Adventures in Thermochemistry

James S. Chickos*

Department of Chemistry and Biochemistry

University of Missouri-St. Louis

Louis MO 63121

E-mail: jsc@umsl.edu

5

Union Station STL

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 1 atm as the number of repeat units .

5. Enthalpies of transfer appear to show curvature with increasing size

Can any more of this be experimentally verified?

Previously we concluded the following:

Applications of Correlation Gas Chromatography Vapor Pressure

Requirements: Vapor pressures of the standards preferably as a function of temperature over a range of temperatures

Retention Times as a Function of Temperature

T/K 354 359 364 369 374 379 384

Retention Times (t/min)

methane 0.563 0.564 0.583 0.579 0.579 0.580 0.585

octane 1.577 1.424 1.301 1.196 1.115 1.03 0.975

1-nonene 2.664 2.319 2.052 1.827 1.661 1.484 1.367

decane 5.389 4.512 3.857 3.31 2.921 2.517 2.238

naphthalene 18.131 14.815 12.307 10.269 8.763 7.384 6.32

dodecane 21.776 17.319 14.038 11.452 9.591 7.912 6.631

tridecane 44.439 34.668 27.458 21.914 17.921 14.546 11.94

Solvent: CH2Cl2 ta = ti –tCH4

Applications of Correlation Gas Chromatography

Vapor Pressure

Using the following series of hydrocarbons as examples:

1/T, K-1

0.00255 0.00260 0.00265 0.00270 0.00275 0.00280 0.00285

Ln(1

/t c)

-5

-4

-3

-2

-1

0

1

2

A plot of natural logarithm of the reciprocal adjusted retention times ln(A plot of natural logarithm of the reciprocal adjusted retention times ln( ttoo//ttaa) for ) for

(top to bottom): (top to bottom): ,n- octane; ,n- octane; , 1-nonene; , 1-nonene; , , n-decane; n-decane; , naphthalene; , naphthalene;

, n-dodecane; , n-dodecane; , n-tridecane as a function of 1/, n-tridecane as a function of 1/T; tT; to o = 1 min.= 1 min.

Plots of ln(to/ta) vs 1/T

Equations resulting from a linear regressionEquations resulting from a linear regression

of ln(tof ln(too/t/taa) versus (1/) versus (1/TT)K)K-1-1

Compound ln(to/ta)= - slngHm/RT + ln(Ai)

n-octane ln(to/ta)= (-32336/RT) + (11.064) r2=0.9995

1-nonene ln(to/ta)= (-35108/RT) + (11.159) r2=0.9993

n-decane ln(to/ta)= (-38973/RT) + (11.655) r2=0.9994

naphthalene ln(to/ta)= (-41281/RT) + (11.176) r2=0.9997

n-dodecane ln(to/ta)= (-46274/RT) + (12.685) r2=0.9996

n-tridecane ln(to/ta)= (-50036/RT) + (13.232) r2=0.9997

to = 1 min

ln(to/ta), where to = 1 min

-8 -7 -6 -5 -4 -3 -2 -1

ln(p

/po)

exp

erim

enta

l

-11

-10

-9

-8

-7

-6

-5

-4

-3

A plot of experimental vapor pressures ln(p/po) against ln(to/ta) at T = 298.15 K; to = 1 min; po= 101 kPa

A Plot of ln(p/po)exp vs ln(to/ta)

octane

decane

dodecane

tridecane

slngHm(368 K) ln (A) ln(to/ta) ln(p/po) ln(p/po) ln(p/po)

lita calc litoctane -32336 11.064 -1.98 -3.99 -3.951-nonene -35108 11.159 -3.00 -5.15 -4.96b

decane -38973 11.655 -4.07 -6.32 -6.39naphthalene -41281 11.176 -5.48 -8.04 -7.98c

dodecane -46274 12.685 -5.98 -8.63 -8.63tridecane -50036 13.232 -6.95 -9.79 -9.76

ln(p/po) = (1.1820.015) ln(to/ta) -(1.53 0.059); r2 = 0.9987

aRuzicka, K.; Majer, V. J. Phys. Chem. Ref. Data 1994, 23, 1-39;

bPhysical Properties of Chemical Compounds II, Dreisbach, R. R. Advances in Chemistry Series 22, ACS, Washington: DC.

cChirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Steele, W. V. J. Chem. Thermodyn. 1993, 25, 1461-4.

Results of Correlating ln(to/ta) with ln(p/po) at T = 298.15 K

Vapor pressures for naphthalene are for the liquid

Provided vapor pressures of the standards are available as a function of temperature, this correlation can be repeated at other temperatures so that a vapor pressure temperature profile can be obtained.

Applying this protocol as a function of temperature at T = 15 K intervals and fitting the data for 1-nonene and naphthalene to a third order polynomial results in:

a predicted boiling temperature for nonene of : 421 K (420 K lit)

a predicted boiling temperature for naphthalene of: 507 K (493 K lit)

Vapor Pressures by Gas Chromatography

Vapor pressure of an analyte off a column is inversely proportion to it adjusted retention, 1/ta.

