What does boiling temperature measure?

Number of methylene groups, NCH2

0 5 10 15 20 25

Boi

ling

tem

pera

ture

, TB/K

200

300

400

500

600

700

800

Figure. The boiling temperatures of the n-alkanes

Why do you suppose that curvature is observed as the size of the n-alkane increases?

3/2*)()( bM

BB eαTMT

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.

Is the boiling temperature of an infinite polymer, finite?

lgSm(TB) / J mol-1 K-1

80 82 84 86 88 90 92 94

lg Hm(T

B)

/ J m

ol-1

10000

20000

30000

40000

50000

60000

70000

Figure. A plot of the lgHm(TB) measured at T = TB versus the l

gSm(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.

lgHm(TB) = m l

gSm(TB) +C

lgHm(TB)/ TB = l

gSm(TB)

Therefore lgHm(TB) = m l

gHm(TB)/ TB +C

Solving for TB:

TB = m lgHm(TB)/( l

gHm(TB) - C)

This is an equation of a hyperbola

As lgHm(TB) ; TB m

Table 1. The Correlation Equations of Figures 1 and 2 Obtained by Plotting l

gHm(TB) Versus lgSm(TB)

 

n-alkanes

lgHm(TB) = (3190.722.6) l

gSm(TB) – (240583350); r2 = 0.9992

n 1-alkenes

lgHm(TB) = (2469.3109.7) l

gSm(TB) – (169585951); r2 = 0.9806

n-alkylbenzenes

lgHm(TB) = (3370.537.3) l

gSm(TB) – (247175296); r2 = 0.9985

n-alkylcyclopentanes

lgHm(TB) = (3028.897.4) l

gSm(TB) – (220567926); r2 = 0.9877

n-alkylcyclohexanes

lgHm(TB) = (3717.887.3) l

gSm(TB) – (284890999); r2 = 0.9918

n-alkanethiols

lgHm(TB) = (2268.7162.6) l

gSm(TB) – (1616931728); r2 = 0.9558

TB() ~ 3000 K

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:

number of methylene groups, n

0 100 200 300 400 500

Tf(

exp)

/ K

50

100

150

200

250

300

350

400

450

Melting temperatures of the even n-alkanes versus the number of methylene

groups

number of methylene groups, n

0 100 200 300 400 500

1/[1

-Tf (

n)/T

f (

0

10

20

30

40

50

60

70

80

number of methylene groups, n

0 100 200 300 400 500

1/[1

-Tf (

n)/T

f (

0

10

20

30

40

50

60

70

80

A plot of 1/[1- TB/TB()] versus the number of methylene groups using a

value of T = 411 K.

N, number of methylene groups

0 5 10 15 20 25

1/[1

- T

B/T

B(

1.05

1.10

1.15

1.20

1.25

1.30

N, number of methylene groups

0 5 10 15 20 25

1/[1

- T

B/T

B(

1.05

1.10

1.15

1.20

1.25

1.30

Figure. A plot of 1/[1- TB/TB()] versus the number of methylene groups using

a value of TB() = 3000 K.

squares: phenylalkaneshexagons: alkylcyclopentanescircles: n-alkanestriangles: 1-alkenes

Use of TB() = 3000 K did not result in straight lines as expected.

Why wasn’t a straight line obtained as suggested by the plot of l

gHm(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:

N, number of repeat units

0 5 10 15 20

1/[1

-TB(N

)/T

B(

1

2

Figure A plot of 1/[1-TB(N)/TB()] against the number of repeat units, N; , 1-alkenes; , n-alkanes; , n-alkylcyclopentanes; , n-alkylcyclohexanes.

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 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

2-alkanones 1440 0.03071 1.2905 1.6 0.0430 1.3613 1.7 8

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() = (1217246) 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.

A value of TB() = (1217246) K is considerably less than TB() = 3000

K, the value obtained by assuming that lgHm(TB) as TB .

Since TB = m lgHm(TB)/( l

gHm(TB) - C)

from the plot of lgHm(TB) vs l

gSm(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

N, number of repeat units

0 2 4 6 8 10 12 14 16 18

1/[1

-lg H

m(T

B)/ lg H

m(T

B m

ax

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

A plot of 1/[1- lgHm(TB)/ l

gHm(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 l

gHm(TB)max..

N, number of repeat units

0 2 4 6 8 10 12 14 16 18 20

lg Hm(T

B)

/ J m

ol-1

20000

30000

40000

50000

60000

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.

