A Comparison of Results by Correlation Gas Chromatography with

Article pubs.acs.org/jced

A Comparison of Results by Correlation Gas Chromatography with Another Gas Chromatographic Retention Time Technique. The Effects of Retention Time Coincidence on Vaporization Enthalpy and Vapor Pressure Chase Gobble and James S. Chickos* Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St Louis, Missouri, 63121, United States S Supporting Information *

ABSTRACT: The vaporization enthalpies of a mixture of n-alkanes, aliphatic esters, and dialkyl phthalates are examined both by correlation gas chromatography and another commonly used gas chromatographic retention time technique according to the protocol described by Hamilton. The resulting vaporization enthalpies and vapor pressures at T/K = 298.15 are compared with respect to the functional groups present. Additionally, two compounds, docosane and ethyl octadecanoate, exhibited retention time coincidence over a T/K = 30 temperature range. These compounds have been examined by correlation gas chromatography to determine how this coincidence affects the thermochemical properties evaluated.

1. INTRODUCTION Gas chromatography has been used to evaluate vapor pressures and vaporization enthalpies of a large variety of organic compounds. Several related but somewhat different protocols have been developed utilizing retention time properties as a means of achieving these evaluations.1−3 Several modifications of this technique, the gas chromatographic−retention time method (GC−RT method), have been experimentally compared by Koutek et al.,3 and the theory has been discussed by Letcher and Naicker.4 Although this technique has provided reliable data in many cases, this has not always been the case.3,5 Letcher and Naicker concluded that one of the largest sources of error in the method was the assumption that the activity of the targets and standards column are similar and cancel. The columns used by the GC−RT method have generally been nonpolar. An alternative approach was initially explored by Peacock and Fuchs.6 Using packed columns, retention time data as a function of temperature were measured and used to calculate the enthalpy of transfer of the analyte from the column to the vapor, ΔtrnHm(Tm). Using an independent measurement of the enthalpy of solution (ΔslnHm(T)) of the analyte in the liquid used as the column coating, and combining the two measurements, they were able, according to eq 1, to obtain a good reproduction of the vaporization enthalpy (ΔlgHm(T)) measured by other methods. We have discussed previously some potential reasons for the slight differences observed.7 g

Δtrn Hm(Tm) = Δl Hm(T ) + Δsln Hm(T ) © 2015 American Chemical Society

We have found that on capillary columns, by choosing the reference compounds carefully, specifically with regards to the functional groups present and demonstrating experimentally that the vaporization enthalpies of the reference compounds correlate linearly with their corresponding enthalpies of transfer, the problem associated with differences in activity appears to be adequately addressed and accurate vaporization enthalpies and vapor pressures of the targets included in the mixture can be obtained.7−9 These correlations have proven successful in providing vaporization enthalpies and vapor pressures at temperatures other than at the mean temperature of measurement, Tm, provided that all the values of the standards used are available at the same temperature. Best results were obtained when the retention times of the target substances are bracketed by related standards. This method has been referred to as correlation gas chromatography (C-GC) in order to distinguish it from other GC−RT methods. Selection of the reference compounds is of utmost importance. For hydrocarbon targets, the structure of the hydrocarbon does not appear to be a significant factor in the selection of standards, provided they are all hydrocarbons. Substitution by functional groups containing heteroatoms, however, frequently does play an important role in affecting the quality of both the vaporization enthalpy and the vapor pressures evaluated. Consequently standards have been chosen to reflect both the nature and the number of functional groups present in the Received: May 27, 2015 Accepted: August 19, 2015 Published: August 25, 2015

(1) 2739

DOI: 10.1021/acs.jced.5b00444 J. Chem. Eng. Data 2015, 60, 2739−2748

Journal of Chemical & Engineering Data

Article

targeted compounds. An examination of the literature reveals that these criteria have not always been rigorously applied by the various other GC−RT methods.4,10 Recently we reported the vaporization enthalpy and vapor pressure of empenthrin, (E)-(RS)-1-ethynyl-2-methylpent-2enyl (1RS)-cis-trans-2,2-dimethyl-3-(2-methylprop-1-enyl)-cyclopropane-carboxylate (CAS [54406-48-3]), a synthetic pyrethrin.8 The commercial material shown in Figure 1 is a

Table 1. Origin of the Standards and Targets compound n-eicosane n-docosane n-tetracosane n-pentacosane n-hexacosane n-octacosane methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate dimethyl phthalate diethyl phthalate di-n-butyl phthalate benzyl butyl phthalate bis (2-ethylhexyl) phthalate di-n-octyl phthalate

Figure 1. Empenthrin [54406-48-3]. 1-Ethynyl-2-methyl-2-penten-1-yl 2,2-dimethyl-3-(2-methyl-1-propen-1-yl)-cyclopropanecarboxylate.

potential mixture of four diastereomers, three of which could be detected by the chromatography, two of equal amounts, and a minor third. The vapor pressure of the mixture was previously reported by Tsuzuki using a variant of the GC−RT method described below.10 The vapor pressure reported for the mixture at T/K = 298.15 using two phthalate esters as standards was p/ Pa = 0.023. This value was within experimental error of the values obtained by correlation gas chromatography, p/Pa = (0.059 ± 0.038) and p/Pa = (0.060 ± 0.038), for the two major diastereomers using monoesters as standards. Previous unreported work in our laboratory suggested that monoesters and diesters did not correlate well with each other. This work examines how the vaporization enthalpies and vapor pressures of esters, diesters, and n-alkanes, another class of compounds used extensively as standards in the GCRT method, compare as evaluated simultaneously by correlation gas chromatography and by the GC−RT method reported by Hamilton.1 In this case the monoesters were used as the standards. The column used was a poly(dimethylsiloxane) column, the column of choice used in the GC−RT method. In the course of this study, these materials were also examined on a poly(5% diphenyl 95% dimethylsiloxane) column. On this column, two of the substances included in the mixture studied, ethyl octadecanoate and docosane, were found to exhibit identical retention times over the entire temperature range, T/K = (495 to 525). This retention time coincidence allows us to address an issue of some concern. Namely, what effect does this coincidence have on the thermodynamic properties evaluated?

