Indirect Determination of Vapor Pressures by Capillary GasâLiquid

Review pubs.acs.org/jced

Indirect Determination of Vapor Pressures by Capillary Gas−Liquid Chromatography: Analysis of the Reference Vapor-Pressure Data and Their Treatment Květoslav Růzǐ čka,*,† Bohumír Koutek,‡ Michal Fulem,† and Michal Hoskovec‡ †

Department of Physical Chemistry, Institute of Chemical Technology, CZ-166 28 Prague 6, Czech Republic. Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, CZ-166 10 Prague 6, Czech Republic

‡

ABSTRACT: Knowledge of low vapor pressures p0 is indispensible for modeling the fate of chemicals in the environment as well as for other important applications. The indirect determination of vapor pressures by the capillary gas−liquid chromatography−relative retention time (GLC−RT) technique has attracted the attention of many research groups, and two review papers devoted to this topic have already been published. To complement these reviews, the quality of the literature vapor pressures for reference compounds is analyzed, along with the influence of the equations used for the temperature dependence of p0 and the effects of the extrapolation interval applied. Since the GLC−RT techniques yield p0 of subcooled liquid even in the case of solid samples, different approaches employed for the recalculation of solid vapor pressures for reference compounds to the values for subcooled liquids are discussed. It is shown that a 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, if improperly selected/applied, even lead to vague and physico-chemically groundless results. In an effort to allow potential users to make an informed decision about what reference data and/or methodology to use to improve the reliability of the GLC−RT based vapor-pressure data, we present a set of recommendations and advisories for appropriate reference data use and manipulation.

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INTRODUCTION Vapor pressure p0 plays a critically important role in a number of applications ranging from technology to ecology. The data for about 9000 compounds have been published,1−4 but for most of the tabulated compounds, the values are available at a limited temperature and/or pressure range. Obviously, for many industrially or environmentally important compounds there are no data at all, and new measurements are still needed, especially in the lowpressure region (below 1 kPa and 1 Pa for technological and environmental applications, respectively). Direct measurements of such low vapor pressures are rare and may be subject to significant systematic errors. There are also indirect methods that rely on the measurement of some other property which is proportional to vapor pressure, and so these techniques require calibration and verification using reliable directly measured vapor-pressure values of reference compound(s). The most frequently used indirect method is the capillary gas−liquid chromatography−retention time (GLC−RT) technique. It is instrumentally simple, requires very small quantities of the test substances in not too high degrees of purity, the temperature is easily modified and a large quantity of data can be collected in relatively short times. There are several modifications of the GLC−RT method which have been reviewed and experimentally compared by Koutek et al.,5 whereas the theory and limitations of the GLC−RT techniques have been discussed by Letcher and Naicker.6 A form commonly used to express the mobile-phase/ stationary-phase equilibrium partition of the target analyte (x) © 2012 American Chemical Society

and reference standard (s) that are run through the gas chromatograph simultaneously in terms of their retention times is7,8 ps0 (T ) (T ) γ∞ t ′ x (T ) Δ(ΔG 0) s ln = ln ∞ + ln 0 =− t ′s (T ) γ x (T ) RT px (T )

(1)

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 vapor pressure, 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), R is the universal gas constant, and Δ(ΔG0) represents the relative change in the molar Gibbs free energy of the interaction of the solutes x and s with the same stationary phase. 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 curve as a function of, e.g., 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 Received: December 13, 2011 Accepted: March 28, 2012 Published: April 30, 2012 1349

dx.doi.org/10.1021/je2013186 | J. Chem. Eng. Data 2012, 57, 1349−1368

Journal of Chemical & Engineering Data

Review

Table 1. Selected Direct Methods of Determining the Vapor Pressures and Their Applicable Pressure Ranges p0min

p0max

method

Pa

Pa

comment

ebulliometry static method gas saturation effusion

102 (Ambrose et al.211) 10−2 (van Ekeren et al.21) 10−7 (Wania et al.172) 10−6 (Booth et al.29)

106 (Ewing et al.212) 106 (Kratzke et al.213) 104 (Mokbel et al.144) 101 (Zaitsau et al.27)

A B C D

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

Thus, for vapor pressures d ln px0 d ln ps0

=

(2)

