Extracting Vapor Pressure Data from GLC Retention Times. Part 1

Sep 19, 2017 - The vapor pressures of 52 compounds including n-alkanes and their monosubstituted derivatives, as well as chloro- and alkylbenzenes wer...
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Extracting Vapor Pressure Data from GLC Retention Times. Part 1: Analysis of Single Reference Approach Bohumír Koutek,*,† Tomás ̌ Mahnel,‡ Pavel Šimácě k,§ Michal Fulem,‡ and Květoslav Růzǐ čka*,‡ †

Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, CZ-166 10 Prague 6, Czech Republic ‡ Department of Physical Chemistry, and §Department of Petroleum Technology and Alternative Fuels, University of Chemistry and Technology, Prague, Technická 5, CZ-166 28 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: The vapor pressures of 52 compounds including n-alkanes and their monosubstituted derivatives, as well as chloroand alkylbenzenes were determined exploring the gas chromatographic relative retention time (GLC-RT) technique in its simplest form, that is, using a single reference standard and neglecting the activity coefficient effect (GLC-RT1S). The selection of compounds was limited to those which are in the liquid state under the measurement conditions and for which high-quality vapor pressures obtained by direct methods are available at temperatures of GLC measurements. This approach should eliminate possible secondary error sources (such as data extrapolation or recalculation from supercooled liquid to solid phase or vice versa). On the basis of a thorough comparison of the GLC-RT1S-based and directly measured vapor pressures for the group of (functionalized) n-alkanes and by exploiting n-alkanes as reference solutes it is clear that deviations from direct data are significant (in many tens of percent) when single reference compounds are used. However, when an n-alkane that has a retention time lower than the test compound but close to it is used as the reference, the relative errors do not exceed 20%. Overall, the method has been found to be rather reliable over a wide range of conditions for nonpolar and slightly polar substances. For polar compounds, such as alcohols or nitriles, the results do confirm the need to carefully select standards with the same functionality as the targets to be evaluated. In contrast to homologous series no regular pattern can be observed for functionalized benzenes even if the reference compounds were selected from the same group of substituted benzenes. where t′i = ti − t0 is the adjusted retention time (ti and t0 are the retention times of the solute and unretained solute, respectively), p0i is the saturated vapor pressure and γ∞ i is the limiting activity coefficient of the solute i in the stationary phase (i = x for the sample being studied and i = s for the standard reference compound). Several related but somewhat different techniques have been developed utilizing retention time properties as a means to determine vapor pressure (and other thermodynamic functions) from GLC data. For reviews on the use of gas chromatography for determining the vapor pressures of organic compounds, the reader is directed to Delle Site,3 Shiu and Ma,4,5 Koutek et al.,6 Letcher and Naicker,7 and Růzǐ čka et al.,8 as well as references found therein. The practical procedure of applying eq 1 to determine vapor pressures derives from the reference substance technique of Othmer,9 which allows extrapolation from a small amount of property data for the target to an extended range of a property

1. INTRODUCTION Knowledge of saturated vapor pressures (p0) is critical for the design of most unit operations in chemical engineering as well as for modeling the fate of chemicals in the environment. However, there is no single direct p0 measurement method that is applicable to the entire range of p0 and temperatures, so that indirect vapor pressure measurements often provide an alternative to direct techniques. Measuring vapor pressure indirectly using the gas liquid chromatography-retention time (GLC-RT) method utilizes the consistent retention time of a compound in a GLC column at a given temperature. The retention is governed by the saturated vapor pressure of the solute and the tendency of the stationary phase to sorb the solute molecule. When absorption in the bulk polymer is the dominant mechanism, a form commonly used to express the mobile-phase/ stationary-phase equilibrium partition of the target solute (x) and reference standard (s) that are run through the gas chromatograph simultaneously in terms of their retention times is1,2 γs∞(T ) ·ps0 (T ) tx′(T ) = ∞ ts′(T ) γx (T ) ·px0 (T )