a

CAS registry no Alkanes 112-95-8 629-97-0 646-31-1 629-99-2 630-01-3 630-02-4 Esters

supplier

mass fraction

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Aldrich Sigma Sigma

0.99 0.99 0.99 0.99 0.99 0.99

112-61-8 111-61-5 1120-28-1 6064-90-0 Diesters 131-11-3 84-66-2 84-74-2 85-68-7 117-81-7

Eastman Sigma-Aldrich Sigma Sigma

0.99 0.99 0.99 0.99

Supelco/Aldrich Supelco/Aldrich Supelco Supelco Supelco/Aldrich

0.99+ 0.99+ 0.99 ASa 0.99+

117-84-0

Supelco

ASa

AS, Analytical Sample, see section 2.1.

were used in one set of runs. These materials were available as analytical standards. The analysis of this mixture has previously been discussed.11 2.2. Methods. Retention times were measured on an HP 5890 gas chromatograph running Chemstation using a Supelco 15 m × 0.32 mm ID SPB-5 capillary column (1.0 μm film thickness, bonded poly(5% diphenyl/95% dimethylsiloxane)), and an HP 5890 Series II gas chromatograph also running Chemstation on a 30 m × 0.32 mm ID Restek RTX-1 crossbonded 100% poly(dimethylsiloxane) capillary column (0.5 μm film thickness), both using helium as the carrier gas. Split ratios of approximately 100/1 were used. The temperature was maintained at ±0.1 K by both instruments and monitored independently using a Fluke 50S K/J digital thermometer. The solvent was not retained by the column at the temperature of the experiments. The adjusted retention time, ta, was calculated from an analyte’s retention time and the retention time of the solvent by difference. Experimental retention times are provided in Supporting Information (Tables S1A-S4A, S9A, S10A). Compounds reported in the tables below are segregated by functional groups in the order of their elusion off the column. 2.3. Correlation Gas Chromatography. Plots of ln(t0/ta) versus 1/T of each analyte resulted in straight lines with correlation coefficients, r2 > 0.99. The term t0 refers to the reference time, 60 s. The enthalpy of transfer of each analyte from the column to the gas phase, ΔHtrn(Tm), was calculated as the product of the slope of the line and the gas constant, slope· R, where Tm refers to the mean temperature of measurement. The term ΔHtrn(Tm) is related to the vaporization enthalpy, ΔlgHm (Tm), by eq 1.6 In this context, the term ΔslnHm(Tm) refers to the enthalpy of interaction of the analyte with the stationary phase of the column. Provided the standards are properly chosen, a second plot of ΔlgHm(T) versus ΔtrnHm(Tm) where Tm and T may differ, is also linear and the resulting correlation equation in conjunction with the appropriate enthalpy of transfer can then be used to

2. EXPERIMENTAL SECTION 2.1. Materials. Table 1 reports the origin and analysis of the materials used in this study. bis (2-Ethylhexyl) phthalate was purchased presumably as a mixture of two diastereomers, a meso and dl pair. This material was used as purchased. The chromatography did not separate the two diastereomers at the temperatures and columns used. Although individual samples of most of the materials have been purchased separately, a phthalate mixture, EPA 606-M Phthalate Esters Mix was also purchased from Supelco. This mixture contained methanol as the solvent and the following phthalates: benzyl butyl, dioctyl, dibutyl, bis(2-ethylhexyl), diethyl, and dimethyl esters which 2740



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evaluate the vaporization enthalpy of the targets. Similarly, if the vapor pressures of the standards (p) are also well-known, plots of ln(p/p0), where p0 is a reference pressure versus ln(t0/ ta) results in a linear relationship that can be used to evaluate the corresponding ln(p/p0) of the target(s). Repeating this process as a function of temperature has been successful in providing a temperature profile of the vapor pressure of the targets as well. 2.4. GC−RT Method. The vapor pressure−retention time method as reported by Hamilton,1 consists in ploting ln[(tr)tar/ (tr)std ]T against ln(pstd,,T) at different temperatures T, where (tr)tar and (ΔlgH)tar are the relative retention time and vaporization enthalpy of the target and (tr)std and (ΔlgH)std refer to the corresponding properties of the standard. This results in the following linear relationship: g

Table 2. Vaporization Enthalpies and Vapor Pressures of the Compounds Investigated ΔlgHm(298.15 K) compounds n-eicosane n-docosane n-tetracosane n-pentacosane n-hexacosane n-octacosane methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate

g

ln[(tr)tar /(tr)std ]T = [1 − (Δl Hm)tar /(Δl Hm)std ]ln(pstd, T ) − C (2)

The slope and intercept of the line obtained is given by [1 − (ΔlgH)tar/(ΔlgH)std] and −C, respectively. The vapor pressure of the target at T = 298.15 K is obtained from

dimethyl phthalate diethyl phthalate di-n-butyl phthalate benzyl butyl phthalate bis(2-ethylhexyl) phthalate di-n-octyl phthalate

ln(ptar,298.15K /Pa) = [(Δl g Hm)tar /(Δl g Hm)std ] ln(pstd,298.15K /Pa) + C

(3)

Although not always reported, the vaporization enthalpy can be calculated from the slope of the line and the vaporization enthalpy of the standard. Two standards bracketing the retention times of the targets frequently have been used. Vaporization enthalpies at T/K = 298.15 were evaluated in this work for the GC−RT method by evaluating vapor pressure as a function of temperature from T/K = (283.15 to 313.15) at 5 K intervals. The standards used in this work included methyl hexadecanoate, methyl octadecanoate, and methyl eicosanoate for the GC−RT method. The latter two compounds were used as standards for the C-GC method. 2.5. Vaporization Enthalpies and Vapor Pressures of the Standards. Table 2 summarizes the vaporization enthalpies and vapor pressures from the literature at T/K = 298.15 of the compounds used in this study. Table 3 provides the constants and reference pressures for eqs 4 to 6 used to evaluate the vapor pressures of these compounds at and around T/K = 298.15. Note that the reference pressure, p0, in Table 3 may be defined differently for each compound. The term T0 refers to a reference temperature.

