What does boiling temperature measure?

1
What does boiling temperature measure?
2
Figure. The boiling temperatures of the n-alkanes
3
Why do you suppose that curvature is observed as
the size of the n-alkane increases?
4
Modeling boiling temperature An exponential
function has previously been used to model the
behavior observed for the n-alkanes.

Woolf, A. A. Relations between the boiling
points of perfluoro-ethers, perfluoroalkanes and
normal alkanes, J. Fluorine Chem. 1993, 63,
19-24. Kreglewski, A. Zwolinski, B. J. A new
relation for physical properties of n-alkanes and
n-alkyl compounds, J. Phys. Chem. 1961 65,
1050-1052.
5
Is the boiling temperature of an infinite
polymer, finite?
6
Figure. A plot of the ?lgHm(TB) measured at T
TB versus the ?lgSm(TB) also calculated at T TB
of the n-alkanes (C3 to C20) circles,
n-alkylcyclo-pentanes (C7 to C21) triangles, and
n-alkylcyclohexanes (C8 to C24) squares.
7
?lgHm(TB) m ?lgSm(TB) C ?lgHm(TB)/ TB
?lgSm(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
8
Table 1. The Correlation Equations of Figures 1
and 2 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(T
B) (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) r2 0.9558 TB(?)
3000 K
9
If TB approaches 3000 k in a hyperbolic fashion,
then a plot of 1/(1 TB/TB(?) versus N, the
number of repeat units should result in a
straight line Recall that
10

Melting temperatures of the even n-alkanes versus
the number of methylene groups
11
A plot of 1/1- TB/TB(?) versus the number of
methylene groups using a value of T 411 K.
12
squares phenylalkanes hexagons
alkylcyclopentanes circles
n-alkanes triangles 1-alkenes
Figure. A plot of 1/1- TB/TB(?) versus the
number of methylene groups using a value of
TB(?) 3000 K.
13
Use of TB(?) 3000 K did not result in straight
lines as expected. Why wasnt a straight line
obtained as suggested by the plot of ?lgHm(TB)
versus ?lgSm(TB) ? Consequently TB(?) was
treated as a variable until the best straight
line was obtained by using a non-linear least
squares program. This resulted in the following
14
Figure A plot of 1/1-TB(N)/TB(?) against the
number of repeat units, N ?, 1-alkenes ?,
n-alkanes ?, n-alkylcyclopentanes ?,
n-alkylcyclohexanes.
15
Table 2. 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 Polyethylene Series TB(?)/K aB
bB ??/K aBm bBm
??/K data points n-alkanes 1076
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 1090
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 1
120 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 118
5 0.04893 1.274 3.4 0.04607
1.267 3.4 15 1-chloro-n-alkanes 1
125 0.05717 1.2831 0.3 0.04775
1.2628 1.6 13 1-bromo-n-alkanes 112
5 0.05740 1.3264 1.0 0.0481
1.2993 1.5 12 1-fluoro-n-alkanes 10
75 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 2-alkanones 1440
0.03071 1.2905 1.6 0.0430 1.3613
1.7 8
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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 methyl
n-alkanoates 1395 0.03158 1.3069 2.6
0.04200 1.3635 2.8 10 Mean
Value of TB(?) (1217?246) K The results for
TB(?) 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) and Somayajulu (TB(?) 1021 K).
Kreglewski, A. Zwolinski, B. J. J. Phys. Chem.
1961 65, 1050-1052. Somayajulu, G. R. Internat.
J. Thermophys. 1990, 11, 555-72.
17
A value of TB(?) (1217?246) K is considerably
less than TB(?) 3000 K, the value obtained by
assuming that ?lgHm(TB) ? ? as TB ? ?. Since
TB m ?lgHm(TB)/( ?lgHm(TB) - C) from the
plot of ?lgHm(TB) vs ?lgSm(TB), solving for
?lgHm(TB)max in this equation results
in ?lgHm(TB)max C (TB(?))/(m - TB(?))
