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In the Laboratory

1086 Journal of Chemical Education Vol. 82 No. 7 July 2005 www.JCE.DivCHED.org

Gas chromatography, GC, is best known for its exten-sive analytical applications. Since its introduction by Jamesand Martin in 1952 (1) countless applications have beenmade in a wide variety of fields. Almost from the beginning,workers were aware that GC might also be used to obtainpurely physicochemical data such as activity coefficients ofsolutes in various solvents, heats of solution, and enthalpiesof vaporization of volatile compounds (29). This experimentis concerned with the latter type of information. The enthalpyof vaporization can be measured calorimetrically, a laboriousprocess, and spectrophotometrically(10), but is usually foundby employing the ClausiusClapeyron equation with mea-surements of the vapor pressure of the liquid at various tem-

peratures (11, 12). The procedure described below can beused with extremely small quantities of material and can workwith impure samples or even with mixtures.

The enthalpy of vaporization, vapH is important forboth practical and theoretical purposes. On a practical levelvapH tells us how much heat will be required to convert aliquid into a vapor, an important consideration in a host ofindustrial operations. For so-called normal liquids, those freeof molecular association in either the liquid or gaseous state,the ratio of the heat of vaporization to the normal boilingtemperature is nearly constant at about 85 J K1 mol 1

(Troutons rule) (13). Thus measurement ofvapH enablesone to estimate the normal boiling point of the liquid. On a

theoretical level the enthalpy of vaporization provides infor-mation about the size and nature of intermolecular forces inliquids. Clearly the stronger these forces are the larger willbe the value of the enthalpy of vaporization.

Theory

Gas chromatography is based on a solute in a mixturepartitioning itself between the mobile phase (He is the usualcarrier gas) and a stationary phase (a liquid coated on sometype of support or on the walls of a capillary column). Thepartition ratio or capacity factor, k, is the most importantquantity in elution chromatography (14). It gives the ratioof the chemical amount of an analyte in the stationary phase,nS, to the chemical amount in the mobile phase,nM:

S

M

S

M M

kn

n

n

C V = = (1)

where CM is the concentration of the analyte in the mobilephase and VM is the volume of the mobile phase. The capac-ity factor basically is a measure of the time an analyte spendsin the stationary phase relative to the time spent in the mo-bile phase and is given by

R M

Mk

t t

t =

(2)

Here tR, is the retention time, thetime the analyte spends inthe column from the point of injection to the point of de-

tection, and tMis the time it takes for the mobile phase topass through the column; typically it is the retention time ofair, a nonretained species.

NowCM is given by the ideal gas law as

MMC

P

RT= (3)

where PMis the pressure of the analyte in the nearly ideal gasphase, Ris the gas constant, and Tis the absolute tempera-ture of the column. Using a standard state based on Raoultslaw we may write

MP a= S P X PM S S M = (4)

Here aS is the activity of the analyte in the stationary phase,PMrepresents the vapor pressure of the pure volatile analyte,S is the activity coefficient of the analyte in the stationarysolvent, andXS is the mole fraction of the analyte in the sta-tionary phase. Since nS is so much smaller than nM we get

Xn

n n

n

nSS

M S

S

M

=+

(5)

Substituting eqs 3, 4, and 5 into eq 1 yields

kR T n

P V

M

S M M

=

(6)

This equation represents a relatively easy way to measure ac-tivity coefficients of solutes in nonvolatile solvents (46). Re-sults agree favorably with values obtained by more traditionalmethods.

To examine the temperature dependence ofk , let us di-vide eq 6 byTand then take the natural logarithms

R n

VPln ln= ( )M

S M

M

k

Tln

(7)

Differentiating with respect to temperature and assuming thatall the quantities in the first term on the right are constantsif the temperature range is not too large, results in

kT

ln ( )d=

( )0

d Mln P

dTdT(8)

This assumption is based on the fact that nM and VM are fixedby the column and activity coefficients of nonelectrolytes varylittle with temperature. Now the ClausiusClapeyron equa-tion gives us an expression for the term on the right side ofthis equation, that is,

( )=

2

d

d

M vapln P

T

H

RT

(9)

Enthalpy of Vaporization by Gas Chromatography W

A Physical Chemistry Experiment

Herbert R. Ellison

Department of Chemistry, Wheaton College, Norton, MA 02766; [email protected]
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In the Laboratory

www.JCE.DivCHED.org Vol. 82 No. 7 July 2005 Journal of Chemical Education 1087

Substituting this into eq 8 and then integrating gives us

=ln

k

T++

+vapH

R TC (10)

where vapH is the standard enthalpy (heat) of vaporizationof the analyte (assumed not to be a function of temperature)and Cis the integration constant. Hence the value ofvapHis found by plotting ln(kT) versus 1Tand measuring theslope. Then vapH is simply equal to Rtimes the slope.