(4)

(5)

Clark and Glew equation R ·ln(p/po ) = −Δl g Gm(θ)/θ + Δl g Hm(θ) ·(1/θ − 1/T ) + Δl g Cp(θ ) ·{θ /T − 1 + ln(T /θ }

(298.15 K)

ref

2091 215 23.7 8.1 2.8 0.31

18 12 12 12 12 12

7142 798 427 104 32

13 8 13 14

304243 98826 3873 199 5.4 0.11

15 16 11 11 11, 17 11

3. RESULTS AND DISCUSSION 3.1. Vaporization Enthalpies by C-GC. To compare the results obtained by the GC−RT and C-CG methods, all compounds were chosen with known vaporization enthalpies and vapor pressures at T/K = 298.15. Two different mixtures containing slightly different compositions were studied, both in duplicate. Since both mixtures contained substances with different functionality, the results were analyzed by correlation gas chromatography using two distinctly different protocols. Tables 4 and 5 contain the results of runs 1 and 3 in which the contents of the mixture are segregated according to functionality and values of ΔtrnHm(Tm) correlated with their respective vaporization enthalpies. This resulted in good linear relationships characterized by eqs 7 to 9 and eqs 10 to 12 located below each respective correlation. Results for the duplicate runs (runs 2 and 4) are available in the Supporting Information (Tables S2B and S4B and all results are summarized in Table S5). Figure 2 illustrates the individual correlations evaluated according to the functional group for each for run 1 reported in Table 4. As shown in the figure, the functional group plays an important role in governing the relationship between ΔtrnHm(Tm) and ΔlgHm(Tm) in C-GC. In this instance, the figure suggests that hydrocarbons and esters should correlate reasonably well with each other regardless of whether an alkane or monoester is chosen as a standard. Distinct differences in the correlative behavior are expected using monoesters as standards for the diesters. This is seen more quantitatively in Tables 6 and 7 where all vaporization

Third order polynomial ln(p /po ) = A ·T 3 + B ·T 2 + C·T + D

kJ·mol

Alkanes 101.81 ± 0.5 111.9 ± 2.7 121.9 ± 2.8 126.8 ± 2.9 131.7 ± 3.2 141.9 ± 4.9 Esters 96.84 ± 0.63 105.87 ± 1.4 109.6 ± 4.4 116.43 ± 1.54 120.9 ± 2.5 Diesters 77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 106.2 ± 2.4 116.7 ± 0.5 122.6 ± 1.4

106·p/Pa

the correlations between ΔHtrn(Tm) and ΔlgHm (Tm) were calculated as (σ12 + σ22 ...)0.5. Vapor pressures fit as a function of temperature were fit by nonlinear least-squares. Uncertainties in boiling temperatures were evaluated by setting ln(p/p0) = 0 and solved by standard methods. Details are provided in the Supporting Information. Uncertainties derived from logarithmic terms are reported as an average value of the two uncertainties evaluated.

Cox equation ln(p /po ) = (1 − To/T ) ·exp(Ao + A1·T + A 2 ·T 2)

−1

(6)

2.6. Uncertainties. Unless noted otherwise, all uncertainties refer to one standard deviation. All slopes and intercepts reported below were calculated by linear regression. Uncertainties (u) for combined results and those associated with 2741



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Table 3. Vapor Pressure Equations of the Compounds Investigated A. Parameters of the Cox Equation, eq 4 Ao a

eicosane dimethyl phthalateb diethyl phthalatec

3.31181 3.076854 3.844479 B. Parameters of the

−103·A1/K

106·A2/K2

2.102218 1.650657 0.9201487 Third Order Polynomial,

1.34878 1.171631 0.5406641 Equation, eq 5; p0/Pa =

10−8·A/T n-heneicosaned n-docosaned n-tetracosaned n-pentacosaned n-hexacosaned n-octacosaned ethyl octadecanoatee methyl heneicosanoatef dibutyl phthalateg bis-2-ethylhexyl phthalateg benzyl butyl phthalateg bis-di-n-octyl phthalateg

10−6·B/T

3

1.9989 2.1713 2.5072 2.6738 2.8244 3.1389 3.2679 4.2013 3.4691 6.2867 5.4237 7.2473 C. Parameters of Clark and Glew ΔlgHm(298 K) J·mol

a

−2.9075 −3.1176 −3.5286 −3.7307 −3.9193 −4.3120 −3.9880 −5.2388 −3.6241 −6.0032 −5.2700 −6.8015 Equation, eq 6; p0/Pa = 1

ΔlgG0(298 K)

−1

−1

J·mol

83320 ± 405 89968 ± 280 97836 ± 204

methyl hexadecanoateh methyl octadecanoateh methyl eicosanoateh

2

−13771 ± 101 −10273 ± 79 −8131 ± 66

p0/kPa / T0/K

Trange/K

101.325/617.415 101.325/555.799 2.9·10−6/269.922 101325

324 to 522 270 to 520

C/T

D

−98.135 110.72 530.15 741.19 910.53 1279.4 2696.76 5943.62 1436.92 5619.8 4726.8 7148.4

6.6591 6.5353 6.2817 6.1496 6.0704 5.8835 4.2020 1.2615 5.780 2.7650 2.9210 1.5480

ΔlgCp(298 K)

θ

J·mol−1·K−1

K

−137 −155 −172

397 401 406

Reference 18. bReference 15. cReference 16. dReference 12. eReference 8. fReference 14. gReference 11. hReference 13.