Received: June 15, 2017 Accepted: August 11, 2017 Published: September 19, 2017

(1) © 2017 American Chemical Society

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structurally very different test compounds and the fact that their vapor pressures as a function of temperature are well documented, we concentrated our attention primarily on n-alkane standards. Besides this the other test compound sets include substitution by functional groups containing heteroatoms and/or an aromatic ring. We addressed the following questions: (i) Does the use of different n-alkane standards significantly influence the vapor pressures of test n-alkanes resulting from the GLC-RT1S framework? (ii) Are the n-alkane standards applicable to sets of compounds including flexible chain molecules, such as the methylene series consisting of the homologous series of the general structure H-(CH2)n-Y (Y = CN, OH, Cl, OCOCH3, NH2) and n varying according to the availability of accurate direct vapor pressure and retention data for the compound at the same temperature? In these systems the solute size is varied progressively and functional groups differing widely in their nature, representing compounds with a high polarinductive effect (Y = CN), capability of H-bonding (Y = OH), and slightly polar (Y = Cl) molecules, have been studied. (iii) To which degree are the n-alkane standards applicable to aromatic compounds such as chloro- or alkyl-substituted benzenes?

curve as a function of, for example, temperature. Briefly, this technique starts from the Clausius−Clapeyron equation (i.e., presuming that at low pressures the compressibility factor of gas zg = 1 and compressibility factor of liquid zl can be neglected), which relates vapor pressure p0 with the enthalpy of vaporization Δgl H Δg H d ln p0 = l 2 dT RT

(2)

where R is the universal gas constant. Thus, for vapor pressures p0x and p0s we can write d ln px0 d ln ps0

=

Δgl Hx Δgl Hs

(3)

and after integration (assuming the ratio Δgl Hx /Δgl Hs is constant) we have ln px0 =

Δgl Hx ln ps0 + C Δgl Hs

(4)

which in combination with eq 1 gives rise to the expression ln

⎛ γ∞ Δg H ⎞ tx′ = ⎜1 − lg x ⎟ ln ps0 − C − ln x∞ γs ts′ ⎝ Δl Hs ⎠ ⎛ Δg H ⎞ = ⎜1 − lg x ⎟ ln ps0 − C′ Δl Hs ⎠ ⎝

2. EXPERIMENTAL SECTION 2.1. Chromatography. The retention times of all samples were determined using three Hewlett-Packard HP 6890 gas chromatographs equipped with a flame ionization detector, electronic pneumatic control (EPC), injection port, HP 6890 automatic injector, and HP VectraVL 2PC with ChemStation software. All measurements were performed on polydimethylsiloxane bonded-phase fused-silica capillary columns (HP-1, 6 m × 310 μm i.d., 0.52 μm film thickness; HP-1, 25 m × 320 μm i.d., 0.52 μm film thickness thickness in split mode with a helium carrier gas). To avoid the necessity of extrapolation of vapor pressures of substances having a relatively high boiling point, chromatographic measurements near room temperature using an extremely short separation column (polydimethylsiloxane bonded-phase fused-silica capillary column RESTEK MXT-1, 20 m × 280 μm i.d., 0.1 μm film thickness in split mode with a nitrogen carrier gas) were also attempted. From this column, a 1.2 m section was separated and performance of the setup was tested using n-triacontane solution (C30H62) as a hydrocarbon having the highest boiling point in the measured series of samples. To minimize retention times, the pressure on the column head was incrementally increased at initial experiments to very high values (relative to column length). At a pressure of 75 kPa and chromatographic furnace temperature 373 K, the hydrogen flame in the FID detector was extinguished due to high carrier gas flow. Considering the nature of gas viscosity dependence on temperature, lower values of pressure limits can be expected at lower temperatures. After several initial measurements, an even shorter column of 0.5 m was used. At a pressure of 50 kPa and chromatographic furnace temperature approaching 373 K flame extinguishing was observed, therefore the carrier gas pressure was set to 30 kPa for the remaining measurements. Measured retention times were not corrected by subtraction of the retention time of methane from the retention time of the analyte. With long columns (6 and 25 m), isothermal measurements were performed in the temperature ranges spanning from 298 to 513 K (see Table 1) with the split ratio 40:1 and the helium head pressure 25 kPa (EPC). Symmetrical peaks indicated that infinite

(5)