Experimental Procedure

Any gas chromatograph that has good temperature con-trol, produces reproducible data, and resolves the tiny air peakwill suffice. In our laboratory we use a Hewlett-Packard 6890Series GCMS that enables us to identify the peaks that are

produced in the chromatogram.1 The column is a 30-m 250-m capillary with a 0.25-m coating of 5% phenyl me-thyl siloxane. The ovens temperature control is ~ 0.5 C; aphysicochemical gas chromatograph (15, 16) would offer bet-ter temperature control. Helium flows at a rate of 1.0mLmin, at a pressure of 7.0 psi. The split ratio is 100:1.The auto sampler injects a 1-L sample and the temperatureis held constant for ten minutes. The samples we have em-

ployed include, but are not limited to, the liquids methylenechloride, carbon tetrachloride, cyclohexane, toluene, aceto-phenone, and o-xylene and the solids naphthalene and p-dichlorobenzene. We have also used mixtures of compounds.

All samples are run as dilute solutions in methylene chlo-ride. Students place one drop of a liquid in 1.5 mL of meth-ylene chloride (the size of the sample vial used in ourGCMS) and produce excellent chromatograms. Even smallerconcentrations will also produce good peaks.

If the sample is a solid, then about 10 mg in 1.5 mL ofmethylene chloride is sufficient to produce a good chromato-gram. The exact concentration of the sample is unimportantfor this experiment. The resulting solution is shaken well to

ensure that it is saturated with air. If the sample is sensitiveto air then another compound that is not retained by thecolumn, such as a fluorinated methane or ethane, might beemployed.

The laboratory instructor provides the details for usingthe instrument. A series of runs are made over a 3040 Cinterval in 5 C increments. The interval may be selected tobracket the boiling point of the sample or so that the runsare completed in less than ten minutes. The average tempera-tures of a few compounds measured in this experiment areshown in Table 1. Two runs should be done at each tem-perature. The procedure to determine the retention times ofthe air and sample peaks will vary from one gas chromato-

graph to another; the instructor needs to provide directions.

Hazards

Methylene chloride is a hazardous chemical and a po-tential carcinogen and care should be taken to avoid spillingthis material on the skin or inhaling it. Care also needs to betaken in handling all of the organics used in this experiment.Prepare all methylene chloride solutions in a fume hood.Waste disposal is simplified because of the small quantitiesof materials used in this experiment.

Results and Discussion

Students use Excel to analyze their data. They enter tem-peratures, C, and retention times of air and analyte, and cal-culate k , 1T, and ln(kT). Typical student results usingtoluene and the phenyl methyl siloxane column are shownin Table 1. Plots of ln(kT) versus 1Tare prepared andthe regression equation for the data is found. A plot of thedata in Table 1 is shown in Figure 1. Equation 10 and theleast-squares slope are used to calculate the value ofvapH(in kJmole).

A literature value ofvapH for their sample is estimatedby using vapor pressuretemperature data found in the Hand-book of Chemistry and Physics (17) and the integrated formof the ClausiusClapeyron equation (eq 9). Alternatively, datamay be found in the NIST Chemistry Web Book(18). Three

y 4408.3x 18.877

R2 0.9992

6.2

6.4

6.6

6.8

7.0

7.2

7.4

7.6

2.55 2.60 2.65 2.70 2.75 2.80 2.85

ln

k

T

1

T(103 K1)

Figure 1. Plot made from the toluene data in Table 1.

eneuloTrofataDlatnemirepxElacipyT.1elbaT

enaxoliSlyhteMlynehPnoT/C tM nim/ tR nim/ k T

1 01(/ 3 )K (nl k/T)

0.08 143.1 721.2 1685.0 138.2 104.6

0.08 933.1 921.2 0095.0 138.2 593.6

0.58 233.1 300.2 8305.0 297.2 765.6

0.58 733.1 310.2 6505.0 297.2 365.6

0.09 623.1 209.1 4434.0 357.2 927.6

0.09 233.1 898.1 9424.0 357.2 157.6

0.59 823.1 618.1 5763.0 617.2 019.6

0.59 623.1 818.1 0173.0 617.2 009.6

0.001 923.1 547.1 0313.0 086.2

480.70.001 623.1 547.1 0613.0 086.2 470.7

0.501 123.1 886.1 8772.0 446.2 612.7

0.501 123.1 986.1 6872.0 446.2 312.7

0.011 913.1 336.1 1832.0 016.2 483.7

0.011 813.1 046.1 3442.0 016.2 853.7
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In the Laboratory

1088 Journal of Chemical Education Vol. 82 No. 7 July 2005 www.JCE.DivCHED.org

or four data points are used such that the average tempera-ture is approximately the same as their experimental averagetemperature. They then compare their experimental valuewith this literature value.