Table 4. Correlation of Vaporization Enthalpies with Enthalpies of Transfer on a Poly(dimethyl siloxane) Column Using All Compounds as Standards; Uncertainties Are One Standard Deviation, po = 101325 Pa −slope Run 1 eicosane docosane tetracosane pentacosane hexacosane octacosane

ΔHtrn(532 K)

T/K

intercept

7147.1 7856.6 8567.8 8924.0 9270.9 9968.2

12.803 13.595 14.398 14.804 15.194 15.985

−1

kJ·mol

ΔlgHm(298 K) −1

kJ·mol

(lit)

ΔlgHm(298 K) kJ·mol−1(calc)

59.42 65.32 71.23 74.19 77.07 82.87

101.81 ± 0.5 111.9 ± 2.7 121.9 ± 2.8 126.8 ± 2.9 131.7 ± 3.2 141.9 ± 4.9

101.8 111.8 121.9 126.9 131.8 141.7

± ± ± ± ± ±

0.7 0.7 0.8 0.8 0.8 0.8

62.43 64.59 68.36 71.32

105.9 ± 1.4 109.6 ± 4.4 116.43 ± 1.5 120.9 ± 2.5

106.0 109.6 116.1 121.1

± ± ± ±

4.1 4.1 4.2 4.3

40.16 44.42 54.85 63.50 71.99 76.92

77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 106.2 ± 2.4 116.7 ± 0.5 122.6 ± 1.4

76.9 ± 0.4 82.2 ± 0.4 95.2 ± 0.5 106.0 ± 0.5 116.6 ± 0.5 122.7 ± 0.5

Δl g Hm(298.15K)/kJ·mol−1 = (1.703 ± 0.007)·ΔHtrn(532K) + (0.590 ± 0.541);

r 2 = 0.9999

methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate

(7) 7509.0 7769.2 8223.0 8579.2

13.175 13.485 13.997 14.380

Δl g Hm(298.15K)/kJ·mol−1 = (1.705 ± 0.044)·ΔHtrn(532K) − (0.490 ± 2.97);

r 2 = 0.9986

dimethyl phthalate diethyl phthalate di-n-butyl phthalate butyl benzyl phthalate bis(2-ethylhexyl) phthalate di-n-octyl phthalate

(8) 4830.3 5343.5 6598.1 7638.6 8659.4 9251.7

9.952 10.537 11.896 12.828 14.245 15.194


r 2 = 0.9999

(9)

enthalpies are evaluated by C-GC using the two esters, methyl octadecanoate and methyl eicosanoate as standards. Equation 2742



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Table 5. Correlation of Vaporization Enthalpies with Enthalpies of Transfer on a (Poly(dimethyl siloxane) Column) Using All Compounds as Standards; Uncertainties in Calculated Values Are One Standard Deviation, po = 101325 Pa −slope Run 3 eicosane docosane tetracosane pentacosane hexacosane

ΔHtrn(516 K)

T/K

intercept

7390.7 8137.5 8880.6 9250.8 9619.4

13.258 14.124 14.99 15.423 15.855

−1

ΔlgHm(298 K)

ΔlgHm(298 K)

−1

kJ·mol−1(Calc)

kJ·mol

kJ·mol

61.44 67.65 73.83 76.91 79.97

101.8 111.9 121.9 126.8 131.7

58.47 64.71 66.99 70.93 74.03

96.8 ± 0.63 105.9 ± 1.4 109.6 ± 4.4 116.4 ± 1.5 120.9 ± 2.5

96.5 ± 3.0 106.3 ± 3.2 109.9 ± 3.2 116.4 ± 3.3 120.9 ± 3.4

41.37 45.84 56.79 74.69

77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 116.7 ± 0.5

76.8 ± 0.6 82.2 ± 0.6 95.2 ± 0.7 116.6 ± 0.8

± ± ± ± ±

(Lit) 0.5 2.7 2.8 2.9 3.2

101.9 111.9 121.8 126.8 131.7

± ± ± ± ±

0.3 0.4 0.4 0.4 0.4


r 2 = 0.9999

methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate

(10) 7032.5 7783.1 8057.4 8532.3 8904.9

12.822 13.688 14.027 14.56 14.995


r 2 = 0.9986

dimethyl phthalate diethyl phthalate di-n-butyl phthalate bis(2-ethylhexyl) phthalate

(11) 4976.4 5513.3 6831.1 8983.8

10.195 10.835 12.327 14.858


r 2 = 0.9999

(12)

at 5 K intervals and the vaporization enthalpy was calculated at the mean temperature, T/K = 298.15, from a plot of ln(p/p0) versus 1/T. The results are shown in columns 2 to 6 of Table 8. The values of the compounds used as standards in each run are reported in bold italics. They were not used in evaluating the average. Column 7 reports the average values obtained by the GC−RT method and columns 8 and 9 compare the results to literature values and the average values evaluated by C-GC, respectively. The average C-CG values are those evaluated using the two monoesters described above as standards from runs 1−4 (see Table S6 for a summary of the individual values). 3.3. Comparison of Vaporization Enthalpy Results. As suggested by Figure 2, the coincidence observed in the slopes and intercepts between ΔtrnHm(Tm) and ΔlgHm(298.15) of the n-alkanes and monoesters by C-CG resulted in good reproduction of the resulting vaporization enthalpies of the nalkanes. Similar results are obtained for the remaining monoesters by this technique using the two esters as standards. Good agreement for eicosane, and methyl and ethyl octadecanoate is also obtained by the GC−RT method but the results appear to diverge as the size of the alkane or monoester increases. The incremental increase per CH2 group does not appear to be modeled as well for these materials by this method. As expected, the C-GC method is considerably less successful in modeling the vaporization enthalpies of the dialkyl phthalate esters except close to where the two lines in Figure 2 intersect. In this instance, the GC−RT method results are considerably closer to the literature values for the larger dialkyl phthalates but also diverge as the size decreases. The average absolute errors relative to the literature values in kJ· mol−1 are as follows. n-alkanes: C-GC, 0.57 and GC−RT method, 6.73. monoesters: C-CG, 0.48 and GC−RT, 2.5; dialkyl phthalates: C-CG, 6.36 and GC−RT: 3.6. While the CGC method using esters as standards does best with both the n-

Figure 2. Correlation between vaporization enthalpies and enthalpies of transfer for run 1 on a dimethyl silicone column as reported in Table 4. Circles (●): dimethyl phthalate, diethyl phthalate, di-n-butyl phthalate, benzyl butyl phthalate, bis(2-ethylhexyl) phthalate, di-noctyl phthalate; triangles (▲): eicosane, docosane, tetracosane, pentacosane, hexacosane, octacosane; squares (■): methyl octanoate, ethyl octanoate, methyl eicosanoate, methyl henicosanoate.