p0x

and

p0s

we can write

Δgl Hx Δgl Hs

and after integration (assuming the ratio stant) we have ln px0 =

closer scrutiny: (i) the accuracy of the vapor pressure data for reference compounds, (ii) the reliability of the equations used for the extrapolation of these data from the temperatures of the GLC measurements to the required temperature (usually 298.15 K), and (iii) the quality of the approximations used for the recalculation of the properties of a solid to those of a subcooled liquid. Important decisions must be made about the experimental reference data and their further transformation to balance effort with accuracy and reliability. It should be emphasized that the vapor-pressure data published are notoriously variable for individual compounds and that in the process of selecting data there is a chance for subjective bias, even when one exercises professional judgment. Hence, an apparent simplicity of the GLC−RT method can be misleading, and in routine applications, the information it brings can be erroneous if some of its complex aspects are not correctly perceived and taken into consideration. Although the number of experimental parameters to be controlled is not small, in eqs 1 to 5, it is possible to see two of the most prominent sources of uncertainties in using the GLC−RT model: (a) potentially large errors in the reference compound vapor pressures (p0s as a function of T) and (b) uncertainty in describing the liquid∞ phase nonideality ratio, represented by γ∞ s (T)/γx (T). In this study, we have focused on an investigation of the uncertainties related to issue (a). An evaluation of the magnitude of the contribution of the reference-data effect represents a necessary prerequisite also for more detailed studies of other (chromatographic) factors, particularly the approximations concerning the activity coefficient ratio. The intent of our study is to investigate the sensitivity of the p0L values on (i) different principal sources for vapor-pressure values including retrieval from original literature, computerized databases, and our own experimental measurements, (ii) different two- and more-parameter vapor-pressure equations as regards their extrapolation ability to lower temperatures, and (iii) different approaches for the recalculation of solid vapor pressures for reference compounds to values for subcooled liquids (and vice versa) based on the use of the entropy of fusion ΔlsS and divergent assumptions regarding heat-capacity change (ΔslCp = 0 vs ΔlsCp ≠ 0). Although the GLC−RT method seems to be less popular now than before, the interest in this area may be renewed in the years to come, provided that all the factors responsible for a certain limitation of the method are controlled and/or critically evaluated.

(3)

Δgl Hx/Δgl Hs

is con-

Δgl Hx ln ps0 + C Δlg Hs

(4)

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

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

(5)

Equation 5 is identical with the equation derived by ∞ Hamilton10 (assuming γ∞ x /γx = 1 or incorporating this ratio into the constant C′). Accordingly, the ratios of the adjusted retention times are obtained over a range of temperatures and correlated with p0s at a given temperature using eq 5 to obtain Δgl Hx/Δgl Hs and the constant C (C′). These values are used to calculate, through eq 4, the vapor pressure of the test compound p0x at the temperature of interest. For thermodynamic reasons, the determined vapor pressures are obtained for the subcooled liquid p0L. Nevertheless, the p0x values thus obtained usually differ from the p0L values measured by direct techniques. This led some authors to moderate the implied (in)accuracy incorporated in the GLC−RT method by referring to them not as the p0L values but as the p0GC values.11,12 In order to obtain the p0L values, the p0GC data have usually been corrected by using a calibration curve constructed from the p0L values derived from direct methods to remove the systematic error(s) inherent in the GLC−RT approach. Under the usual assumption of error-free system variables such as the retention times, oven temperature, and hold-up time, there are two possible general sources of bias in the model performance to consider. The first concerns the chromatographic factors that include the sets of theoretical equations describing the retention mechanism as well as the imposed physical and chemical constraints of a given chromatographic situation. The second source of bias arises from nonchromatographic factors, whose impact needs to be assessed prior to evaluating the chromatography-related factors and the validity of eq 1. Particularly, the following nonchromatographic factors require

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SURVEY OF THE MAIN DIRECT METHODS FOR VAPOR-PRESSURE DETERMINATION AND THEIR LIMITATIONS Reliable vapor pressures of a reference compound obtained by the direct method provide indispensable input information for indirect GLC−RT techniques. There are many methods for determining pure-component vapor pressures (for a thorough review, see e.g., refs 13−17). However, none of these methods is able to measure p0 over the whole range of pressures and the accurate experimental measurement of low and very low vapor pressures is still a significant challenge. 1350



Review

measured in their laboratory were in error, probably owing to a violation of the isotropy for the gas that is close to effusion.28 This results in the enthalpies of vaporization from the Knudsen method being systematically higher than those measured calorimetrically. Several apparatuses have recently been built with an effort to avoid above-mentioned systematic errors.29−31 In some configurations, the influence of impurities can be eliminated. All direct methods tend to be labor-intensive and timeconsuming. While precisions of a few percent appear to be attainable in a single laboratory, agreement between laboratories is far less satisfactory. Bidleman11 quoted papers reporting the results obtained by the effusion and transpiration methods in the subpascal pressure region with an agreement of no better than a factor of 2 to 3. Similarly Delle Site16 summarized the ratios of the maximum to minimum reported p0 values for a number of chemicals ranging from 1.35 to 77.3 (see Table 6 in ref 16).