Equation 5 is used for the determination of parameters of eq 4. Equations 4 and 5 are identical with the equations derived by ∞ Hamilton10 (assuming γ∞ x /γref = 1 or incorporating this ratio into the constant C′). In general, the reference compound can have a retention time differing considerably from that of the test compound. This assumption has not yet been validated and is only treated implicitly in this method. Anyway, selection of the reference compounds is of utmost importance. Regardless of the advantages the GLC-RT method based on eqs 4 and 5 offers, its widespread usage is hampered by a number of limitations originating, in principle, from the complexity of the retention process. Implicit in the use of eqs 4 and 5 is the requirement that (i) accurate vapor pressure data for reference compounds and their temperature dependence from the temperatures of the GLC measurements to the required temperature are available, and (ii) the variation in the value of ∞ γ∞ s (T)/γx (T) representing the liquid-phase nonideality ratio over the entire working temperature range is either known or can be seriously modeled. Both equations also have in common considerations leading them to ignore the nonideality of solute vapors and adsorption of solutes to the stationary phase. In the preceding article8 we have investigated issue (i) and found that an improper selection and/or application of the physicochemical properties of the reference compounds can significantly influence the quality of the GLC-RT-based vapor pressures and even lead to vague and physico-chemically meaningless results. As a continuation of this effort, we assess herein issue (ii), focusing particularly on the GLC-RT technique ∞ applied assuming the ratio of activity coefficients γ∞ s /γx is unity and therefore a single standard reference compound is needed; this methodology will be abbreviated as GLC-RT1S in the remainder of this paper (approaches using two or more standard reference compounds will be evaluated in the next article). Considering that n-alkanes, for example, n-octadecane or n-eicosane have often been used as reference compounds for 3543

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Table 1. Sample Description Table compound tetradecane pentadecane hexadecane heptadecane octadecane nonadecane eicosane heneicosane docosane tricosane tetracosane pentacosane hexacosane heptacosane octacosane nonacosane triacontane 1-chlorohexane 1-chlorooctane 1-chlorodecane 1-hexanol 1-heptanol 1-octanol 1,2-dichlorobenzene 1,3-dichlorobenzene 1,4-dichlorobenzene 1,2,3-trichlorobenzene 1,2,4-trichlorobenzene 1,3,5-trichlorobenzene pentachlorobenzene 1,2-dimethylbenzene 1,3-dimethylbenzene 1,4-dimethylbenzene 1,2,3-trimethylbenzene 1,2,4-trimethylbenzene 1,3,5-trimethylbenzene toluene ethylbenzene propylbenzene 3-ethyltoluene p-di-tert-butylbenzene n-butylbenzene n-pentylbenzene 1,4-diisopropylbenzene tert-butylbenzene sec-butylbenzene octanenitrile decanenitrile dodecanenitrile hexyl acetate heptyl acetate octylamine

CASNR 629-59-4 629-62-9 544-76-3 629-78-7 593-45-3 629-92-5 112-95-8 629-94-7 629-97-0 638-67-5 646-31−1 629-99-2 630-01-3 593-49-7 630−02−4 630-03-5 638-68-6 544-10-5 111-85-3 1002-69-3 111-27-3 111-70-6 111−87−5 95-50-1 541-73-1 106-46-7 87-61-6 120-82-1 108-70-3 608-93-5 95−47−6 108-38-3 106-42-3 526-73-8 95-63-6 108-67-8 108-88-3 100-41-4 103-65-1 620-14-4 1012-72-2 104-51-8 538-68-1 100-18-5 98−06-6 135-98-8 124−12−9 1975-78-6 2437-25-4 142-92-7 112-06-1 111-86-4

supplier Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Fluka Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich IOCBc IOCBc IOCBc IOCBc IOCBc Aldrich

mole fraction puritya >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.98 >0.98 >0.98 >0.98 >0.98 >0.98 >0.98 >0.98 >0.97 >0.97 >0.97 0.999 0.9992 0.9994 0.9998 0.9955 >0.9991 >0.9960 0.9987 >0.9963 0.9992 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99 >0.98 >0.98 >0.98 >0.99 >0.99 >0.99

temp range of GC-RT/K 347−473 347−473 347−473 408−483 347−498 347−513 367−513 367−417 367−417 333−393 333−393 353−413 353−413 353−413 363−423 363−423 373−423 363−383 363−383 363−383 308−423 308−423 313−413 313−413 313−413 313−413 338−448 323−428 323−428 373−473 298−393 298−423 298−398 308−408 308−408 313−423 298−413 298−398 303−403 303−423 353−453 313−413 313−423 338−443 313−413 313−413 313−423 323−433 353−443 363−383 363−383 313−423