13 and 14 listed below each correlation describe the relationship between ΔlgHm(Tm) and ΔtrnHm(Tm) for these two compounds. 3.2. Vaporization Enthalpies by GC−RT. Using the retention times provided in the Supporting Information and discussed in section 3.1, three esters, methyl hexanoate, methyl octanoate, and methyl eicosanoate, were chosen as standards, and the vaporization enthalpies of the remaining compounds were evaluated using the protocol described in section 2.4. Vapor pressures were evaluated from T/K = (283.15 to 313.15) 2743



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Table 6. Correlation of Vaporization Enthalpies with Enthalpies of Transfer Using Methyl Octadecanoate and Methyl Eicosanoate as the Only Standards for Run 1 (Poly(dimethyl siloxane) Column, po = 101325 Pa) −slope

ΔHtrn(532 K)

Run 1

T/K

intercept

eicosane docosane tetracosane pentacosane hexacosane octacosane methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate dimethyl phthalate diethyl phthalate di-n-butyl phthalate butyl benzyl phthalate bis(2-ethylhexyl) phthalate di-n-octyl phthalate

7147.1 7856.6 8567.8 8924.0 9270.9 9968.2 7509.0 7769.2 8223.0 8579.2 4830.3 5343.5 6598.1 7638.6 8659.4 9251.7

12.803 13.595 14.398 14.804 15.194 15.985 13.175 13.485 13.997 14.380 9.952 10.537 11.896 12.828 14.245 15.194

Δl g Hm(298.15K)/kJ·mol−1 = (1.781)·ΔHtrn(532K) − (5.304) a

−1

kJ·mol

59.42 65.32 71.23 74.19 77.07 82.87 62.43 64.59 68.36 71.32 40.16 44.42 54.85 63.50 71.99 76.92

ΔlgHm(298 K) −1

kJ·mol

(lit)

ΔlgHm(298 K) −1

kJ·mol

(calc)a

100.5 ± 2.9 111 ± 0.01 121.5 ± 2.9 126.8 ± 4.4 131.9 ± 5.8 142.3 ± 8.6 105.9 ± 1.4 109.7 ± 0.3 116.4 ± 1.5 121.7 ± 2.9 66.2 ± 12.2 73.8 ± 10.2 92.4 ± 5.1 107.8 ± 0.9 122.9 ± 3.3 131.7 ± 5.7

105.9 ± 1.4 116.4 ± 1.5

kJ·mol−1 (lit) 101.81 ± 0.5 111.9 ± 2.7 121.9 ± 2.8 126.8 ± 2.9 131.7 ± 3.2 141.9 ± 4.9 109.6 ± 4.4 120.9 ± 2.5 77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 106.2 ± 2.4 116.7 ± 0.5 122.6 ± 1.4

(13)

Uncertainties estimated by using values of (105.9 + 1.4) and (116.4−1.5) kJ·mol−1 for the two standards.

Table 7. Correlation of Vaporization Enthalpies with Enthalpies of Transfer (C-GC) Using Methyl Octadecanoate and Methyl Eicosanoate as the Only Standards for Run 3 (Poly(dimethyl siloxane) Column, po = 101325 Pa) −slope

ΔlgHm(298 K) kJ·mol−1 (lit)

Run 3

T/K

intercept

kJ·mol−1

eicosane docosane tetracosane pentacosane hexacosane methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate dimethyl phthalate diethyl phthalate di-n-butyl phthalate bis(2-ethylhexyl) phthalate

7390.7 8137.5 8880.6 9250.8 9619.4 7032.5 7783.1 8057.4 8532.3 8904.9 4976.4 5513.3 6831.1 8983.8

13.258 14.124 14.99 15.423 15.855 12.822 13.688 14.027 14.56 14.995 10.195 10.835 12.327 14.858

61.44 67.65 73.83 76.91 79.97 58.47 64.71 66.99 70.93 74.03 41.37 45.84 56.79 74.69

Δl g Hm(298.15K)/kJ·mol−1 = (1.6984)·ΔHtrn(516K) − (3.99) a

ΔHtrn(516 K)

105.9 ± 1.4 116.4 ± 1.5

ΔlgHm(298 K) kJ·mol−1 (calc)a

kJ·mol−1 (lit)

100.3 ± 2.9 110.9 ± 0.01 121.4 ± 2.9 126.6 ± 4.3 131.8 ± 5.7 95.3 ± 4.3 105.9 ± 1.4 109.7 ± 0.4 116.4 ± 1.5 121.7 ± 3.0 66.2 ± 12.3 73.8 ± 10.2 92.4 ± 5.1 122.8 ± 3.2

101.81 ± 0.5 111.9 ± 2.7 121.9 ± 2.8 126.8 ± 2.9 131.7 ± 3.2 96.8 ± 0.63 109.6 ± 4.4 120.9 ± 2.5 77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 116.7 ± 0.5

(14)

Uncertainties estimated by using values of (105.9 + 1.4) and (116.4−1.5) kJ·mol−1 for the two standards.13

Vapor pressures of the n-alkanes as evaluated by the GC−RT method appear to diverge significantly as the size of the molecule increases. The ratio of plit/pcalc by the GC−RT method varies from 0.78 to 20.2 increasing as the value of the vapor pressure decreases. Just the opposite effect is observed for the same compounds by the C-GC method decreasing from 0.8 to 0.31. The GC−RT methods shows a similar but somewhat attenuated increasing trend for the monoesters increasing from 0.35 to 2.06 as the size of the molecule increases while for the C-GC method, excluding the compounds used as standards, the method decreases from 1.15 to 0.84. The GC−RT method reproduces the dialkyl phthalates quite well but also shows a similar divergence as the size of the molecule increases. For the dialkyl phthalates, both methods generally show an increase in the ratio with increasing size, from 0.7 to 3.98 for the GC−RT method and 0.23 to 0.90 for the C-GC method.

alkanes and monoesters, the results for the dialkyl phthalates as evaluated by the GC−RT method are considerably better. 3.4. Comparison of Vapor Pressures by C-GC and GC− RT. The relative vapor pressures evaluated by the GC−RT and C-GC methods are compared in Table 9. Column 2 reports literature vapor pressures. Results for the GC−RT method are reported as a ratio relative to the literature values in columns 3−7. Column 8 reports the average of 5 evaluations by the GC−RT method. The compounds used as standards are indicated by the number 1 provided in bold italics in each column and were not included in generating the statistics. Column 9 reports the average value evaluated by C-GC using the values for methyl octadecanoate and methyl eicosanoate as standards (Table S8 in the Supporting Information contains a summary of the ratio of the individual values from runs 1−4). 2744



