3717.887.3) lgSm(TB) – (284890999);
r2 = 0.9918
n-alkanethiols
lgHm(TB) = (2268.7162.6) lgSm(TB) – (1616931728);
TB() ~ 3000 K
r2 = 0.9558
If TB approaches 3000 K in an ascending hyperbolic
fashion, then a plot of 1/[1 – TB/TB()] versus n, the
number of repeat units, should result in a straight line.
A plot of 1/[1- TB/TB()]
versus the number of
methylene groups using
a value of TB() = 3000 K.
1.30
1/[1 - TB/TB(
1.25
1.20
1.15
squares: phenylalkanes
hexagons: alkylcyclopentanes
circles: n-alkanes
triangles: 1-alkenes
1.10
1.05
0
5
10
15
20
N, number of methylene groups, n
25
Use of TB() = 3000 K did not result in straight lines as
expected.
Therefore:
TB() was treated as a variable and allowed to vary in 
5 K increments until the best straight line was obtained
by using a non-linear least squares program resulting in
the following.
1/[1-TB(N)/TB(
2
squares: phenylalkanes
hexagons: alkylcyclopentanes
circles: n-alkanes
triangles: 1-alkenes
1
0
5
10
15
N, number of methylene groups
1/[1- TB/TB()] = aN + b
20
The Results Obtained by Treating TB of a Series of Homologous Compounds as Function of the Number of
Repeat Units, N, and Allowing TB() to Vary; aBm, bBm: Values of aB and bB Obtained by Using the Mean
Value of TB() = 1217 K
Using TB()avg = 1217 K
/K
aBm
/K
data points
0.06231 1.214
0.9
0.04694
1.1984
3.6
18
2-methyl-n-alkanes 1110
0.05675 1.3164
0.2
0.0461
1.2868
0.3
8
1-alkenes
0.06025 1.265
0.4
0.04655
1.242
2.7
17
n-alkylcyclopentanes 1140
0.05601 1.4369
0.6
0.04732
1.4037
1.3
15
n-alkylcyclohexanes 1120
0.05921 1.5054
0.1
0.04723
1.4543
1.2
13
n-alkylbenzenes
1140
0.05534 1.5027
1.1
0.05684
1.5074
1.4
15
1-amino-n-alkanes
1185
0.04893 1.274
3.4
0.04607
1.267
3.4
15
1-chloro-n-alkanes
1125
0.05717 1.2831
0.3
0.04775
1.2628
1.6
13
1-bromo-n-alkanes
1125
0.05740 1.3264
1.0
0.0481
1.2993
1.5
12
1-fluoro-n-alkanes
1075
0.05833 1.2214
0.4
0.04495
1.1987
2.1
9
1-hydroxy-n-alkanes 1820
0.01806 1.220
0.8
0.03953
1.3559
3.6
12
2-hydroxy-n-alkanes 1055
0.05131 1.4923
1.8
0.03732
1.4031
1.8
7
n-alkanals
910
0.08139 1.4561
1.4
0.04277
1.3177
2.5
7
1440
0.03071 1.2905
1.6
0.0430
1.3613
1.7
8
Polyethylene Series TB()/K
n-alkanes
2-alkanones
1076
1090
aB
bB
bBm
Polyethylene Series TB()/K
aB
bB
/K
aBm
bBm
/K data points
n-alkane-1-thiols
1090
0.06170 1.3322 0.2
0.042
1.3635 2.8
14
n-dialkyl disulfides
1190
0.08720 1.4739 0.4
0.08207
1.4608 0.6
9
n-alkylnitriles
1855
0.01907 1.2294 2.6
0.04295
1.3869 3.4
11
n-alkanoic acids
1185
0.0440
1.4964 1.3
0.04100
1.4790 1.3
16
0.03158
1.3069 2.6
0.04200
1.3635 2.8
10
methyl n-alkanoates 1395
Mean Value of TB() = (1217246) K
The results for TB() for polyethylene are remarkably constant considering the use
of data with finite values of n to evaluate TB(n) for n ().
These results are also in good agreement with the values reported previously for
the n-alkanes by Kreglewski and Zwolinski (TB() = 1078 K), Somayajulu (TB() =
1021 K), Stiel and Thodos ((TB() = 1209) K.
Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem. 1961 65, 1050-1052.
Somayajulu, G. R. Internat. J. Thermophys. 1990, 11, 555-72.
Stiel, L. T.; Thodos, G. AIChE. J. 1962, 8, 527-9.
A value of TB() = (1217246) K is considerably less than TB() =
3000 K, the value obtained by assuming that lgHm(TB)   as TB  .
Why is TB() = (1217246) K, not ~3000 K?