source of literature data 11

Lemmon and Goodwin Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Lemmon and Goodwin11 Kemme and Kreps12 Kemme and Kreps12 Kemme and Kreps12 Štejfa et al.13 Štejfa et al.14 Štejfa et al.14 Roháč et al.15 Roháč et al.15 Roháč et al.15 Roháč et al.15 Roháč et al.15 Roháč et al.15 Roháč et al.15 Chirico et al.16 Chirico et al.17 Chirico et al.18 Růzǐ čka et al.19 Růzǐ čka et al.19 Růzǐ čka et al.19 Chirico et al.20 Chirico et al.21 Růzǐ čka et al.19 Růzǐ čka et al.19 Steele et al.22 Steele et al.23 Růzǐ čka et al.19 Steele et al.24 Steele et al.23 Steele et al.23 Meyer et al.25 Meyer et al.25 Meyer et al.25 Meyer et al.26 Meyer et al.26 Steele et al.27

mole fraction purityb see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 see ref 11 >0.99 >0.99 >0.99 0.999 0.9992 0.9994 0.9998 0.9955 >0.9991 >0.9960 0.9987 >0.9963 0.9992 0.9993 0.9990 0.99996 see ref 19 see ref 19 see ref 19 >0.999 0.9999 see ref 19 see ref 19 >0.9995 >0.9995 see ref 19 >0.9995 >0.9995 >0.9995 0.995 0.994 0.999 >0.999 >0.999 >0.999

a c

Mole fraction purity of samples used for GLC-RT experiments. bMole fraction purity of samples used for direct vapor pressure experiments. Synthesized in the Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Prague.

2.2. Chemicals. The alkanes, chloroalkanes, amines, alcohols, alkylbenzenes, and chlorobenzenes were mostly the commercial products (see Table 1). Some odd carbon atom halogen derivatives, acetates, and nitriles were synthesized in our laboratory as previously described.6 n-Pentane, n-hexane, toluene, (SupraSolv solvents from Merck) were used as common solvents.

dilution has been attained for all the distribution processes. A series of n-alkanes ranging from n-tetradecane to n-eicosane was used as reference compounds. Adjusted retention times were calculated by subtracting the retention time of methane from the retention time of the analyte. All retention times used for calculations were the means of three separate runs (RSD ≤ 0.04%). 3544

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3. RESULTS AND DISCUSSION In the present article, all experimental data were treated using eq 1 in its simplified version γs∞(T ) ·ps0 (T ) ps0 (T ) tx′(T ) = ∞ ≐ 0 ts′(T ) γx (T ) ·px0 (T ) px (T )

GLC-RT1S-based vapor pressures, our choice of experimental conditions involved the following specific criteria: 1) Selection of chromatographic conditions: (1a) We used low-polar stationary phases with two different film thicknesses, and all the peaks were checked for symmetry to ascertain that the gas− liquid partitioning (and not adsorption) directs the retention process; absorption was confirmed to be the main sorption mechanism. Note that this test is not mentioned (and presumably not performed) in most of GLC-RT1S papers. (1b) Adjusted retention times were carefully determined using methane as an unretained solute. (2) Selection of test and reference compounds: (2a) Only those compounds were considered for which high-quality vapor pressure values (i.e., directly measured and taken from the primary literature) exist. (2b) Only compounds for which GLC-RT1S based and direct vapor pressure measurements have been carried out at identical temperatures were considered and compared (i.e., no extrapolation was necessary). (2c) Only liquid compounds were taken into account (i.e., no recalculation from supercooled liquid to solid phase or vice versa was needed).