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Table 8. A Comparison of Vaporization Enthalpies in kJ·mol−1 at T/K = 298.15 (po = 101325 Pa) Evaluated by GC−RT and by C-GC Using Monoesters as Standardsa GC−RT run 1 eicosane docosane tetracosane pentacosane hexacosane octacosane methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate dimethyl phthalate diethyl phthalate di-n-butyl phthalate benzyl butyl phthalate bis(2-ethylhexyl) phthalate di-n-octyl phthalate

102.9 108.8 114.7 117.6 120.5 126.3

± ± ± ± ± ±

1.5 3.1 7.2 9.2 11 16

105.9 ± 1.4 108.0 ± 1.6 111.8 ± 4.6 114.8 ± 6.1 83.6 ± 6.6 87.9 ± 5.8 98.3 ± 3.3 107.9 ± 1.5 115.4 ± 1.6 120.3 ± 2.3

run 2 102.6 108.8 115.0 118.1 121.1

± ± ± ± ±

2.2 4.2 6.2 7.1 8.1

99.6 ± 2.7 105.9 ± 1.4 108.1 ± 3.4 112.1 ± 4.9 115.2 ± 5.6 82.6 ± 4.2 87.0 ± 3.9 98.0 ± 2.8 115.8 ± 3.2

run 2

avg

lit

C-GCb

5.1 1.5 2.6 4.4 6.3

99.8 ± 2.0 106.0 ± 5.9 112.2 ± 9.8 115.3 ± 12 118.3 ± 11

104.0 ± 7.1 110.2 ± 4.3 112.5 ± 2.9 116.4 ± 1.5 119.5 ± 1.5 86.9 ± 9.9 91.3 ± 9.2 102.3 ± 7.3

96.8 ± 0.6 103.1 ± 2.9 105.4 ± 4.3 109.3 ± 7.1 112.4 ± 8.6 79.8 ± 2.7 84.2 ± 2.1 95.2 ± 0.6 113.0 ± 3.7

101.8 ± 0.5 111.9 ± 2.7 121.9 ± 2.8 126.8 ± 2.9 131.7 ± 3.2 141.9 ± 4.9 96.8 ± 0.6 105.9 ± 1.4 109.6 ± 4.4 116.4 ± 1.5 120.9 ± 2.5 77.0 ± 1.2 82.1 ± 0.5 95.0 ± 1.1 106.2 ± 2.4 116.7 ± 0.5 122.6 ± 1.4

100.4 ± 2.9 111.0 ± 0.1 121.5 ± 2.9 126.7 ± 4.4 131.8 ± 5.7 142.3 ± 8.6 95.3 ± 4.3

120.2 ± 3.5

103.9 ± 3.2 110.0 ± 3.2 116.1 ± 3.1 119.1 ± 3.1 122.0 ± 3.1 128.6 ± 3.3 101.8 ± 3.1 107.9 ± 4.2 109.3 ± 3.2 111.1 ± 1.5 116.3 ± 3.1 84.2 ± 3.4 88.6 ± 3.4 99.3 ± 3.2 109.8 ± 2.6 116.9 ± 3.8 122.7 ± 3.2

run 1 107.5 113.4 119.3 122.3 125.1 130.9

± ± ± ± ± ±

run 2

5.7 1.5 2.6 4.6 6.6 11

106.9 113.1 119.3 122.4 125.5

110.5 ± 14 112.7 ± 3.0 116.4 ± 1.5 119.4 ± 1.5 88.2 ± 11.2 92.5 ± 10 102.9 ± 0.1 111.6 ± 6.8 120.1 ± 4.9 125.0 ± 4.0

± ± ± ± ±

109.7 ± 0.3 121.7 ± 2.9 66.4 ± 12 73.9 ± 10 92.4 ± 5.1 107.9 ± 0.9 122.8 ± 3.3 131.6 ± 5.7

a

Vaporization enthalpies in bold italics in columns 2 to 6 used as standards in the GC−RT protocol. Not included in the average value. Uncertainties in columns 2 through 6 are an average of the uncertainty calculated using the uncertainty associated with the vaporization enthalpy of the standard. Uncertainties in column 7 are the standards deviation associated with the mean. bAverage values from runs 1 through 4 using only methyl octadecanoate and methyl eicosanoate as standards for all runs; uncertainties were generated using the standard deviations associated with the values of the two standards.13

Table 9. A Comparison of the Ratio of Literature Vapor Pressures (plit) to Those Evaluated by C-GC and GC−RT (pcalc) Using Monoesters as Standards at T/K = 298.15 K, po = 101325 Pa

eicosane docosane tetracosane pentacosane hexacosane octacosane methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate dimethyl phthalate diethyl phthalate di-n-butyl phthalate benzyl butyl phthalate bis(2-ethylhexyl) phthalate di-n-octyl phthalate

plit/pcalc

plit/pcalc

plit/pcalc

GC−RTa

GC−RTb

C-GCc

104·plit/Pa

Run 1

Run 2

Run 1

Run 2

Run 2

avg

avg

20.9 2.15 0.24 0.081 0.028 0.0032 71.4 8.0 4.3 1.04 0.32 3042 988 38.7 2.0 0.23 0.055

0.89 1.76 3.28 4.35 5.82 11.0

0.93 1.75 3.12 4.05 5.25

0.23 0.84 2.79 4.95 8.82 29.5

0.24 0.85 2.79 4.91 8.64

1.59 3.01 5.36 6.95 9.02

0.11 0.36 0.48 1 1.97 0.04 0.05 0.21

1 1.72 1.8 2.56 3.71 1.67 1.62 2.21

1.93

3.4

0.78 ± 0.57 1.64 ± 0.89 3.47 ± 1.08 5.04 ± 1.13 7.51 ± 1.82 20.2 ± 13.1 0.35 ± 0.33 0.81 ± 0.79 0.97 ± 0.55 2.06 ± 0.71 2.43 ± 0.73 0.71 ± 0.69 0.7 ± 0.66 1.03 ± 0.085 1.28 ± 0.78 2.27 ± 0.63 3.98 ± 1.1