?lgHm(TB)max 154.5 ? 18.5 kJ mol-1 Why do
all of the polyethylene series converge to
approximately 154.5 ? 18.5 kJ mol-1? A limiting
value 154.5 kJ mol-1 for ?lgHm(TB)max suggests
that this property may also be modeled
effectively by a hyperbolic function
18
A plot of 1/1- ?lgHm(TB)/ ?lgHm(TB(?) against
the number of repeat units, N For the 1-alkenes
(circles) and n-alkylcyclohexanes (squares) using
a value of 154 kJ mol-1 for ?lgHm(TB)max..
19
A plot of ?lgHm(TB) against the number of repeat
units, N points experimental values lines
calculated values circles n-alkanes triangles
alkylthiols squares alkylcyclopentanes.
20
Table. 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 0.0
2960 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
21
Why does ?lgHm(TB)max reach a limit of 154 kJ
mol-1?

22
TC TB TB/c d(N2) Ambroses
Equation where c and d are constants and N refers
to the number of methylene groups. Since this
equation is an equation of a hyperbola, a plot of
Ambrose, D. "NPL Report Chemistry 92" (National
Physical Laboratory, Teddington, Middlesex UK,
1978).
23
Figure. A plot of experimental critical
temperatures versus N, the number of methylene
groups for (top to bottom) the alkanoic acids
(hexagons), 2-alkanones (diamonds),
1-hydroxalkanes (solid circles) 1-alkenes
(triangles), and the n-alkanes (circles)
24
Since Ambrose equation is an equation of a
hyperbola, a plot of 1/1- TB/TB(?) versus the
number of methylene groups should result in a
straight line.
25
Table. Results Obtained for the Constants aC and
bC by Treating 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
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What are the consequences if TB TC ?
27
At TC, ?lgHm(TB) 0 This explains why
?lgHm(TB) fails to continue to increase but
infact decreases as the size of the molecule get
larger. Any inconsistancies here? What does
?lgHm(TB) measure?
28
An equation reported by Somayajulu provides a
means of describing the possible behavior of
?lgHm(TB) as a function of TB and TC.  
?lgHm(TB) e1X e2X2 e3X3 e4X4 where X
(TC-TB)/TC   Somayajulu, G. R. The critical
constants of long chain normal paraffins,
Internat. J. Thermophys. 1991, 12, 1039-62.
29
?lgHm(TB) against the number of repeat units, N.
30
If we know how ?lgHm(TB) varies as a function of
the number of repeat units, and we know how TB
also varies, we can determine how a plot of
?lgHm(TB) versus ?lgSm(TB) should vary.
31
Figure. Experimental values of ?lgHm(TB) as a
function of ?lgSm(TB) n-alkanes circles,
experimental values solid line, calculated
values.
32
Are their any other consequences if TB TC ?
33
If TB TC , what about PC? PC the pressure
necessary to keep the material as a liquid at T
TC PB 1 atm (101.325 kPa) If TC ? TB , then
shouldnt PB ? 1 atm (101.325 kPa) Furthermore,
if PC is finite at TC and approaches 101.325 kPa
as the size of the molecule increases, then
shouldnt it also be modeled by a hyperbolic
function? Remember for a descending hyperbolic
function X Xmin/ 1- 1/(mN b) as
X ? Xmin
34
X Xmin/ 1- 1/(mN b) as X ? Xmin In
this case PC PCmin/ 1- 1/(mN b) as P
? 101.325 kPa (0.101 MPa)
35
Figure. A plot of the critical pressure versus
the number of repeat units for the 1-alkanols
(triangles), the n-alkanes (circles), and the
2-methylalkanes (squares).
36
Figure. A plot of the critical pressure versus
the number of repeat units for the n-alkanoic
acids (circles), and 1-alkenes (squares). The
data for the alkanoic acids includes a few
multiple determinations to give a sense of the
scatter in the experimental data.
37
Summary All of the homologues series examined
related to polyethylene 1. approach a limiting
boiling temperature, 1217 K 2. approach a
limiting critical temperature, 1217 K 3. have
vaporization enthalpies that increase initially,
and then decrease to 0 kJ mol-1 4. have critical
pressures that can be modeled as approaching a
limiting pressure of 101.325 kPa .