A brief overview of the measurable-pressure ranges of the most frequently used methods together with some of their limitations is presented in Table 1. Although there are also other methods (e.g., optical, thermogravimetric, spectroscopic, etc.), the number of data obtained by these methods is limited and qualified judgment of their uncertainty is beyond the scope of this paper. Comment A. Ebulliometry is well established for the measurement of vapor pressures of liquids in the medium pressure range, where it is capable of achieving a precision of 10−5·p0. It was successfully applied at pressures as low as 2 kPa,18,19 but at lower pressures smooth boiling can only be achieved with difficulty and the uncertainty rises significantly.13 In the GLC−RT context, ebulliometry is an important source of the p0 data for calibration compounds. Comment B. Contrary to ebulliometry, both the solid and liquid samples can be studied by the static method, which is nowadays performed almost exclusively by means of capacitance manometers. The use of modern pressure gauges means that it is theoretically possible to use the static method down to very low pressures, but the adsorption of volatiles (especially of water, inevitably present in a minute amount in most commercially available chemicals) onto the surface of the apparatus and the presence of impurities and gases dissolved in the sample make this method difficult to use in practice at subpascal pressures. For example, in our study on naphthalene with the static method,20 we found that vapor pressures lower than 0.7 Pa are not consistent with the thermodynamically derived data. Generally, such a test can be done only in cases where the relevant auxiliary data (heat capacities, enthalpies of the phase transitions) are available; in most cases such systematic errors remain undetected. Reliable subpascal values of p0 were however obtained by van Ekeren et al.21 using a spinning rotor gauge. While incomplete degassing tends to increase the p0 measured, adsorption can induce the opposite effect in the subpascal pressure region. Comment C. The gas saturation (or transpiration) method is suitable for both solid and liquid samples below approximately 3 kPa. If a suitable method is used for the analysis of the sample transported by a carrier gas, the results are not disturbed by impurities. Common problems encountered when using gassaturation methods include a quite long measurement period if a large volume of carrier gas is needed in order to collect a sufficient amount of vapor for analysis and susceptibility to certain types of systematic errors (e.g., leaks) that can be difficult to detect (for a detailed analysis of these errors, see, e.g., the recent paper by Widegren and Bruno22). Additional errors can result from the adsorption of the sample on the apparatus' walls before the sample can be analyzed. This phenomena was monitored online and discussed in detail by Sinke.23 Adsorption and (in some configurations) incomplete trapping and/or recovering of the trapped sample tends to lower the vapor pressures measured. Comment D. Knudsen effusion methods are usually applicable over a short temperature and pressure range and are among the most widely used for measuring the vapor pressures of crystalline organic compounds with pressures under 1 Pa. However, interlaboratory comparison reveals usually only moderate agreement. One possible reason can be the temperature gradient in the sample caused by insufficient heat transfer, as described by van Ginkel et al.24 (which leads to lower p0 values). Despite great care to eliminate this source of errors, the results obtained simultaneously by two modifications of the effusion method (weighing and torsion effusion, respectively) yielded somewhat different results.25 There might be an additional problem as reported by Zaitsau et al.,26,27 who found that most of the results previously

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SELECTION OF A SUITABLE VAPOR-PRESSURE EQUATION Establishing reliable data for reference and calibration compounds and their reliable extrapolation to the required temperature (usually 298.15 K) is closely interconnected with the selection of an appropriate vapor-pressure equation. Many correlation equations have been proposed and there are several comparative studies focused on the flexibility and extrapolation behavior of respective equations.32−34 It is known35 that ln(p0) vs 1/T is not linear but exhibits an S-shape for most compounds (see, e.g., Figure 5 in ref 36). Below the normal boiling temperature, this curve is concave, the enthalpy of sublimation/ g vaporization Δcd H is always decreasing with increasing temperature, and the difference of the heat capacities between the ideal gas and condensed phase ΔgcdCp is always negative. In contrast, a two-parameter equation ln(p0 /Pa) = A − B /(T /K)

(6)

can be derived from the Clapeyron equation assuming that ΔgcdH is constant and ΔgcdCp is zero (the ideal behavior of the gas phase is also assumed) and is therefore accurately applicable over short ranges only, where these approximations are valid (typically for p0 obtained by the effusion method). The application of eq 6 for extrapolation over an extended temperature range leads to significant errors. More parameters are needed for a realistic description of the saturation curve, and even three-parameter Antoine equation ln(p0 /Pa) = A − B /(T /K + C)

(7)

as well as other three-parameter equations were found to be unsuitable for extrapolation32,34 and also for a correct description of not only p0 but also ΔgcdH and ΔgcdCp over a moderate temperature range.34 According to Scott and Osborn,32 the Cox equation37 ln(p0 /p ref ) = (1 − T ref /T ) exp(A + B(T /K) + C(T /K)2 )

(8)

performed the best extrapolation for n-decane, and this conclusion was later confirmed by Růzǐ čka and Majer34 for an extended set of compounds. The Wagner equation38 in the form ln(p0 /pc ) = (Tc/T )(A τ + Bτ1.5 + C τ2.5 + D τ5) 1351

(9)



Review

where τ = 1 − T/Tc, also performs very well, but it requires critical temperature Tc and pressure pc, which are seldom available for compounds of environmental interest. Finally, the equation

Simple extrapolation using high-quality data measured over an extended temperature and pressure range in connection with a reasonable vapor pressure equation [the Cox equation (8) or Wagner equation (9)] can yield reliable data even far below the temperatures of measurement. Examples of such reliable data are the results reported by the former Bartlesville laboratory,19 where the vapor pressures for a number of compounds were measured by two complementary techniques, namely by the static method (a pressure range from (0.01 to 2) kPa) and ebulliometry (2 to 270) kPa. For most compounds, the situation is however less favorable and the available data exhibit either higher scatter or shorter temperature/pressure range or both. In such cases, thermodynamically controlled extrapolation (hereafter denoted as SimCor) can be used.20,34,42,43 This method employs exact thermodynamic relationships between vapor pressure and its derivatives with respect to temperature (vaporization/ sublimation enthalpies ΔgcdH and gas−liquid/solid heat capacity differences ΔgcdCp), which are accessible with reasonable accuracy at temperatures, where vapor pressures are so low that their direct measurement is prone to significant systematic errors or even impossible. Simultaneous correlation of the above properties (p0, ΔgcdH, and ΔgcdCp) yields vapor pressure equation valid over combined temperature ranges of p0, ΔgcdH, and ΔgcdCp. Although this method is somewhat data-demanding (besides vapor pressures at least the heat capacities of the gas and condensed phase are required), it can yield reliable data well below the experimentally accessible pressure range (p0 5000