0.80 ± 0.17 0.62 ± 0.14 0.51 ± 0.13 0.48 ± 0.12 0.44 ± 0.12 0.31 ± 0.16 1.15 ± 0.002 1 1.1 ± 0.002 1 0.84 ± 0.001 0.23 ± 0.04 0.31 ± 0.05 0.45 ± 0.09 0.54 ± 0.021 0.90 ± 0.23 0.89 ± 0.59

1 1.07 1.56 2.32 0.83 0.82 1.22 1.83 2.12 3.19

0.58 1 1.05 2.16 0.98 0.94 1.29 1.98

0.36 0.47 1 1.99 0.03 0.05 0.2 0.73 1.94 4.77

Values of 1 in bold italics in columns 3 to 7 and column 9 used as standards in the GC−RT and C-GC protocols, respectively. bUncertainties in column 8 represent one standard deviation associated with the average of columns 3−7; standards not included. cAverage values from runs 1 through 4 using methyl octadecanoate and methyl eicosanoate as standards for all runs; uncertainties represent one standard deviation associated with the average value (see Supporting Information, Table S7, for more information). a

Unlike vaporization enthalpies, the vapor pressures of the nalkanes evaluated by C-GC using the two esters as standards are also not as well reproduced and the quality of the reproduction decreases as the size of the alkane increases. This suggests that the near coincidence in both slope and intercept observed in Figure 1 does not necessarily guarantee the same quality in vapor pressures as observed for vaporization

enthalpies. Vapor pressures of the monoesters are reproduced quite well using only two standards. Considerably less scatter in the average value is observed between runs as indicated by the magnitude of the uncertainty. For the dialkyl phthalates, best results are obtained with compounds close to where the lines in Figure 2 intercept. Since the point of intersection is unpredictable, the quality of the results obtained for the dialkyl 2745



Article

Table 10. Results on the Effects of Retention Time Coincidence on Vaporization Enthalpy (Poly(5% diphenyl/95% dimethyl siloxane Column, po = 101325 Pa)a −slope run 5 docosane tetracosane pentacosane hexacosane octacosane

ΔHtrn(510 K)

T/K

intercept

8191.5 8968.8 9338.2 9713.0 10453.8

14.921 15.827 16.253 16.691 17.555

kJ·mol

−1

68.10 74.56 77.63 80.75 86.91

ΔlgHm(298 K) kJ·mol 121.9 126.8 131.7 141.9

−1

± ± ± ±

(lit) 2.8 2.9 3.2 4.9

ΔlgHm(298 K)

ΔlgHm(298 K)

−1

kJ·mol (calc)

kJ·mol−1 (lit)

111.4 ± 1.5 121.8 ± 1.5 126.8 ± 1.6 131.8 ± 1.6 141.8 ± 1.7

111.9 ± 2.7


r 2 = 0.9998

methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate

(15)

7153.1 7914.5 8191.5 8674.8 9053.7

13.701 14.579 14.921 15.462 15.904

96.84 ± 0.63 105.87 ± 1.4

59.47 65.80 68.10 72.12 75.27

116.43 ± 1.5 120.9 ± 2.5

96.6 ± 3.4 106.4 ± 3.5 109.9 ± 3.6 116.1 ± 3.7 121.0 ± 3.8

109.6 ± 4.4

Δl g Hm(298.15K)/kJ ·mol−1 = (1.54 ± 0.037)·ΔHtrn(510K) + (4.96 ± 2.5); r 2

(16)

= 0.9988 a

Values in bold correspond to the compounds with identical retention times. Uncertainties represent one standard deviation.

Table 11. Correlation of ln(p/po) with ln(to/ta) and Evaluated Vapor Pressures at T/K = 298.15 for Docosane and Ethyl Octadecanoate for Run 5; (Poly(5% diphenyl/95% dimethyl siloxane Column, po/Pa = 101325)a run 5 docosane tetracosane pentacosane hexacosane octacosane

−slope

intercept

−ln(t0/ta)

8191.5 8968.8 9338.2 9713.0 10453.8

14.921 15.827 16.253 16.691 17.555

12.553 14.255 15.067 15.886 17.507

ln(p /po ) = (1.326 ± 0.007) ln(to/ta) − (3.259 ± 0.117); methyl hexadecanoate methyl octadecanoate ethyl octadecanoate methyl eicosanoate methyl heneicosanoate

7153.1 7914.5 8191.5 8674.8 9053.7

13.701 14.579 14.921 15.462 15.904

ln(p /po ) = (1.286 ± 0.0207) − (3.235 ± 0.263);

r 2 = 0.9999

−ln(p/p0)lit 22.175 23.244 24.309 26.490

−ln(p/p0)calc

ln(p/p0)lit

104·(pcalc/plit)

19.91 22.17 23.24 24.33 26.48

± ± ± ± ±

0.15 0.16 0.16 0.17 0.18

−19.97

(2.29 ± 0.34)b/2.15

16.47 18.63 19.38 20.77 21.84

± ± ± ± ±

0.43 0.47 0.26 0.5 0.52

−19.29

(3.88 ± 1.0)c/4.25

(17)

10.290 11.966 12.553 13.663 14.462

16.468 18.659 20.697 21.885

r 2 = 0.9995 (18)

a Uncertainties represent one standard deviation. bA vapor pressure of p/Pa = (2.24 ± 0.21)·10−4 is calculated at T/K = 298.15 on a poly(dimethylsiloxane) column (Run 1). cA vapor pressure of p/Pa = (3.82 ± 0.5)·10−4 is calculated at T/K = 298.15 on a poly(dimethylsiloxane) column (Run 1).