Why is 1/ta proportional to the vapor pressure of the pure material when the enthalpy of transfer is a measure of both the vaporization enthalpy and the interaction on the column?

slngHm(Tm) = l

gHm(Tm) + slnHm(Tm)

Raoult’s Law:: the vapor pressure of component a is equal to the product of vapor pressure of pure a (pa

o) times its mole fraction, χ a

pa(obs) = pao·χ a

Since the stationary phase is a polymer, χ a ≈ 1

Returning to the n-alkanes

Daltons Law of Partial Pressures pT = panalyte + pstationary phase = panalyte

The effects of slnHm(Tm) are small and compensated by the standards.

Vapor Pressures of the Standards

• literature vapor pressure evaluated using the Cox equationa

• ln (p/po) = (1-Tb/T)exp(Ao +A1T +A2T 2)

Tb Ao 103A1 106A2

tetradecane 526.691 3.13624 -2.063853 1.54151

pentadecane 543.797 3.16774 -2.062348 1.48726

hexadecane 559.978 3.18271 -2.002545 1.38448

heptadecane 575.375 3.21826 -2.04 1.38

octadecane 590.023 3.24741 -2.048039 1.36245

nonadecane 603.989 3.27626 -2.06 1.35

eicosane 617.415 3.31181 -1.02218 1.34878

octacosaneb 705 3.41304 -1.8894 1.04575

aRuzicka, K.; Majer, V. Simultaneous Treatment of Vapor Pressures and Related Thermal data Between the Triple Point and Normal Boiling Temperatures for n-Alkanes C5-C20. J. Phys. Chem. Ref. Data 1994, 23, 1-39.

po = 101.325 kPa

Equations for the temperature dependence of ln(to/ta)

for C14 to C20 where to = 1 min:

Tm = 449 K sln

gHm/R intercept r2

tetradecane -6393.895 14.1610.01 0.9989

pentadecane -6787.973 14.5970.01 0.9994

hexadecane -7251.562 15.1900.01 0.9996

heptadecane -7612.665 15.5870.01 0.9996

octadecane -8014.871 16.0700.01 0.9996

nonadecane -8457.474 16.6400.01 0.9996

eicosane -8919.685 17.2570.01 0.9995

ln(to/ta) = -slnHm(Tm)/R*1/T + intercept

Vapor pressures of n-alkanes (C14 to C20) at T = 298.15 K:

ln(to/ta) at 298.15 K

ln (p/po) at 298.15 K from

Cox eq.

ln (p/po) at 298.15 K from correlation eq.

tetradecane -7.3 -10.9 -10.9

pentadecane -8.2 -12.1 -12.1

hexadecane -9.2

heptadecane -10.0 -14.3 -14.3

octadecane -10.8 -15.4 -15.4

nonadecane -11.8 -16.6 -16.6

eicosane -12.7 -17.8 -17.8

ln(p/po) = (1.27 0.01) ln(to/ta) - (1.693 0.048); r 2 = 0.9997

-13.3?-13.3unknown

po = 101.325 kPa

ln(1/ta)

-13 -12 -11 -10 -9 -8 -7

ln(p

/p o)

-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

Correlation between ln(1/ta) calculated by extrapolation to T = 298.15 K versus ln(p/po) calculated from the Cox

equation for C14 to C20 (po = 101.325 kPa)

ln(p/po) = (1.27 0.01) ln(to/ta) - (1.693 0.048); r 2 = 0.9997

1/T, K-1

0.0018 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036

ln(p

/po)

-14

-12

-10

-8

-6

-4

-2

0

Vapor pressure -temperature dependence for hexadecane; line: vapor pressure calculated from the Cox equations for C14, circles; vapor pressures calculated by correlation treating hexadecane as an unknown and correlating ln(to/ta) with ln(p/po) for C14, C15, C17-C20 as a function of temperature from T = (298.15 to 500) K.Normal boiling temperature: 560.2 (expt); 559.9 (calcd)

Correlations of Vapor Pressures of Hexadecane from T/K = (298.15 to 500) K

500 K

By a process of extrapolation, vapor pressures of C17 to C20 were used to evaluate C21 to C23; C19 to C23 were used to evaluate C24 and C25, ...

By such a process of extrapolation, vapor pressure equations were obtained for C21 through to C38 using commercially available samples from T = (298.15 to 540) K at 30 K intervals and the resulting vapor pressures were fit to the following third order equation which has been found to extrapolate well with temperature:

ln(p/po) = A (T/K)-3 + B(T/K)-2 + C(T/K)-1 + D;

Using this equation the boiling temperatures of C21 to C38 could be predicted

a Literature value. b This work. c Mazee, W. M., “Some properties of hydrocarbons having more than twenty carbon atoms,” Recueil trav. chim 1948, 67, 197-213. Francis, F.; Wood, N. E., The boiling points of some higher aliphatic n-hydrocarbons, J. Chem. Soc. 1926, 129, 1420.

Some Available Comparisons With Direct Measurements

Experimental vapor pressures for the n-alkanes larger than C38 are not available. What are available are estimated values.a,b The values are available in the form of a program called PERT2 that runs in Windows

a Morgan, D. L.; Kobayashi, R. Extension of Pitzer CSP models for vapor pressures and heats of vaporization to long chain hydrocarbons.Fluid Phase Equilib. 1994, 94, 51–87.