type

a

compounds coveredb

PCBh ENVi

n-alkanes AHm CLn alkanes PCBh HCHq PAHs PAHs

vapor pressure eq used

used byf

no

eq 7 eq 7 eq 7 no psj eq 7

53,86,120 1,137 4,119,120,122,126,132 84 none 4,122,126,129,130

yes yes yes yes yes yes yes

yes yes yes no no no yes

no eq 7 eq 8 psj psj eq 7 eq 9

120 1,120 5,39,56,57,106,107,120 none none 122,126 none

yes yes yes no yes yes yes no

yes no no

eq 6 eq 7 eq 6 psj no eq 10 no no

none none none 63 none none 77,86,94,119,122,126 none

all datad

recommendation

yes yes yes yes yes no

no yes no yes yes no

no yes no no no yes

yes yes yes yes yes no yes

no yes yes yes yes no yes

yes yes yes yes yes yes yes yes

yes no yes yes yes yes no yes

citations

c

tracebility yes

yes no no

e

a References are divided into following categories: B (bibliographic), E (for engineering use), S (for scientific use); for more details see text. bUsed only in cases when given data source is focused to defined group of compounds. cIndicates whether citations to primary data sources are given. d Indicates whether the authors included all data available at the time of publishing. eDenotes whether process of recommended data selection is fully documented (for more details see the text). fList of references to GLC-RT users (or other datasources related to GLC-RT) who utilized data from a given reference. gDykyj tables115,116 were extended and superseded by Dykyj et al.1−3 hPolychlorinated biphenyls. iPolycyclic aromatic hydrocarbons, polychlorinated biphenyls, polychlorinated dibenzo-p-dioxins and furans, selected pesticides, and some reference compounds. jVarious equations as used in the primary literature source are listed. kStephenson and Malanowski handbook137 is in fact an English version of the original work by Dykyj115,116 however without literature sources. lTRC tables113,114 were extended and superseded by Dykyj et al.;1−3 electronic up-to-date version can be obtained via http://trc.nist.gov. mAromatic hydrocarbons. nChlorobenzenes, polychlorinated biphenyls, polychlorinated dibenzo-p-dioxins, and dibenzofurans. oLi et al.124 used two-parameter eq 6 which substantially decrease usefulness of this work. pIn order to trace data selection, for many compounds one has to possess either TRC tables113,114 or Dykyj compilations115,116 in order to avoid using rather old and possibly inaccurate data. For some compounds, data tabulated by Stull112 were used. Also recall that extrapolation from eq 7 yields incorrect values (see “Selection of a Suitable Vapor-Pressure Equation” section). qHexachlorocyclohexanes. rThis data source contains enthalpies and temperatures of fusion, which are in the GLC - RT context indispensable for recalculation of vapor pressures of solids to those of subcooled liquid and vice versa (see “Recalculation from Solid to Subcooled Liquid and Vice Versa” section). sPolyaromatic hydrocarbons. tMa et al.129 published comprehensive database as a supporting info of their paper, but this database contains too many errors to be fully listed (e.g., for acenaphthene several data sets measured well below the melting point 366 K are reported as liquid vapor pressures, temperatures for data44 are shifted by100 K, temperature for two data sets is −273.15 °C, some important data sources are omitted (e.g., refs 89 and 107), recommendation by Roux et al.125 is ignored etc.).

As a starting point, the paper by Stull112 must be mentioned. Stull112 collected data for over 1200 organic compounds published prior to 1942 and graphically extended the existing vapor-pressure data sets to a uniform pressure range of 1−760 Torr (ten discrete values are published along with the references to the literature used). Although it was excellent at the time of its publication, using the values derived from this paper is no longer recommended, as it is in many cases based on 19th-Century results. All of the relevant data sources used by Stull112 (and many more) were later used, e.g., by the staff of the Thermodynamic Researcher Center (TRC)113,114 and also by Dykyj et al.,115,116 so there is no need to use the data from Stull112 anymore. Unfortunately, the values from this paper are commonly used in many data handbooks and review papers as well as in scientific papers including those using the GLC−RT technique.1,4,61,69,75,81,107,117−122 An optimal source of vapor pressures for the reference/ calibration compounds is the critical review (denoted S in

the success of the indirect GLC−RT technique is based on reliable data for the reference compounds obtained by direct methods, some authors did not report the origin of the data for reference/calibration compounds and/or other important information51,73,77,83,87−89,91,93,95 or used secondary sources (so that the original data cannot be easily traced)78,94 or used data previously obtained by indirect GLC−RT techniques.39,67,68,72,73,79,93,95,97,98,101,105 Sources of Data for the Reference/Calibration Compounds. Prior to addressing the approach of individual researchers to the selection of the “best” data for reference and/or calibration compounds, we found it useful to classify the vapor-pressure data sources into several categories. Only those data sources used by the authors of the GLC−RTderived vapor pressures (or data sources relevant to this technique) are mentioned and summarized in Table 3 (a more extensive list of p0 data sources can be found, e.g., in ref 111). 1354