phthalates by either method is highly dependent on the compounds chosen for study. 3.5. Effects of Retention Time Coincidence. 3.51. Vaporization Enthalpies. One of the advantages of gas chromatography is that it is capable of providing pure component properties on materials that can be complex mixtures. Some properties previously evaluated have been for mixtures, frequently diastereomers that are either not resolved by the chromatography as is the case here for the two diastereomers of bis (2-ethylhexyl) phthalate or only partially resolved.8,11 An ongoing concern in its use of C-GC is related to the effects of retention time coincidence on the thermochemical results evaluated in cases where the chromatography is unable to resolve all the components. As noted in the introduction, the components used in this study were also analyzed on a poly(5% diphenyl/95% dimethylsiloxane) column. This column failed to resolve two of the components, docosane and ethyl octadecanoate, over the

entire 30 K temperature range studied. Since the thermochemical properties of these two materials are available, it became of interest to evaluate the effect this coincidence on the vaporization enthalpy and vapor pressure evaluated. Table 10 summarizes the correlation of ΔlgHm(298.15) with ΔtrnHm(Tm), again segregated according to functional group for run 5. Retention times and the complete correlation table and a summary of the two runs that also include results for the dialkyl phthalates in the mixture are available in the Supporting Information (Tables (S9A & S9B), (S10A & S10B), and S11). Both docosane and methyl octadecanoate had identical retention times, therefore their slopes and intercepts are identical. The resulting vaporization enthalpies, though similar, do differ since the two are correlated with different standards. Comparison of the values obtained by correlation with literature values, the last two columns in Table 10, reveals that any effect of this coincidence on the vaporization enthalpy is quite small. Both results are reproduced well within the 2746



Article

Table 12. Parameters of eq 5 and A Comparison of Boiling Temperatures (BT) at p/Pa = 101325 Evaluated for Docosane and Ethyl Octadecanoate from Run 5 from T/K = (298.15 to 500) 10−8·A/T docosane ethyl octadecanoate a

3

2.1812 ± 0.00001 3.523 ± 0.0598

10−6·B/T

10−2·C/T

D

Tboil/K calc/lit

1.5076 ± 0.00113 36.0768 ± 1.276

6.4725 ± 0.0001 3.5143 ± 0.112

644.1 ± 0.1/642.2a 447.4 ± 1.8/443.2b

2

−3.1217 ± 0.0001 −4.2925 ± 0.048

Reference 19. bBoiling temperature at p/Pa = 267, ref 20.

temperature at a reference pressure p0/Pa = 267 of Tb/K = 443.2 was reproduced within 4.2 K.

experimental uncertainties cited. It appears that retention time coincidence is not a major concern, at least not for the compounds of this study. Table S11 in the Supporting Information also compares vaporization enthalpy results obtained on the two columns with literature values; all results are well within experimental error. 3.52. Vapor Pressures. Table 11 examines what effect retention time coincidence has on the resulting vapor pressures from run 5 derived from correlation of ln(p/p0) with ln(t0/ta) of the standards at T/K = 298.15. The calculated vapor pressures for both docosane and ethyl octadecanoate at T/K = 298.15 are also in good agreement with literature values as indicated by the comparison provided in the last column of Table 11. Also included as footnotes a and b of the table are the vapor pressures calculated from run 1 for the two esters on a poly(dimethylsiloxane) column. Both sets of values are within experimental error of each other and with the literature value, demonstrating that the vapor pressure results are also independent of which of the two columns is used. The correlation between ln(p/p0) and ln(t0/ta) of the standards from run 5 was then repeated from T/K = (298.15 to 500) at 10 K intervals and the results fit to the third order polynomial, eq 5, All correlations were characterized with r2 > 0.99. The coefficients of eq 5 for docosane and ethyl octadecanoate are provided in Table 12. Figure 3 illustrates

4. CONCLUSION The results of this study support the importance of proper selection of standards regardless of which GC method is chosen. Much better results are obtained when the functional group of the standards matches that of the targets. Vaporization enthalpies within 10% of the literature value were generally obtained regardless of which method was chosen. Considerably more scatter is observed with the GC−RT method and this is probably in part due to the use of a single standard for each calculation as opposed to the averaging out that occurs when more than one is used. The CH2 increment frequently observed in homologous series appears to be attenuated in this study by the GC−RT method. Both methods were able to reproduce the vapor pressures of the compounds in this study within an order of magnitude regardless of the standards used. Depending on the application, a value within this range may be sufficient. Vaporization enthalpies and the vapor pressures are improved significantly when the functional groups of the standards match those of the targets. The results obtained by the GC−RT method for the dialkyl phthalates using esters as standards also provides an explanation for the success in evaluating the vapor pressure and vaporization enthalpy of empenthrin discussed in the Introduction even though in this case the functional groups of the target and standards were reversed. The standards used by Tsuzuki included dibutyl phthalate and bis(2-ethylhexyl) phthalate, two compounds with vaporization enthalpies close to where the two lines representing esters and diesters in Figure 2 intersect. These results do confirm the need to carefully select standards with the same functionality as the targets to be evaluated. Finally, within experimental error, there does not seem to be a measurable effect of retention time coincidence on the either the vaporization enthalpy or vapor pressure.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00444. Tables of the experimental retention times and other tables described in the text and a summary of vaporization enthalpies and vapor pressures measured by C-GC using only esters as standards (PDF)

Figure 3. A comparison of calculated (symbols) and literature vapor pressures (lines). Docosane, circles (●), and ethyl octadecanoate, squares (□) plotted as ln(p/p0) versus 1/T (K) evaluated from coincidental retention times (p0/Pa = 101325).

the temperature dependence of both compounds. The symbols represent the value calculated by correlation and the line represents the literature values calculated using eqs 4 and 6 and the appropriate constants from Table 3. Boiling temperatures were then predicted by extrapolating the temperature until ln(p/p0) = 0. The boiling temperature for docosane at p/Pa = 101325 was predicted within T/K = 2. The normal boiling temperature of ethyl octadecanoate is not available. The boiling

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel./Fax: 314 516 5377/5342. Notes

The authors declare no competing financial interest. 2747



■

Article

(20) Becker, H. J.; Strating, J. Preparation of several crystalline aliphatic hydrocarbons in the pure state. Recl. Trav. Ch. Pays-BA 1940, 59, 933−46 SciFinder Scholar accessed 4/29/15..

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A Comparison of Results by Correlation Gas Chromatography with

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