(6)

∞ that is, assuming the ratio of activity coefficients γ∞ s (T)/γx (T) is unity and a single standard reference compound is needed (GLC-RT1S). This approach has been used by a number of authors.6,10,28−39 It should be stressed that the only difference between exploitation of eq 6 and using the Hamilton approach (eq 5) lies in smoothing retention times with a two-parameter equation, as shown in Figures S1 to S4 in the Supporting Information; only eq 6 will be considered in the remainder of this paper. However, previous approaches have typically required serious approximations and/or extrapolations to be made, necessitating a subsequent calibration with more or less related compounds. Closer inspection of some of these pioneering studies suggests that the experimental designs might not have been sufficient to be able to ascertain maximum attainable accuracy of the GLC-RT1S-based vapor pressures. To deal with apparently incorrect GLC-RT1S based vapor pressures, empirical corrections were applied by some authors (e.g., Bidleman40). To evaluate whether such corrections are successful is almost impossible since four different factors contributed to the errors: (i) inappropriate selection of standard reference compound; (ii) extrapolation; (iii) recalculation between the solid and supercooled liquid state; (iv) uncertainty in vapor pressure data for the reference compounds. It is apparent from eq 6 that the capability of the GLC-RT1S model to generate accurate vapor pressure determinations of test compounds (it means comparable with the accuracy of directly measured literature data) should primarily depend on the high quality of adjusted retention times and vapor pressures of reference substances. A systematic analysis is needed to find out whether and to what extent the appropriate selection of experimental conditions influence the results. Therefore, in order to allow more direct comparison with the accurate vapor pressures given in the literature, and to achieve maximum attainable accuracy of the

Figure 2. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) for selected n-alkanes with n-alkanes as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with GLC-RT1S methodology and prec is the vapor pressure recommended by Lemmon and Goodwin.11 CX stands for n-alkane with X carbon atoms. (a) Results for several n-alkanes with n-hexadecane as a reference compound. (b) Results for pairs of adjacent n-alkanes (n-alkane with z − 1 carbon atoms serves as a reference for n-alkane with z carbon atoms).

Figure 1. Effects of extrapolations of recommended vapor pressure data for n-octadecane and n-eicosane11 fitted with the simplest vapor pressure equation ln p = A−B/T. Solid lines indicate the temperature range used for establishing parameters A, B (345 K to 380 K for short extrapolations; 433 K to 493 K for long extrapolations). Δprel stands for 100(pextrap − prec)/ prec, where prec is the recommended vapor pressure11 and pextrap is the value obtained from parameters A and B. Triangles and squares represent Δprel for n-octadecane and n-eicosane, respectively. 3545

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Figure 3. Relative errors in vapor pressures Δprel obtained with the GLC-RT1S methodology (eq 6) for different types of functionalized alkanes with n-alkanes with nearest lower retention time as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with GLC-RT1S methodology and prec is the recommended vapor pressure (for recommendation, see Table 1). CX stands for n-alkane with X carbon atoms. (a) Full scale figure covering all groups of compounds. (b) Detailed figure focusing on selected groups of compounds with reasonable deviations from the literature data.

Figure 4. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) for selected nitriles and 1-alkanols with nitriles and 1-alkanols, respectively, as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with GLC-RT1S methodology and prec is the recommended vapor pressure (for recommendation, see Table 1). CXCN and CXOH stand for nitrile and 1-alkanol, respectively, with the alkyl chain having X carbon atoms. (a) Results for several nitriles with nitriles used as reference compounds. (b) Results for several 1-alkanols with 1-alkanols used as reference compounds.

Using these criteria, data for 52 compounds were found in the primary literature. Earlier we demonstrated8 that if any of the three selection factors 2a−2c is not taken into account, final vapor pressure results can be distorted in the order of tens to hundreds percent. This can be demonstrated by evaluating errors arising from extrapolation of recommended vapor pressure data11 for n-octadecane and n-eicosane measured at two temperature ranges, namely from 433 to 493 K and 345 to 380 K. Figure 1 shows the low capability of the simplest vapor pressure equation ln p0 = A − B/T in extrapolating the vapor pressure of the two n-alkanes beyond the experimental temperature intervals, that is, to 298 K. Clearly, the error at 298 K depends on extrapolation distances. While the larger relative errors, 372 and 466%, respectively, are the result of larger extrapolation distances, the lower but still considerable relative errors 36 and 40% are due to the shorter extrapolation. 3.1. Homologous Series and/or Compounds with Different Functional Groups. As a logical starting point, the homologous series of n-alkanes was studied. The reason is obvious: reference vapor pressure data as a function of temperature for this series are well documented. In this work, the recommendations by Lemmon and Goodwin11 covering n-alkanes up to n-triacontane were used. At first, n-hexadecane was selected as a reference compound and n-alkanes from n-tetradecane to n-eicosane were treated as unknown samples. Figure 2a shows