38
All of the homologous series examined so far, in
the limit, become polyethylene. Hypothesis If a
homologous series is related related to a
different polymer, that series in the limit
should also approach the boiling temperature of
that polymer. For example, how do the boiling
temperatures of the perfluorinated compounds
compare to each other?
39
Boiling temperatures of the perfluoro-n-alkanes
and perfluoro-n-alkanoic acids
40
1/1-TB/TB(?) was plotted against the number of
CF2 groups using TB(?) as a variable
41
Table. Values of the Parameters of aB and bB
Generated in Fitting TB of Several Homologous
Perfluorinated Series 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(?)/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 n-perfluoroalkanoic acids
950 0.06313 1.5765 1.2
915 0.07053 1.6085 1.3 8 methyl
n-perfluoroalkanoates 915 0.06637
1.5000 1.6 4 1-iodo-n-perfluoroalkan
es 915 0.07409 1.3751
1.8 5
42
Figure. A plot of 1/1-TB/TB(?) vs the number of
CF2 groups using TB(?) 915 K squares
perfluorocarboxylic acids circles
perfluoro-n-alkanes.
43
What about TC of the perfluorinated compounds?
44
Figure. A plot of experimental critical
temperatures versus N, the number of methylene
groups for (top to bottom) the alkanoic acids
(hexagons), 2-alkanones (diamonds),
1-hydroxalkanes (solid circles) 1-alkenes
(triangles), the n-alkanes (circles), and
n-perfluoroalkanes (solid squares). The lines
were calculated using of TC(?) 1217 K for the
hydrocarbons and derivatives and TC(?) 915 K
for the fluorocarbons.
45
Polyperfluoroethylene Series
TC(?)/K aC bC ??/K TC(?)/K aCm bCm
??/K N   n-perfluoroalkanes
920 0.1166 1.4813 1.1 915 0.1203
1.487 1.6 8
Despite the limited amount of available data, TC
of the perfluorinated compounds behave
analogously to the corresponding hydrocarbons.
46
Recall the equation reported by Somayajulu as a
means of describing the possible behavior of
?lgHm(TB) as a function of TB and TC.  
?lgHm(TB) e1X e2X2 e3X3 e4X4 where X
(TC-TB)/TC   Somayajulu, G. R. The critical
constants of long chain normal paraffins,
Internat. J. Thermophys. 1991, 12, 1039-62.
47
Figure. Values of ?lgHm(TB) as a function of
the number of repeat units n-alkanes solid
line, calculated values circles, experimental
values n-perfluoro-alkanes dashed line,
calculated values, triangles, experimental
values.
48
Figure. Experimental values of ?lgHm(TB) as a
function of ?lgSm(TB) n-alkanes circles,
experimental values solid line, calculated
values n-perfluoroalkanes triangles,
experimental values dashed line, calculated
values.
49
What about PC for the perfluorinated
compounds? Remember for a descending hyperbolic
function P Pmin/ 1- 1/(mN b) as
P ? Pmin or 0.1 MPa
50
Figure. A plot of the critical pressure versus
the number of repeat units for the n-alkanoic
acids (circles), 1-alkenes (squares), and
perfluoroalkanes (solid diamonds). The data for
the alkanoic acids includes a few multiple
determinations to give the reader a sense of the
scatter in the experimental data.
51
Summary both homologous series composed of
hydrocarbons related to polyethylene and
perfluorinated compounds related to Teflon behave
similarly in their properties as the size of the
series incresaes.
52
Figure . Calculated boiling temperatures, TB,
versus experimental values circles series
related to polyethylene using TB(?) 1217 K
solid triangles series related to
polytetrafluoroethylene using TB(?) 915 K. The
equation of the line is given by TB (calc)
(1.000?0.001)TB (expt) (0.117?2.23)
correlation coefficient r2 0.9994 for 262
observations.
53
Figure. Calculated critical temperatures, TC,
versus experimental values circles series
related to polyethylene using TC(?) 1217 K
solid triangles series related to
polytetrafluoro-ethylene using TC(?) 915 K. The
equation of the line is given by TC(calc)
(1.003?0.006)TC (expt) - (2.07?5.22)
correlation coefficient r2 0.9968 for 106
observations.