Table. Values of the Parameters of aH and bH Generated in Fitting

lgHm(TB) of Several Homologous Series Using a Value of l

gHm(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

Why does lgHm(TB)max reach a limit of 154 kJ mol-1?

TC = TB + TB/[c + d(N+2)]

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).

N, number of methylene groups

0 5 10 15 20 25

TC /

K, C

riti

cal t

empe

ratu

re

300

400

500

600

700

800

900

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)

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.

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

What are the consequences if TB = TC ?

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?

An equation reported by Somayajulu provides a means of describing the possible behavior of l

gHm(TB) as a function of TB and TC.

 

lgHm(TB) = e1X + e2X

2 + e3X3 +e4X

4 where X = (TC-TB)/TC

 

Somayajulu, G. R. “The critical constants of long chain normal paraffins”, Internat. J. Thermophys. 1991, 12, 1039-62.

N, number of repeat units

0 50 100 150 200 250 300

lg Hm

(TB)

/ kJ

mol

-1

20

30

40

50

60

70

lgHm(TB) against the number of repeat units, N.

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 l

gSm(TB)

should vary.

lgSm(TB) / J. mol-1.K-1

0 20 40 60 80 100

lg Hm(T

B)

/ kJ. m

ol-1

0

10

20

30

40

50

60

70

80

Figure. Experimental values of lgHm(TB) as a function of l

gSm(TB);

n-alkanes: circles, experimental values; solid line, calculated values.

Are their any other consequences if TB = TC ?

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 shouldn’t 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 shouldn’t it also be modeled by a hyperbolic function?

Remember for a descending hyperbolic function:

X = Xmin/ [1- 1/(mN + b)] as X Xmin

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)

N, number of repeat units

0 5 10 15 20 25

PC /

MP

a

0

1

2

3

4

5

6

7

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).

N, number of repeat units

0 2 4 6 8 10 12 14 16

PC /

MP

a

1

2

3

4

5

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.

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 .

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?

Number of CF2 groups

0 2 4 6 8 10 12 14 16

Boi

ling

Tem

pera

ture

/ K

200

250

300

350

400

450

500

550

600

Boiling temperatures of the perfluoro-n-alkanes and perfluoro-n-alkanoic acids

1/[1-TB/TB()] was plotted against the number of CF2 groups using TB() as a variable

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-perfluoroalkanes

915 0.07409 1.3751 1.8 5

Number of CF2 groups

0 2 4 6 8 10 12 14 16

1/[1

-TC/T

C(

0

1

2

3

4

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.

What about TC of the perfluorinated compounds?

N, number of methylene groups

0 5 10 15 20 25

TC /

K, C

riti

cal t

empe

ratu

re

300

400

500

600

700

800

900

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.

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.

Recall the equation reported by Somayajulu as a means of describing the possible behavior of l

gHm(TB) as a function of TB and TC.

 

lgHm(TB) = e1X + e2X

2 + e3X3 +e4X

4 where X = (TC-TB)/TC

 

Somayajulu, G. R. “The critical constants of long chain normal paraffins”, Internat. J. Thermophys. 1991, 12, 1039-62.

N, number of repeat units

0 50 100 150 200 250 300

lg Hm

(TB)

/ kJ

mol

-1

20

30

40

50

60

70

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.

l

gSm(TB) / J. mol-1.K-1

0 20 40 60 80 100

lg Hm(T

B)

/ kJ. m

ol-1

0

10

20

30

40

50

60

70

80

Figure. Experimental values of lgHm(TB) as a function of l

gSm(TB); n-alkanes: circles,

experimental values; solid line, calculated values; n-perfluoroalkanes: triangles, experimental values; dashed line, calculated values.

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

N, number of repeat units

0 2 4 6 8 10 12 14 16

PC /

MP

a

1

2

3

4

5

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.

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.

TB, experimental / K

200 300 400 500 600 700

TB

cal

cula

ted

/ K

200

300

400

500

600

700

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) = (1.0000.001)TB (expt) +

(0.1172.23); correlation coefficient r2 = 0.9994 for 262 observations.

TC , experimental / K

300 400 500 600 700 800 900

TC

, ca

lcul

ated

/ K

300

400

500

600

700

800

900

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) =

(1.0030.006)TC (expt) - (2.075.22); correlation coefficient r2 = 0.9968 for 106 observations.