From the plot of lgHm(TB) vs lgSm(TB), shown earlier:
TB = m lgHm(TB)/( lgHm(TB) - C)
Rearranging and solving for lgHm(TB)max using TB() = 1217 results in:
lgHm(TB)max = C (TB())/(m - TB())
lgHm(TB)max = 154.5  18.5 kJ mol-1
A limiting value of 154.5  18.5 kJ mol-1 for lgHm(TB)max at TB is
predicted where C and m are from plots of lgHm(TB) vs lgHm(TB)
A limiting value for lgHm(TB)max suggests that this property may also be
modeled effectively by a hyperbolic function
1.8
1/[1-lgHm(TB)/lgHm(TBmax
1.7
A plot of
1/[1- lgHm(TB)/ lgHm(TB)max]
against the number of repeat
units, n
1.6
1.5
1-alkenes: circles
1.4
n-alkylcyclohexanes: squares
1.3
using a value of 154 kJ mol-1
for lgHm(TB)max..
1.2
1.1
0
2
4
6
8
10
12
14
16
18
n, number of repeat units, n
Data from: Wilhoit, R. C.; Zwolinski B. J. Handbook of Vapor Pressures and Heats of Vaporization
of Hydrocarbons and Related Compounds. TRC, Texas A&M Univ. College Station TX
Values of the Parameters of aH and bH Generated in Fitting lgHm(TB) of Several
Homologous Series Using a Value of lgHm(TB)max = 154.5  18.5 kJ mol-1.
aH
bH
/kJ.mol-1 data points
n-alkanes
0.02960
1.1235
0.4
18
n-alkylbenzenes
0.02741
1.284
0.5
15
n-alkylcyclohexanes
0.02697
1.2754
0.2
15
n-alkylcyclopentanes
0.02821
1.2475
0.2
15
n-alk-1-enes
0.02796
1.1554
0.4
17
n-alkane-1-thiols
0.03172
1.1854
0.5
13
At this point it might be useful to ponder why vaporization
enthalpies may approach a limiting value.
Consider what vaporization enthalpies measure:
intermolecular forces
As the size of a flexible molecule increases, what trend would
be expected in the ratio of intermolecular/intramolecular
interactions?
In the limiting case, for a flexible molecule the ratio between
intermolecular/intramolecular interactions might be expected
to go as the ratio of the surface area of a sphere to its volume:
4r2/4/3 r3 ~ 1/r
Why do all of the series related to polyethylene converge to a value for
lgHm(TB)max = 154.5  18.5 kJ mol-1 ?
Why do all of the series related to polyethylene converge to a value for
lgHm(TB)max = 154.5  18.5 kJ mol-1 ?
Ambroses’ Equation
TC = TB + TB/[c + d(n+2)]
where c and d are constants and n refers to the number of
methylene groups.
This equation suggests that TC  TB as n  .
How do critical temperatures of homologous series vary with n?
Ambrose, D. "NPL Report Chemistry 92" (National Physical Laboratory, Teddington,
Middlesex UK, 1978).
Experimental Critical Temperatures
900
A plot of experimental critical
temperatures versus n, the
number of methylene groups
for (from top to bottom):
TC / K, Critical temperature
800
700
alkanoic acids: hexagons,
600
2-alkanones: diamonds,
1-alkanols: solid circles,
500
1-alkenes:
400
triangles,
and n-alkanes: circles.
300
0
5
10
15
number of methylene groups, n
20
25
According to Ambroses’ equation and the previous plots, the critical
temperatures of series related to polyethylene appear to behave in an
ascending hyperbolic fashion. This suggests that a plot of
1/[1- TC /TC()]
versus the number of methylene groups n should also be a linear
function provided a suitable value of TC() was used.