the effect of the reference n-alkane selection on the relative errors for several temperatures. It is apparent from Figure 2a that the errors in vapor pressures based on GLC-RT1S method may vary from about −20% to more than 50% and a regular pattern can be seen. The errors for more volatile samples (n-tetradecane, n-pentadecane) were negative while those for less volatile samples were positive. Qualitatively similar results were obtained when another n-alkane was selected as a reference compound instead of n-hexadecane (see Figures S1 to S4 in the Supporting Information). These results clearly show that inappropriate selection of reference compounds can lead to very significant departure from the assumption that the ratio γx/γs can be equated to unity, and consequently to significant errors in determination of vapor pressures. In the next step, we investigated whether the accuracy of GLC-RT1S method can be improved by using test n-alkanes with z carbon atoms and references with z − 1 carbon atoms. Hence, as a rule, n-alkane with closest lower retention time was used as a reference standard. Figure 2b exemplifies these alternatives. Inspection of Figure 2b reveals that in this case the relative errors range from approximately 12% at lower temperatures to 10% at higher temperatures. Therefore, let us emphasize that the 3546

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In view of the foregoing, we performed experiments using, instead of n-alkanes, the reference compounds selected from the same group of substituted benzenes as the test compound. Nonetheless, as shown in Figure 6 for chlorobenzenes and

uncertainties associated with the GLC-RT1S method as used in this work are the lowest attainable. In other words, applying the GLC-RT1S method without adopting the above criteria must lead to errors significantly larger. In an effort to understand how the nature of functional groups in the test compound affects the results, a series of test compounds with differing functionalities have been examined. Again, on the basis of the results for n-alkane series (see Figure 2b), as a rule, the n-alkane with the closest lower retention time was used as a reference standard. It is obvious from the plots shown for several homologous series in Figure 3a that changes in both the functional group and chain length dramatically influence the relative error. While the errors for alkyl acetates were found to be always positive reaching about 20%, both negative and positive errors were observed in the case of chloroalkanes (negative for lower members, positive for higher members of the series). Rather surprisingly, results for octylamine were rather good (positive error below 10%). Taken together these observations indicate that under carefully selected experimental conditions, the strategy to rely solely on a single reference alkane to describe retention behavior yields a satisfactory description of the transfer properties and accordingly quite accurate vapor pressures for homologues of the type H−(CH2)n−Y (Y = CH3, Cl, OCOCH3, NH2). As expected, the same cannot be said for the description of behavior of polar alcohols and nitriles for which large discrepancies between the GLC-RT1S-based and directly measured saturated vapor pressures were observed. Relative deviations would be significantly lower in cases where a member of the same homologous series is used as a single reference, as shown in Figure 4. To examine the GLC-RT1S methodology further, Figure 5 presents the relative errors for two environmentally more

Figure 6. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) for a group of selected chlorobenzenes with chlorobenzenes as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with GLC-RT1S methodology and prec is the recommended vapor pressure (for recommendation, see Table 1). dcb stands for dichlorobenzene, tcb for trichlorobenzene, and pcb for pentachlorobenzene. (a) Full scale figure. (b) Detailed deviation plot for selected pairs dichlorobenzene− dichlorobenzene and trichlorobenzene−trichlorobenzene.

Figure 7 for alkylbenzenes, only in cases where the pairs of test compound−reference compound are selected so that both components of the pair possess the same number of ring substituents (i.e., chlorine atoms or methyl groups) this approach led to improved results. At 400 K, for example, this approach affords vapor pressures within 10% of those from direct measurements for 1,2-dichlorobenzene, 1,4-dichlorobenzene, 1,2,3-trichlorobenzene, 1,2,4-trichlorobenzene, 1,2-dimethylbenzene, 1,4-dimethylbenzene, 1,2,3-trimethylbenzene, and 1,2,4-trimethylbenzene, respectively. 3.2. Measurements with Short GLC Column. A serious problem of the GLC-RT1S method (and, of course, all gas chromatographic methods) regarding particularly low volatile compounds includes very long retention times at ambient temperatures and subsequently long extrapolation of results from high temperature measurements to ambient conditions. Note that many compounds of environmental interest are far less volatile than substances discussed in foregoing sections, which implies using higher temperatures for obtaining retention times

