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

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?

Previously we concluded the following:

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?

lgHm(Tm) = (5.01±0.007)N + (1.487±0.1) r2 = 0.99997

N, Number of Carbons

4 6 8 10 12 14 16 18 20 22

lg Hm(2

98.1

5 K

) kJ

. mol

-1

20

40

60

80

100

120

Literature Vaporization Enthalpies of the n Alkanes

C5 to C20 at T = 298.15 K

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.

The measurement of vaporization enthalpies

A. Calorimetric

B. Vapor pressure dependency on temperature

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

Applications of gas chromatography

The measurement of vapor pressure

A. Various static method

B. Effusion methods

C. Transpiration methods

Time (sec)0 100 200 300 400 500

Sig

nal I

nten

sity

0

50

100

150

200

250

A series of isothermal runs. The compounds are n-alkanes

Basic Considerations in Using Gas ChromatographyIn 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, sln

gHm(Tm)/R.

Both terms are predicted to have the same dependence on size. Coiling of the n-alkane decreasing intermolecular interactions will lead to an attenuation of both sln

gHm(Tm) and lgHm(Tm).

slngHm(Tm) = l

gHm(Tm) + slnHm(Tm)

1/T / K

0.00188 0.00192 0.00196 0.00200

ln(t

o/t a)

whe

re t o

= 1

min

-5

-4

-3

-2

-1

0

1

2

A plot of ln(to/ta) versus 1/T (K-1)

From top to bottom:docosanetetracosanehexacosanenonacosanedotriacontanetetratriacontanehexatriacontaneoctatriacontane

to = 1 minln(to/ta) = -sln

gHm(Tm)/RT +C

Enthalpies of transfer measured at Tm = 520 K vs the number of carbon atoms

from C21 to C38

slngHm(520 K) = (3005±13.1)N+(3054±287); r2 = 0.9997

N, number of carbon atoms

20 22 24 26 28 30 32 34 36 38 40

slng H

m(5

20 K

) / k

J m

ol-1

6.0e+4

7.0e+4

8.0e+4

9.0e+4

1.0e+5

1.1e+5

1.2e+5

slngHm(Tm) = l

gHm(Tm)+ slnHm(Tm)

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

C60

Even Alkanes from Polywax1000

C86

Slope Intercept slngHm(653 K)

kJ mol-1

N

dotetracontane -11790 19.069 98.02 42tetratetracontane -12378 19.708 102.91 44hexatetracontane -12965 20.347 107.79 46octatetracontane -13532 20.955 112.50 48pentacontane -14106 21.577 117.27 50dopentacontane -14651 22.155 121.80 52tetrapentacontane -15197 22.736 126.34 54hexapentacontane -15734 23.304 130.81 56octapentacontane -16260 23.857 135.18 58hexacontane -16782 24.403 139.52 60dohexacontane -17288 24.93 143.73 62tetrahexacontane -17804 25.472 148.02 64hexahexacontane -18324 26.02 152.34 66octahexacontane -18769 26.457 156.04 68heptacontane -19259 26.963 160.11 70doheptacontane -19736 27.451 164.08 72tetraheptacontane -20187 27.899 167.83 74hexaheptacontane -20656 28.377 171.73 76

N

40 45 50 55 60 65 70 75 80

slng H

m (

653

K)

/J m

ol-1

8.0e+4

1.0e+5

1.2e+5

1.4e+5

1.6e+5

1.8e+5

N

20 40 60 80 100 120 140 160 180

slng H

m (

653

K)

/J m

ol-1

8.0e+4

1.0e+5

1.2e+5

1.4e+5

1.6e+5

1.8e+5

2.0e+5

2.2e+5

2.4e+5

2.6e+5

2.8e+5

The equation of the linear fit:

slngHm(653 K) = (299913)N +

(3039286); r2 = 0.9997.

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.

A plot of slngHm(T) against the number of carbon atoms, N for N = 42 to 76.

N

40 50 60 70 80 90 100

slng H

m (

Tm)

/ kJ

mol

-1

100

120

140

160

180

200

220

Enthalpies of transfer kJ/mol as a function of the number of carbon atoms from C50 to C92

circles: slngHm(676 K) = (2.12±0.016)N + (12.43±0.92); r2 =

0.9909circles: sln

gHm(676 K) = -(5.64±0.56)10-3N 2+(2.93±0.08)N –(15.1±2.8); r2 = 0.9998

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

squares: slngHm(676 K)= (2.12±0.018)N + (11.42±0.78); r2 = 0.9989squares: sln

gHm(676 K)= -(7.47±0.42)10-3N 2+(3.24±0.06)N –(29.8±2.3); r2 = 0.9999

to a third order polynomial

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 l

gHm(Tm) or slnHm(Tm) or both is not known from these results.

Hui Zhao William Hanshaw T

Richard Heinze Tom Murphy

Hui Zhao William Hanshaw Patamaporn Umnahanant (T)