Review

whereas Lemmon and Goodwin123 treated a number of compounds simultaneously, which makes this correlation robust in terms of inter- and extrapolations. The values calculated from the correlation by Ambrose and Walton36 and by Lemmon and Goodwin123 are in most cases practically identical and rather close to those reported by Růzǐ čka and Majer.43 The disagreement is most significant in the case of n-eicosane (16.8 %, i.e., 3.5·10−4 Pa at 298.15 K) as shown in Figure 3. As can be seen in Figure 3, the correlation by

Table 3), where all of the published data are compiled, the reasoning for the selection of the recommended values is presented, and the accepted/rejected sources are clearly identified. This approach enables an easy upgrade of a recommendation once new data become available. In S-category sources, only original data are considered, i.e., no smoothed, extrapolated, estimated, or quoted values should be included, thereby avoiding multilevel referencing. Examples (relevant to this review) are the papers by Růzǐ čka and Majer,43 Lemmon and Goodwin,123 Li et al.,124 and for the recalculation of p0solid to p0liquid (see “Recalculation from Solid to Subcooled Liquid and Vice Versa” section) also Roux et al.125 This category also includes these values from the TRC Tables113,114 and tables by Dykyj et al.115,116 which are based on not-too-old data and assigned the highest degree of reliability. The last source is however becoming obsolete and has been superseded by new, three-volume tables,1−3 containing the parameters of the Antoine equation (7) with the applicable temperature range and “quality grade” for almost 9000 compounds. New Dykyj et al. tables1−3 were created by merging the TRC datafiles113,114 with the work of Dykyj et al.115,116 and still belong to the S category, although with restrictions for some compounds (see Table 3). Data sources containing a comprehensive list of literature references to p0 data or even p0 data itself are also very valuable; they are denoted as B in Table 3.4,16,119,122,126−130 Some of these sources contain also recommended values, however without traceable arguments.122,126−129 Sources from the B category are an excellent starting point for anyone who wants to produce a recommendation which aspires to become an S-category source. The remaining sources listed in Table 3 (marked E), despite their being excellent or at least sufficient for engineering use, should be avoided in scientific applications, especially in connection with the GLC−RT technique. The E-category sources are either not comprehensive118,120,131−136 or of uncertain origin (without traceable sources).137,138 It should be noted that a lack of information about the accepted/rejected data sets is presumably unimportant for authors of reviews,124,128,129,139 as the “best” vapor pressures are subsequently corrected to be consistent with several other properties, which are subject to thermodynamic constraints (solubility in water, Henry’s law constant). This type of thermodynamic consistency check, established by Beyer et al.,139 however differs significantly from SimCor described in “Selection of a Suitable Vapor-Pressure Equation” section. Solubility in water and Henry’s law constant are (in most cases) subject to similar uncertainties as vapor pressures, and therefore Beyer’s procedure rather than improves the reliability of vapor pressures leads to the averaging of errors of the individual properties. n-Alkanes. The most frequently used reference/standard compounds are n-alkanes.11,39,48,59−61,64,65,81,84,93,95,101,105−107 There are several review papers dealing with the vapor pressures of n-alkanes, e.g., Ambrose and Walton,36 Růzǐ čka and Majer,43 and Lemmon and Goodwin.123 The papers by Ambrose and Walton36 and by Lemmon and Goodwin123 cover the entire liquid saturation curve from the triple point to the critical temperature for n-alkanes from methane up to neicosane and n-hexatriacontane, respectively. The paper by Růzǐ čka and Majer43 is limited to pressures of less than 101.325 kPa. It should be noted that the correlation by Ambrose and Walton36 and Růzǐ čka and Majer43 treated each compound separately,

Figure 3. Relative deviations {p0(lit) − p0(rec)}/p0(rec) of the literature vapor pressures p0(lit) for n-eicosane from the values recommended by Růzǐ čka and Majer43 p0(rec). □, Macknick and Prausnitz;146 ●, Chirico et al.;140 −, Lemmon and Goodwin;123 ◑, Viton et al.;142 ⬠, Razzouk et al.;145 ◨, NIST Standard Reference Database #103 as quoted by Widegren and Bruno;22 ☆, Widegren and Bruno;22 ·····, absolute deviations.