Figure 5. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) for a group of selected alkylbenzenes, and chlorobenzenes with n-alkanes with nearest lower retention time as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with the GLC-RT1S methodology and prec is the recommended vapor pressure (for recommendation, see Table 1). CX stands for n-alkane with X carbon atoms, dcb for dichlorobenzene, tcb for trichlorobenzene, pcb for pentachlorobenzene, dmb for dimethylbenzene, and tmb for trimethylbenzene. Analogous figures of more compounds can be found in the Supporting Information (Figures S5 and S6 for alkylbenzenes and Figure S7 for chlorobenzenes).

important aromatic systems, namely alkylated and chlorinated benzenes. Both positive and negative deviations can be observed for some compounds; however, in contrast to homologous series no regular pattern can be observed. 3547

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Figure 7. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) for a group of selected alkylbenzenes with alkylbenzenes as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is the vapor pressure obtained with GLC-RT1S methodology and prec is the recommended vapor pressure (for recommendation, see Table 1). dmb and tmb stand for dimethylbenzene and trimethylbenzene, respectively.

Figure 8. Relative errors in vapor pressures Δprel obtained with GLC-RT1S methodology (eq 6) using a short column (0.5 m) for selected n-alkanes with n-alkanes as reference compounds. Δprel stands for 100(pGC − prec)/prec, where pGC is vapor pressure obtained with GLC-RT1S methodology and prec is vapor pressure recommended by Lemmon and Goodwin.11 CX stands for n-alkane with X carbon atoms.

Answering the initially formulated questions, we can conclude that (i) based on a thorough comparison of the GLC-RT1Sbased and directly measured vapor pressures for the group of n-alkanes it is clear that deviations from direct data are significant (in many tens of percent) when using single reference compounds (see e.g., Figures S1 to S4). It is, however, generally possible to minimize the difference by using reference alkanes with z carbon atoms for test alkanes with z + 1 carbon atoms. Then, the relative errors decrease from approximately 12% at lower temperatures to 10% at higher temperatures (see Figure 2b). To conclude, using the same single reference compound for several unknown compounds is not recommended even within the same homologous series. (ii) As it is evidenced in Figure 3, with a good choice of reference substance, such as an n-alkane that has a lower retention time than the test compound but close to it, the errors for homologous series members do not exceed 20%. However, although this holds for alkyl chlorides, octylamine and acetates, it does not hold for polar alcohols and nitriles. This shows that if some polar (hydrogen bonding, dipole−induced dipole) interactions with the chromatographic stationary phase are involved, the retention times are increased relatively to those of the n-alkane reference compounds and consequently, relative errors amounting to several hundred percent occur. Inspection of Figure 4 reveals that the errors can be significantly lowered provided that a compound of similar structure and polarity is used as the reference compound for alkanols and nitriles. (iii) The results obtained for alkylbenzenes and some chlorobenzenes according to the GLC-RT1S method are also within ±20% of values obtained by direct methods (Figure 5). However, for most chlorobenzenes (Figure 5 and Figure S7) the GLC-RT1S based vapor pressures are burdened with significant errors and it is questionable what results can be expected for multifunctional compounds. Moreover, it should be stressed that relatively optimistic results for some groups of compounds were obtained without employing any extrapolation and that no recalculation from solid to supercooled liquid was involved; those two factors can dramatically increase the error in resulting vapor pressure values (see Figure 1 and the section Recalculation f rom solid to subcooled liquid and vice versa in Růzǐ čka et al.8) Summarizing, the acceptable agreement of the GLC-RT1S results with the literature data justifies the use of this method

