In the Laboratory
W
Enthalpy of Vaporization by Gas Chromatography A Physical Chemistry Experiment Herbert R. Ellison Department of Chemistry, Wheaton College, Norton, MA 02766;
[email protected] Gas chromatography, GC, is best known for its extensive analytical applications. Since its introduction by James and Martin in 1952 (1) countless applications have been made in a wide variety of fields. Almost from the beginning, workers were aware that GC might also be used to obtain purely physicochemical data such as activity coefficients of solutes in various solvents, heats of solution, and enthalpies of vaporization of volatile compounds (2–9). This experiment is concerned with the latter type of information. The enthalpy of vaporization can be measured calorimetrically, a laborious process, and spectrophotometrically (10), but is usually found by employing the Clausius–Clapeyron equation with measurements of the vapor pressure of the liquid at various temperatures (11, 12). The procedure described below can be used with extremely small quantities of material and can work with impure samples or even with mixtures. The enthalpy of vaporization, ∆vapH is important for both practical and theoretical purposes. On a practical level ∆vapH tells us how much heat will be required to convert a liquid into a vapor, an important consideration in a host of industrial operations. For so-called normal liquids, those free of molecular association in either the liquid or gaseous state, the ratio of the heat of vaporization to the normal boiling temperature is nearly constant at about 85 J K1 mol1 (Trouton’s rule) (13). Thus measurement of ∆vapH enables one to estimate the normal boiling point of the liquid. On a theoretical level the enthalpy of vaporization provides information about the size and nature of intermolecular forces in liquids. Clearly the stronger these forces are the larger will be the value of the enthalpy of vaporization. Theory Gas chromatography is based on a solute in a mixture partitioning itself between the mobile phase (He is the usual carrier gas) and a stationary phase (a liquid coated on some type of support or on the walls of a capillary column). The partition ratio or capacity factor, k´, is the most important quantity in elution chromatography (14). It gives the ratio of the chemical amount of an analyte in the stationary phase, nS, to the chemical amount in the mobile phase,nM: nS nS = (1) nM C MVM where CM is the concentration of the analyte in the mobile phase and VM is the volume of the mobile phase. The capacity factor basically is a measure of the time an analyte spends in the stationary phase relative to the time spent in the mobile phase and is given by
tection, and tM is the time it takes for the mobile phase to pass through the column; typically it is the retention time of air, a nonretained species. Now CM is given by the ideal gas law as CM =
tR − t M tM
(2)
P M = a S P M° = γ S XS PM°
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(4)
Here aS is the activity of the analyte in the stationary phase, PM represents the vapor pressure of the pure volatile analyte, γS is the activity coefficient of the analyte in the stationary solvent, and XS is the mole fraction of the analyte in the stationary phase. Since nS is so much smaller than nM we get XS =
nS n 艐 S nM nM + nS
(5)
Substituting eqs 3, 4, and 5 into eq 1 yields R T nM γ S P M° VM
k ′ =
(6)
This equation represents a relatively easy way to measure activity coefficients of solutes in nonvolatile solvents (4–6). Results agree favorably with values obtained by more traditional methods. To examine the temperature dependence of k´, let us divide eq 6 by T and then take the natural logarithms ln
k ′ T
= ln
R nM γ S VM
− ln ( P M° )
(7)
Differentiating with respect to temperature and assuming that all the quantities in the first term on the right are constants if the temperature range is not too large, results in d ln (k ′ T ) dT
= 0 −
d ln ( PM° ) dT
(8)
This assumption is based on the fact that nM and VM are fixed by the column and activity coefficients of nonelectrolytes vary little with temperature. Now the Clausius–Clapeyron equation gives us an expression for the term on the right side of this equation, that is, ∆ vapH ° d ( ln P M° ) = dT RT 2