Růzǐ čka and Majer43 better describes the high-quality data by Chirico et al.140 Moreover, the latter correlation is constrained near the triple-point temperature to describe correctly the calorimetric enthalpies of the vaporization and heat capacity differences Δgl Cp = Cgp − Clp (Cgp stands for the ideal gas capacity and Clp for the heat capacity of liquid). Although there were no reliable Clp for n-heptadecane to n-eicosane and this constrain could not be used for these compounds, such data became available later,141 and it can be shown that the heat-capacity difference of n-eicosane is described better by Růzǐ čka and Majer43 than by Ambrose and Walton36 or by Lemmon and Goodwin.123 Also the current electronic version of the TRC tables yields for n-eicosane values which are closer to Růzǐ čka and Majer43 than to Lemmon and Goodwin123 (see Table 2 in ref 22 and Figure 3). Additional results for other n-alkanes and temperatures are presented in Table 4. To conclude, the data from any of the three correlations36,43,123 can be used for the calculation of vapor pressures of n-alkanes with reasonable accuracy, although the thermodynamically constrained values by Růzǐ čka and Majer43 are preferable at low pressures. For n-alkanes higher than C20, the correlation by Lemmon and Goodwin123 has no alternative. There are some recent measurements of p0 for higher n-alkanes by direct methods,22,142−145 but the relatively small number of new data points in combination with their experimental uncertainty (see Figure 3) makes the probability of an updated recommendation in the near future unlikely. Although most papers using the GLC−RT techniques with n-alkanes as reference compounds have been published after Ambrose and Walton’s recommendations,36 this review has never been used as a source of data for n-alkanes. Similarly, a paper by Lemmon 1355



Review

Table 4. Differences between Vapor-Pressure Data Reported by Růzǐ čka and Majer43 and Lemmon and Goodwin123 for nAlkanes at Several Temperatures T/K

NCa

13

14

15

16

17

18

19

20

298.15

σrb σb σr σ σr σ σr σ

3.85 0.22 2.17 0.95 0.41 3.9 −0.09 −7.2

5.56 0.10 3.33 0.54 0.84 3.7 −0.04 −1.8

7.37 4.2·10−2 4.54 0.27 1.31 2.7 0.05 1.3

5.77 1.1·10−2 3.74 8.6·10−2 1.23 1.2 0.11 1.5

7.99 4.9·10−3 5.07 4.4·10−2 1.65 0.77 0.20 1.6

9.39 1.9·10−3 5.93 2.0·10−2 1.96 0.44 0.29 1.3

11.07 7.3·10−4 6.95 8.7·10−3 2.29 0.25 0.38 0.94

16.84 3.5·10−4 10.55 5.0·10−3 3.59 0.18 0.74 1.0

323.15 373.15 423.15

Number of carbon atoms of n-alkane. bRelative σr = 100(p0(LG) − p0 (RM)))/p0 (RM), and absolute σ/Pa = p0(LG) − p0 (RM) deviations, where p0(LG) and p0(RM) are the vapor pressures based on correlation by Lemmon and Goodwin123 and Růzǐ čka and Majer,43 respectively.

a

and Goodwin123 has never been used either as a source of reference data or for comparison by any author. While Ballschmiter 84,90−95 and Govers 53,85−89 groups developed generalized equations for the vapor pressures of n-alkanes, all but one52 of the other authors used the twoparameter eq 6 for reference n-alkanes.11,48,59−61,64,65,81 The poor extrapolation behavior of eq 6 was already described in the “Selection of a Suitable Vapor-Pressure Equation” section by using high-quality data for n-decane. It was also already stated that using eq 6 over an extended temperature interval leads to errors significantly exceeding the experimental uncertainty in p0 and biased values of vaporization enthalpies. This is demonstrated in Figure 4, where deviation from the recommended p0 is shown along with the enthalpies of the vaporization of n-alkanes used in papers.11,48,59−61,64,65,81 Vapor pressures are commonly extrapolated by the users of the GLC−RT techniques outside the temperature interval where the parameters of eq 6 were established, which leads to additional errors. To evaluate the approximate error caused by the combination of using both extrapolation and unsuitable eq 6, the calculations were performed of how such data treatment would influence the vapor pressure of another n-alkane using Othmer’s eq 4. Temperature ranges used for the derivation of the parameters of eq 4 were the same as those utilized by the GLC−RT users. The results are summarized in Table 5. It is apparent that the length of the temperature range used for the derivation of the parameters of eq 4 as well as the extrapolation interval play an important role. The deviation of the vapor pressures along with the enthalpies of the vaporization (at 298.15 K) from the recommended values are shown in the last two columns of Table 5; the errors caused by such data treatment (i.e., by the combination of using unsuitable eq 6 and of extrapolation) significantly exceed experimental uncertainty. Some authors (e.g., Hinckley et al.,60 Falconer and Bidleman,62 and Tittlemier and Tomy67) have used this extrapolated enthalpy of vaporization for the reference compound for establishing the enthalpy of the vaporization of the compound in question, which in turn was converted into parameter B of eq 6. Parameter A of eq 6 was then calculated from the extrapolated p0 at 298.15 K, and this equation was claimed to be valid also at temperatures lower than 298.15 K. It is apparent that the values calculated from eq 6 with the parameters obtained in this way are prone to errors exceeding those in Table 5. Ballschmiter et al. published seven papers reporting the p0 obtained by the GLC−RT technique,84,90−95 but in many cases the description of the methodology is insufficient and it is not clear which reference/calibration compounds were used. In three