and employing extrapolation to 298 K. To circumvent these difficulties the use of the short capillary GLC columns has been proposed by Bidleman (Westcott and Bidleman,29 Bidleman,40 Bidleman and Renberg,41) who demonstrated that a 1 m capillary BP-1column can be used for estimation of vapor pressures and still provide enough resolution to separate several pesticides, polychlorinated biphenyls, and chlorinated phenols. Later on, the short capillary columns (1 or 2 m) were used by several authors (e.g., Kim et al.,42 Koutek et al.,34 Tittlemier and Tomy43). In this study, motivated by the need to avoid prohibitively long retention times, particularly at lower temperatures, we have tried to avoid extrapolation by using a very short (0.5 m) MXT-1 capillary GLC column. However, even with this very short column the retention times of C20 to C30 n-alkanes were found to be in some cases a few hours at low temperatures (e.g., more than 6 h at 313 K for n-docosane). Moreover, compounds with long retention times gave broad peaks spread over a rather long time scale and it was sometimes difficult to discern the peak when small sample quantities were used. Given the very long retention times t, only some experiments were repeated with reproducibility ±0.05 t. It should be however noted that some measurements were unsuccessful (results were clearly off-trend within the n-alkanes series) for unknown reasons. In contrast to results using longer columns at higher temperatures no trends were observed due to high scatter of data on a short column (compare Figure 2b with Figure 8). While advantages from using shorter GLC columns are apparent, results with extremely short columns (which would enable to provide vapor pressures near ambient temperatures) are unlikely to provide data associated with reasonable uncertainty.

4. CONCLUSIONS We have made use of gas chromatographic retention time measurements of model organic compounds in calculating vapor pressures of these compounds. The purpose of this work was to establish whether the simplest GC vapor pressure model based on single reference compound and neglecting the activity coefficient effect (GLC-RT1S method) yields acceptable vapor pressure results. We selected reference compounds carefully and it is believed that uncertainty in their vapor pressures is at least 1 order of magnitude lower than errors attributed to the GLC-RT1S method. 3548

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Funding

particularly as a guide for estimating volatility of members in homologous series and for the rapid analysis of the fate of compounds entering the environment in cases when no other directly measured vapor pressure data are available. However, predictive power is weak in the group of compounds possessing the same molecular formula but different structures, as demonstrated on a group of alkylbenzenes; a similar conclusion can be derived for a group of chlorobenzenes. Certainly, a larger database of accurate vapor pressures for aerosol-forming compounds for use in air quality models would be highly desirable for developing more accurate computational methods. However, new data for semivolatile multifunctional compounds are difficult to measure by absolute methods, and computational methods are still susceptible to relatively large uncertainties. Rather surprisingly, based on a comparison of different methods for the determination of vapor pressures, Delle Site3 came to the conclusion that the GC-retention time method “can be recommended as one of the most suitable for the determination of the vapor pressure of low volatility compounds”. We would like to stress that the GLC-RT1S method should never be used as an equivalent to the traditional vapor pressure methods to generate vapor pressures as input data for development of estimation methods (they are often mixed with vapor pressures obtained with direct methods) or as reference data for GLC-RT methods. In this regard we agree with Guthrie46 who states that the GLC-RT method “is an empirical correlation and thus its reliability depends on how closely the new compounds resemble the original parameterization set. The values of subcooled vapor pressure are necessarily less reliable than values from more direct measurement.” A subsequent paper dealing with approaches using two or more reference compounds will follow. Finally, we would like to recommend that authors publishing GLC-RT-based vapor pressures tabulate vapor pressures evaluated at the temperature of chromatographic measurements (not only values extrapolated to 298 K). If pGC (or retention times as a function of temperature) at original temperatures were reported, more reliable data could probably be derived using the framework presented in this paper. Recalculation of vapor pressures to 298 K (or to any other temperature) can be performed using thermodynamic extrapolation,44,45 thus avoiding a linear equation for extrapolation, which leads necessarily to large errors.

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The authors acknowledge financial support from specific university research (MSMT No 20-SVV/2017) and the Czech Science Foundation (GACR No. 17-03875S). Notes

The authors declare no competing financial interest.

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ASSOCIATED CONTENT

S Supporting Information *

This file contains . The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jced.7b00548. (i) Four figures (S1 to S4) documenting that eqs 1, 4, and 5 (“Hamilton’s method”) yield identical results; (ii) three figures (S5 to S7) extending information included in Figure 5, and showing relative deviations in vapor pressures for alkylbenzenes (Figures S5 and S6) and chlorobenzenes (Figures S7) (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Michal Fulem: 0000-0002-5707-0670 Květoslav Růzǐ čka: 0000-0001-9048-1036 3549

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