Here tR, is the retention time, the time the analyte spends in the column from the point of injection to the point of de1086
(3)
where PM is the pressure of the analyte in the nearly ideal gas phase, R is the gas constant, and T is the absolute temperature of the column. Using a standard state based on Raoult’s law we may write
k ′ =
k ′ =
PM RT
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(9)
In the Laboratory
Substituting this into eq 8 and then integrating gives us ln
k ′ T
= +
∆ vap H ° RT
+ C
(10)
where ∆vapH is the standard enthalpy (heat) of vaporization of the analyte (assumed not to be a function of temperature) and C is the integration constant. Hence the value of ∆vapH is found by plotting ln(k´兾T) versus 1兾T and measuring the slope. Then ∆vapH is simply equal to R times the slope. Experimental Procedure Any gas chromatograph that has good temperature control, produces reproducible data, and resolves the tiny air peak will suffice. In our laboratory we use a Hewlett-Packard 6890 Series GC–MS that enables us to identify the peaks that are
Table 1. Typical Experimental Data for Toluene on Phenyl Methyl Siloxane T/C
tM/min
tR/min
k´
T 1/(103 K)
ln(k´/T)
80.0
1.341
2.127
0.5861
2.831
6.401
80.0
1.339
2.129
0.5900
2.831
6.395
85.0
1.332
2.003
0.5038
2.792
6.567
85.0
1.337
2.013
0.5056
2.792
6.563
90.0
1.326
1.902
0.4344
2.753
6.729
90.0
1.332
1.898
0.4249
2.753
6.751
95.0
1.328
1.816
0.3675
2.716
6.910
95.0
1.326
1.818
0.3710
2.716
6.900
100.0
1.329
1.745
0.3130
2.680
7.084
100.0
1.326
1.745
0.3160
2.680
7.074
105.0
1.321
1.688
0.2778
2.644
7.216
105.0
1.321
1.689
0.2786
2.644
7.213
110.0
1.319
1.633
0.2381
2.610
7.384
110.0
1.318
1.640
0.2443
2.610
7.358
ⴚ6.2 ⴚ6.4
y 4408.3x 18.877 R 2 0.9992
k T ln
ⴚ6.8 ⴚ7.0 ⴚ7.2 ⴚ7.4
2.60
2.65
1 T
2.70
Hazards Methylene chloride is a hazardous chemical and a potential carcinogen and care should be taken to avoid spilling this material on the skin or inhaling it. Care also needs to be taken 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 quantities of materials used in this experiment. Results and Discussion
ⴚ6.6
ⴚ7.6 2.55
produced in the chromatogram.1 The column is a 30-m × 250-µm capillary with a 0.25-µm coating of 5% phenyl methyl siloxane. The oven’s temperature control is ~ ±0.5 C; a physicochemical gas chromatograph (15, 16) would offer better temperature control. Helium flows at a rate of 1.0 mL兾min, at a pressure of 7.0 psi. The split ratio is 100:1. The auto sampler injects a 1-µL sample and the temperature is held constant for ten minutes. The samples we have employed include, but are not limited to, the liquids methylene chloride, carbon tetrachloride, cyclohexane, toluene, acetophenone, and o-xylene and the solids naphthalene and pdichlorobenzene. We have also used mixtures of compounds. All samples are run as dilute solutions in methylene chloride. Students place one drop of a liquid in 1.5 mL of methylene chloride (the size of the sample vial used in our GC–MS) and produce excellent chromatograms. Even smaller concentrations will also produce good peaks. If the sample is a solid, then about 10 mg in 1.5 mL of methylene chloride is sufficient to produce a good chromatogram. The exact concentration of the sample is unimportant for this experiment. The resulting solution is shaken well to ensure that it is saturated with air. If the sample is sensitive to air then another compound that is not retained by the column, such as a fluorinated methane or ethane, might be employed. The laboratory instructor provides the details for using the instrument. A series of runs are made over a 30–40 C interval in 5 C increments. The interval may be selected to bracket the boiling point of the sample or so that the runs are completed in less than ten minutes. The average temperatures of a few compounds measured in this experiment are shown in Table 1. Two runs should be done at each temperature. The procedure to determine the retention times of the air and sample peaks will vary from one gas chromatograph to another; the instructor needs to provide directions.
2.75
2.80
(10ⴚ3 Kⴚ1)
Figure 1. Plot made from the toluene data in Table 1.