In deriving eq 10 it was necessary to assume that all ofthe values in the first term on the right side of eq 7 are con-stants. Students are asked to comment on this assumptionand discuss what might happen to their experimental vapHif this is not strictly correct. They note that the retention timefor the methylene chloride also varies with temperature andso come to the conclusion that it is indeed possible to mea-sure vapH of two or more compounds at the same time.

They are also impressed that they were able to measure thisphysical property of a molecule using such a tiny quantity.Students also became aware of some of the thermodynamicfactors involved in the separation of compounds by gas chro-matography.

Some student results obtained over the past few yearsusing this method are shown in Table 2. Also shown are val-ues ofvapH calculated from literature (17) values of vaporpressure versus temperature data using the integrated formof eq 9. Because vapH is temperature dependent it was nec-essary to select data such that their average temperature wouldbe close to the average temperature of the experiment. Theagreement is reasonably good, within 5%, when the averagetemperature is below 115C. At higher temperatures the ex-

perimental enthalpies of vaporization are low, indicating abreakdown in the assumption that the first term on the rightin eq 7 is independent of temperature.

WSupplemental Material

Instructions for the students and notes for the instruc-tor are available in this issue ofJCE Online.

Note

1. We have also performed this experiment using a much oldergas chromatograph; a Wilkens Aerograph Model A-90-P3 with aconductivity detector and a strip chart recorder for readout. A

Carbowax 1540 column was employed. Samples were injected neat with this experimental setup. The resulting values ofvapH arevery similar to what we obtain today using a modern instrument,indicating that any gas chromatograph with good temperature con-trol might be used for this experiment.

Literature Cited

1. James, A. T.; Martin, A. J. P.J. Biochem. 1952,50, 679680.2. Littlewood, A. B.; Phillips, C. G. S.; Price, D. T. J. Chem.

Soc. Abstracts1955, 14801489.3. Hoare, M. R.; Purnell, J. H. Trans. Faraday Soc.1956,52,

222229.4. Ashworth, A. J.; Everett, D. H. Trans. FaradaySoc. 1960,56,16091618.

5. Langer, S. H.; Purnell, J. H. J. Phys. Chem. 1963,67, 263270.

6. Kenworthy, S.; Miller, J.; Martire, D. E.J. Chem. Educ. 1963,40, 541543.

7. Purnell, J. H. Endeavor1964,23, 142147.8. Peacock, L. A.; Fuchs, R.J. Am. Chem. Soc.1977, 99, 55245525.9. Chicos, J. S.; Hosseini, S.; Hesse, D. G. Thermochimica Acta

1995,249, 4161.10. Marin-Puga, G.; Guzman, M.; Hevia, F.J. Chem. Educ. 1995,

72, 91, 92.11. Schaber, P. M.J. Chem. Educ. 1985,62, 345.

12. Van Hecke, G. R.J. Chem. Educ. 1992,69, 681683.13. Atkins, P.; de Paula, J. Physical Chemistry, 7th ed.; W. H. Free-

man and Company: New York, 2002; pp 101102.14. Harris, D. C. Quantitative Chemical Analysis, 6th ed.; W. H.

Freeman: New York, 2002; p 557.15. Laub, R. J.; Pecsok, R. L. Physicochemical Applications of Gas

Chromatography; Wiley: New York, 1978.16. Jennings, W.; Mittlefehld, E.; Stremple, P.Analytical Gas Chro-

matography, 2nd ed.; Academic Press: New York, 1997.17. Handbook of Chemistry and Physics, 66th ed.; Weast, R. C.,

Ed.; CRC Press: Boca Raton, FL, 1985.18. NIST Chemistry WebBook Home Page. http://webbook.nist.gov/

chemistry/(accessed Mar 2005).

stluseRtnedutSlacipyT.2elbaT

dnuopmoCVH )lom/Jk(/ ffiD

ni V )%(H

evA T/C

pxE tiL a pxE tiL

enonehpotecA 57.34 16.84 00.01 021 821

dicaciozneB 30.15 90.56 06.12 031 951

edirolhcartetnobraC 84.33 41.13 15.7 57 08

dicacitecaorolhC 18.55 31.55 32.1 09 601

mroforolhC 23.03 83.03 02.0 57 36

enaxeholcyC 75.03 80.13 46.1 57 38

p enezneborolhciD- 22.24 06.44 43.5 501 201

rehtelyporpiD 61.33 71.33 30.0 08 08

etatecalyhtE 37.43 73.33 80.4 57 08

enelahtpaN 16.64 12.84 23.3 511 611

eneuloT 56.63 88.53 51.2 59 18

a ferniataderutarepmetsusreverusserpropavmorfdetaluclaC .11
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