Treating TC() as a variable in ± 5 K increments, a non linear least
squares fit the data resulted in the following:
5
•carboxylic acids
1/[1-Tc/Tc()]
4
2-alkanones
3
 n-alkanes
2
1
0
0
5
10
15
Number of CH2 groups
20
25
Results Obtained for the Constants aC and bC by plotting 1/[1-TC(n)/ TC() as a
Function of the Number of Repeat Units, N, and Allowing TC() to Vary; aCm, bCm:
Values of aC and bC Obtained by Using the Mean Value of TC = 1217 K
Polyethylene
data
Series
TC()/K aC
bC /K TC()/K aCm
bCm /K
points
n-alkanes
1050 0.1292 1.4225 1.7 1217
0.07445 1.4029
9.8
16
n-alkanals
1070 0.1171 1.7753 1.0 1217
0.07756 1.6355
1.8
8
alkanoic acids 1105 0.0961 2.1137 3.4 1217
0.06456 1.9329
3.9
31
1-alkanols
1045 0.1157 1.8362 3.6 1217
0.06773 1.6639
4.7
11
2-alkanones
1105 0.10063 1.8371 1.3
1217
0.07193 1.718
1.9
11
3-alkanones
1185 0.07827 1.8168 1.3
1217
0.07158 1.7811
1.3
10
1-alkenes
1035 0.1327 1.5496 0.3 1217
0.08278 1.4518
3.1
8
2-methylalkanes 950 0.16282 1.7767 0.6 1217
0.07862 1.5329
1.7
5
Critical Temperatures vs n
900
TC / K, Critical temperature
800
A plot of experimental
critical temperatures versus
n, the number of methylene
groups for (from top to
bottom):
alkanoic acids: hexagons,
700
2-alkanones: diamonds,
600
1-alkanols: solid circles,
500
1-alkenes:
triangles,
400
and n-alkanes: circles.
300
The lines were calculated
using TC() = 1217 K.
25
0
5
10
15
number of methylene groups, n
20
What are the consequences if TB () = TC ()?
What are the consequences if TB () = TC ()?
At TC,
lgHm(TC) = 0
This explains why lgHm(TB) fails to continue to increase but may
infact decrease as the size of the molecule get larger.
What does lgHm(TB) measure?
If vaporization enthalpies are a measure of intermolecular interactions,
as the size of the molecule get larger, the ratio of
intermolecular/intramolecular interactions  0 as n  .
Are there any additional consequences if TB () = TC ()?
Since TB is the normal boiling temperature,
If TC () = TB (), then in the limit,
PC () = PB () = 101.325 kPa; 0.1 MPa.
The critical pressure should decrease with increasing n asympotically
approaching 0.1MPa as n  .
Therefore a plot of 1/[1- PC()/PC (n)] versus n using PC() = 0.1
MPa should result in a straight line.
1/[1-Pc () /Pc] vs n
1.09
A Plot of
1.08
1/[1-Pc () /Pc] vs n
1/[1-Pc/Pc()]
1.07
for carboxylic acids
1.06
1.05
1.04
1.03
1.02
1.01
0
2
4
6
8
10
12
n, number of CH2 groups
14
16
18
Critical Pressures vs n
A. plot of the critical
pressure versus the
number of repeat units
for the
1-alkanols: triangles,
n-alkanes: circles,
2-methylalkanes: squares
7
6
PC / MPa
5
4
3
2
1
0
0
5
10
15
number of repeat units, n
20
25
What about other series?
What about other series?
How about the fluorocarbons?
Boiling Temperatures Versus the Number of CF2 Groups
TB /K
600
550
symbols:
experimental TB / K
500
lines:
450
calculated TB / K
circles:
prefluoroalkanes
400
350
squares:
300
perfluorocarboxylic
acids
250
200
0
2
4
6
8
10
12
n, number of CF2 groups
14
16
Table 7. Values of the Parameters of aB and bB Generated in Fitting TB of
Several Homologous Perfluorinated Series Using Equation 3 and
Allowing TB() to Vary in 5 K Increments; aBm, bBm: Values of aB and bB
Using an Average Value of TB() = 915 K
TB = TB()[1-1/(1-aBN + bB)] (3)
TB()/K
aB
bB
/K TB()/K aBm
bBm
/K
N
n-perfluoroalkanes
880
0.07679 1.2905 2.1
915
0.06965 1.2816
2.2
13
915
0.07053 1.6085
1.3
8
n-perfluoroalkanoic acids
950 0.06313 1.5765 1.2
methyl n-perfluoroalkanoates
915
0.06637 1.5000
1.6
4
915
0.07409 1.3751
1.8
5
1-iodo-n-perfluoroalkanes
Critical Temperatures Versus the Number of CF2 Groups
600
symbols:
experimental TC / K
550
lines:
500
calculated TC / K
450
using TC = 915 K
400
for the nperfluoroalkanoic acids
350
300
0
1
2
3
4
5
6
7
n, number of CF2 groups
8
9
Perfluoroalkanes
4
A plot of the critical
pressure versus the
number of repeat
units using PC () =
0.101 (MPa)
3
2
1
0
0
1
2
3
4
5
6
7
8
n, number of CF2 groups
9
Conclusions:
1. Boiling temperatures appear to converge to a finite limit.
2. Vaporization enthalpies are predicted to approach a limiting
value and then decrease as the size of the homologous series
increases.
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 finite pressure
(~1 atm) as the number of repeat units  .
Can any of this be experimentally verified?