Figure 4. A. Relative deviations {p0(lit) − p0(rec)}/p0(rec) of the vapor pressures of n-alkanes used as a reference in the papers reporting vapor pressures determined by GLC-RT, p0(lit), from the values recommended by Růzǐ čka and Majer43 p0(rec). B. Comparison of vaporization enthalpies Δgl H of n-alkanes obtained from p0(lit) used as a reference in the papers reporting vapor pressures determined by GLC-RT from those derived from p0(rec) by Růzǐ čka and Majer.43 −■−, Bidleman (C18);11 −□−, Lei et al. (C18);64 −▲−, Lei et al. (C18);65 −Δ−, Hinckley et al. (C20);60 −★−, Sherblom et al. (C16);61 −○−, Lei et al. (C13);81 −◑−, Lei et al. (C15);81 −●−, Lei et al. (C18);81 −☆−, Yamasaki48 (C19, partially displayed); −, recommended values by Růzǐ čka and Majer.43

papers,84,93,95 the utilization of n-alkanes was explicitly reported; in another two papers,91,92 it is implicit (Kováts indices82 were used). Fischer et al.84 used a generalized equation for the vapor pressure of n-alkanes C15 to C28. Their simple equation log10(p0(298.15 K)) = −0.45nC + 6.6, where nC stands for the number of carbon atoms, is based on the extrapolated data by Macknick and Prausnitz,146 1356



Review

Table 5. Differences in Vapor Pressures and Vaporization Enthalpies between Those Recommended by Růzǐ čka and Majer43 and Used by GLC-RT Usersa ref n-alkane f

n-tridecane n-pentadecanef n-pentadecanef n-hexadecaneh n-octadecane n-octadecane n-octadecane n-octadecane n-octadecane n-octadecane n-octadecane n-nonadecane n-nonadecane n-nonadecane n-eicosane n-eicosane n-eicosane

lit. for reference n-alkane 81

Lei et al. Lei et al.81 Lei et al.81 Sherblom61 Macknick and Macknick and Macknick and Macknick and Macknick and Lei et al.81 Macknick and Morecroft147 Morecroft147 Morecroft147 Macknick and Sasse et al.178 Macknick and

Prausnitz146 Prausnitz146 Prausnitz146 Prausnitz146 Prausnitz146 Prausnitz146

Prausnitz146 Prausnitz146

GLC-RT lit. using reference n-alkane

Tmin − Tmax/Kb 298−368 298−438 298−438 298−423 318−361 318−361 318−361 318−361 318−361 298−383 318−361 306−328 306−328 306−328 344−380 363−466 344−380

81

Lei et al. Lei et al.81 Lei et al.81 Sherblom et al.61 Lei et al.65 Bidleman11 Bidleman11 Bidleman and Renberg59 Lei et al.64 Lei et al.81 Koutek et al.52 Yamasaki48 Yamasaki48 Yamasaki48 Hinckley et al.60 Koutek et al.52 Bidleman11

c GC TGC min − Tmax/K

308−368 338−438 398−438 353−423 293−323 313−373 313−373 323−383 323−423 338−418 363−413 383−473 383−543 483−543 343−453 363−413 383−403

test n-alkane n-hexadecane n-hexadecane n-hexadecane n-octadecane n-eicosane n-hexadecane n-eicosane n-eicosane n-eicosane n-eicosane n-eicosane n-eicosane n-eicosane n-eicosane n-octadecane n-octadecane n-octadecane

g

σpd

σHe

9.4 56.7 134 75.2 1.3 12.8 16.7 35.6 47.8 63.3 79.3 232.2 407.5 1118 85 −17.8 70.3

−5.8 −12.6 −17.0 −13.1 −2.3 −6.6 −6.7 −9.0 −10.9 −11.8 −13.9 −18.6 −22.2 −27.5 −14.1 5.6 −12.6

a

Equation 6 was used in all cases except by Koutek et al.,52 who used parameters of Antione equation (7) published by Sasse et al.178 bTemperature range of experimental vapor pressure data for reference n-alkane. cTemperature range of chromatographic experiment. dRelative error σp = 100(p0(calc)−p0(rec))/p0(rec), where p0(calc) is the vapor pressure at 298.15 K calculated from Othmer’s equation (4) whose parameters were 43 e GC 0 Relative error determined in temperature range TGC min − Tmax; p (rec) is the vapor pressure at 298.15 K calculated according to Růzǐ čka and Majer. g g g g σH = 100(Δl H(calc) − Δl H(rec))/Δl H(rec) where Δl H(calc) is the vaporization enthalpy at 298.15 K calculated from Othmer’s equation (4) GC g whose parameters were determined in temperature range TGC min − Tmax; Δl H(rec) is the vaporization enthalpy at 298.15 K calculated according to 43 f Růzǐ čka and Majer. Both experimental and treated (recommended) data were used, which might result in multilevel referencing. gVapor pressure of n-hexadecane, n-octadecane, and n-eicosane at 298.15 K is 0.191 Pa, 2.01·10−2 Pa, and 2.09·10−3 Pa, respectively.43 hData selection is described only in Ph.D. Thesis by Sherblom.