PERT2 is a FORTRAN program written by D. L. Morgan in 1996 which includes parameters for n-alkanes from C1 to C100 and heat of vaporization and vapor pressure correlations. The parameters for C51 to C100 are unpublished based on the critical property (Tc, Pc) correlations of Twu and the Kudchadker & Zwolinski extrapolation of n-alkane NBPs presented in Zwolinski & Wilhoit (1971).

Using vapor pressures calculated from C24 through to C38, values for C40 through to C76 were evaluated.

b Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.

a Kudchadker, A. P.; Zwolinski, B. J. Vapor Pressures and Boiling Points of Normal Alkanes, C21 to C100. J. Chem. Eng. Data 1966, 11, 253.

The vapor pressures were fit to the following third order polynomial:

ln(p/po) = A(T/K)-3 + B(T/K)-2 +C(T/K) + D

10-8A T 3

10-6 B T 2

CT D

heneicosane 1.9989 -2.9075 -98.135 6.6591

docosane 2.1713 -3.1176 110.72 6.5353

tricosane 2.3386 -3.322 310.77 6.4198

tetracosane 2.5072 -3.5286 530.15 6.282

pentacosane 2.6738 -3.7307 741.19 6.150

hexacosane 2.8244 -3.9193 910.53 6.070

heptacosane 3.0092 -4.1253 1198.8 5.811

octacosane 3.1389 -4.3120 1279.4 5.884

nonacosane 3.2871 -4.5043 1431.2 5.841

triacontane 3.4404 -4.6998 1601.6 5.770

hentriacontane 3.6037 -4.9002 1791.2 5.679

dotriacontane 3.7524 -5.0921 1947.2 5.630

tritriacontane 3.8983 -5.2809 2098.0 5.585

tetratriacontane 4.0435 -5.4679 2249.5 5.537

pentatriacontane 4.1746 -5.6480 2363.8 5.544

hexatriacontane 4.3320 -5.8432 2553.2 5.447

heptatriacontane 4.4890 -6.0370 2743.2 5.347

octatriacontane 4.6330 -6.2230 2891.9 5.304

tetracontane 4.9289 -6.6065 3183.3 5.270

dotetracontane 5.1471 -6.9224 3348.9 5.291

tetratetracontane 5.5011 -7.3467 3778.6 5.117

hexatetracontane 5.6451 -7.5992 3810.6 5.224

octatetracontane 5.8908 -7.9326 4039.6 5.187

10-8A T 3

10-6 B T 2

CT D

pentacontane 6.1330 -8.2602 4268.3 5.143

dopentacontane 4.8707 -7.4087 1564.8 7.455

tetrapentacontane 5.0959 -7.7167 1772.4 7.410

hexapentacontane 5.3213 -8.0192 1997.2 7.326

octapentacontane 5.5446 -8.3203 2215.7 7.251

hexacontane 7.3061 -9.8448 5365.4 4.957

dohexacontane 6.1197 -9.0298 2863.7 7.000

tetrahexacontane 6.2051 -9.2215 2812.1 7.149

hexahexacontane 6.2905 -9.4126 2761.7 7.295

octahexacontane 6.3771 -9.5964 2731.5 7.398

heptacontane 6.4622 -9.7833 2688.6 7.527

doheptacontane 6.5473 -9.9677 2650.7 7.646

tetraheptacontane 6.6325 -10.1491 2619.6 7.750

hexaheptacontane 6.7165 -10.3320 2580.8 7.870

octaheptacontane 6.9185 -10.6352 2862.6 7.718

octacontane 7.0339 -10.8450 2927.0 7.731

dooctacontane 7.1142 -11.0100 2862.8 7.852

tetraoctacontane 7.2562 -11.2545 3066.0 7.726

hexaoctacontane 7.3278 -11.4184 2970.3 7.897

octaoctacontane 7.4656 -11.6595 3147.1 7.810

nonacontane 7.5587 -11.8287 3121.0 7.885

dononacontane 7.7815 -12.1830 4010.6 6.856

N - 2

0 20 40 60 80 100

BT

/ K

0

200

400

600

800

1000

1200

N = the number of carbon atoms. The solid symbols represent the experimental and the others the calculated boiling temperatures of C3 to C92. The dotted line was calculated for the n-alkanes using a limiting boiling temperature of TB(∞) = 1076 K. The solid line was obtained by using a by fitting the experimental data to the hyperbolic function previously described and a value of TB(∞) = (1217 ± 246) K

Using the constants of the previous slide, the normal boiling temperatures were predicted by extrapolation.

A plot of the normal boiling temperatures of the n-alkanes as a function of the number of methylene groups resulted in the following:

Conclusions:

Based on the data available, it appears that boiling temperature appear consistent with the prediction that boiling temperatures would approach a limiting value. The agreement with average value of 1217 obtained previously is probably fortuitous

Rachael Maxwell, Boy friend, Richard Heinze Dmitry Lipkind Darrel Hasty