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2.85
Students use Excel to analyze their data. They enter temperatures, C, and retention times of air and analyte, and calculate k´, 1兾T, and ln(k´兾T ). Typical student results using toluene and the phenyl methyl siloxane column are shown in Table 1. Plots of ln(k´兾T) versus 1兾T are prepared and the regression equation for the data is found. A plot of the data in Table 1 is shown in Figure 1. Equation 10 and the least-squares slope are used to calculate the value of ∆vapH (in kJ兾mole). A literature value of ∆vapH for their sample is estimated by using vapor pressure–temperature data found in the Handbook of Chemistry and Physics (17) and the integrated form of the Clausius–Clapeyron equation (eq 9). Alternatively, data may be found in the NIST Chemistry Web Book (18). Three
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In the Laboratory
Table 2. Typical Student Results Compound
∆VH/(kJ/mol) Exp
Lit
Diff in ∆VH (%)
a
Ave T/C Exp
Lit
Acetophenone
43.75
48.61
10.00
120
128
Benzoic acid
51.03
65.09
21.60
130
159
Carbon tetrachloride
33.48
31.14
7.51
75
80
Chloroacetic acid
55.81
55.13
1.23
90
106
Chloroform
30.32
30.38
0.20
75
63
Cyclohexane
30.57
31.08
1.64
75
83
p-Dichlorobenzene
42.22
44.60
5.34
105
102
Dipropyl ether
33.16
33.17
0.03
80
80
Ethyl acetate
34.73
33.37
4.08
75
80
Napthalene
46.61
48.21
3.32
115
116
Toluene
36.65
35.88
2.15
95
81
a
Calculated from vapor pressure versus temperature data in ref 11.
or four data points are used such that the average temperature is approximately the same as their experimental average temperature. They then compare their experimental value with this literature value. In deriving eq 10 it was necessary to assume that all of the values in the first term on the right side of eq 7 are constants. Students are asked to comment on this assumption and discuss what might happen to their experimental ∆vapH if this is not strictly correct. They note that the retention time for the methylene chloride also varies with temperature and so come to the conclusion that it is indeed possible to measure ∆vapH of two or more compounds at the same time. They are also impressed that they were able to measure this physical property of a molecule using such a tiny quantity. Students also became aware of some of the thermodynamic factors involved in the separation of compounds by gas chromatography. Some student results obtained over the past few years using this method are shown in Table 2. Also shown are values of ∆vapH calculated from literature (17) values of vapor pressure versus temperature data using the integrated form of eq 9. Because ∆vapH is temperature dependent it was necessary to select data such that their average temperature would be close to the average temperature of the experiment. The agreement is reasonably good, within 5%, when the average temperature is below 115 C. At higher temperatures the experimental enthalpies of vaporization are low, indicating a breakdown in the assumption that the first term on the right in eq 7 is independent of temperature. W
Supplemental Material
Instructions for the students and notes for the instructor are available in this issue of JCE Online. Note 1. We have also performed this experiment using a much older gas chromatograph; a Wilkens Aerograph Model A-90-P3 with a conductivity detector and a strip chart recorder for readout. A
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Carbowax 1540 column was employed. Samples were injected neat with this experimental setup. The resulting values of ∆vapH are very similar to what we obtain today using a modern instrument, indicating that any gas chromatograph with good temperature control might be used for this experiment.
Literature Cited 1. James, A. T.; Martin, A. J. P. J. Biochem. 1952, 50, 679–680. 2. Littlewood, A. B.; Phillips, C. G. S.; Price, D. T. J. Chem. Soc. Abstracts 1955, 1480–1489. 3. Hoare, M. R.; Purnell, J. H. Trans. Faraday Soc. 1956, 52, 222–229. 4. Ashworth, A. J.; Everett, D. H. Trans. Faraday Soc. 1960, 56, 1609–1618. 5. Langer, S. H.; Purnell, J. H. J. Phys. Chem. 1963, 67, 263– 270. 6. Kenworthy, S.; Miller, J.; Martire, D. E. J. Chem. Educ. 1963, 40, 541–543. 7. Purnell, J. H. Endeavor 1964, 23, 142–147. 8. Peacock, L. A.; Fuchs, R. J. Am. Chem. Soc. 1977, 99, 5524–5525. 9. Chicos, J. S.; Hosseini, S.; Hesse, D. G. Thermochimica Acta 1995, 249, 41–61. 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, 681–683. 13. Atkins, P.; de Paula, J. Physical Chemistry, 7th ed.; W. H. Freeman and Company: New York, 2002; pp 101–102. 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 Chromatography, 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).
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