Morecroft,147 and a compilation of literature data by Stein.148 The results of this generalization are compared with the values calculated from the correlation by Lemmon and Goodwin123 in Figure 5. Kurz et al.93 only mention using n-alkanes C8 to C34 while Hackenberg et al.95 only state that “n-alkanes have been used as standard compounds”. Govers et al. have published six papers reporting the p0 obtained by the GLC−RT techniques.53,85−89 Several different approaches have been tested and used, but n-alkanes were used as reference compounds in all cases. In contrast to all the other GLC−RT users, not only the vapor pressures but also the enthalpies of vaporization and heat capacities were considered in order to ensure thermodynamically meaningful results. Unfortunately, the p0 data used by Govers came from unreliable sources, and/or their origin is not reported. In the first three papers,53,85,86 data were taken from the handbook by Ohe;118 in the second and third paper, also data by Macknick and Prausnitz146 and data from the 72nd edition of the CRC Handbook120 were used, respectively. As already discussed in the “Sources of Data for the Reference/ Calibration Compounds” section, the first edition of the handbook by Ohe118 belongs in the E(ngineering) category of the p0 data sources. It provides the parameters of the Antoine equation (7). For some compounds including C4 to C10 n-alkanes, Ohe listed multiple sets of the parameters of Antoine equation (7) and it is not clear which sets were used by Govers group. For the C6 to C16 n-alkanes, reliable ebulliometric data by the Rossini group149−151 are given; however, for C6 to C10 n-alkanes, also parameters based on data by Carruth and Kobayashi (shown by many authors32,43 to be of low quality) are given. The situation is worse for higher n-alkanes: for the C17 and C18 n-alkanes, for instance, data by Kraft from 1882 are used;152 for the C21,C23−C26, the data compiled and graphically extrapolated by Stull112 are employed; and for the

Figure 5. Relative deviations {p0(gen) − p0(rec)}/p0(rec) of the vapor pressures of n-alkanes at 298.15 K obtained from the generalized correlations suggested by the GLC-RT users p0(gen) from the recommendation by Lemmon and Goodwin123 p0(rec). −○−, Govers et al.86 (partially displayed); −■−, Krop et al.;87 −★−, Fischer et al.84

C19 and C27 n-alkanes, data published by Morecroft147 are utilized. Vapor pressures published by Ohe for n-alkanes with more than twenty carbon atoms differ from the recommendation by Lemmon and Goodwin123 by several hundreds of percent when extrapolated to 298.15 K. Generalized equations based on these literature data118,120,146 were established by Spieksma et al.85 and van Haelst et al.,53 who published equations relating vapor pressure to the Kováts indices; a comparison with the recommended p0 data cannot be readily performed. The generalized relation of vapor pressure to both temperature and the number of carbons was published by Govers et al.86 and is compared (at 298.15 K) with data by Lemmon and Goodwin123 in Figure 5. According to Govers at al.,86 this 1357



Review

generalized equation was based on data from n-butane to n-hexacosane; it was extended by Krop et al.87 by using the p0 from propane to n-pentatriacontane and subsequently used by van Roon et al.88 and Haftka et al.89 Also this extended correlation is shown in Figure 5. According to van Roon et al.,88 “no experimental values were omitted, even if the difference between the experimental value and the model was more than three times the standard deviation”, which can explain the large difference between the data used by Govers and the recommendation by Lemmon and Goodwin.123 Despite the fact that the two correlations by Govers group published in 199686 and 199787 differ significantly, the authors did not comment on it. Koutek et al.5,56,57,74 and Chickos et al.39,106,107 used the data by Růzǐ čka and Majer.43 Taken together, most of the GLC−RT-technique users quoted in this section could introduce errors in p0 of up to several orders of magnitude by using unreliable data for the reference n-alkanes. Any conclusions derived from such data might be dubious. Dibutylphthalate. The vapor pressures of butylphthalate (CAS RN 84−74−2) measured by direct methods have been published by Gardner and Brewer,153 Hickman et al.,154 Verhoek and Marshall,155 Burrows,156 Small et al.,157 Birks and Bradley,158 Perry and Weber,159 Hammer and Lydersen,160 Franck,161 and Hales et al.162 A summary by Mackay et al.4 contains (besides the above-mentioned vapor pressures by direct methods) also indirect data and parameters of Antoine equation (7) by Werner,163 which are obviously misprinted in original paper already. Dibutylphthalate was used as a reference compound by Jensen and Schall,46 Hamilton,10 and indirectly by Westcott and Bidleman.47 In all cases, the authors used the recommendation by Small et al.,157 who combined their results with selected previously published values.154,156 Note that for more volatile dimethylphthalate and diethylphthalate the agreement of the data by Small et al.157 with thermodynamically consistent data measured on several apparatuses164,165 is only moderate (12 % and 18 %, respectively, at 303 K). The usage of dibutylphthalate was later questioned due to a possible specific interaction with some gas chromatographic phases by Bidleman11 and by Kuo et al.51 Still, dibuthylphthalate was later used as a reference compound by Donovan96 and by Tsuzuki;99 both authors followed the recommendation by Hamilton,10 i.e., values calculated from the equation by Small et al.157 Newer data,158−162 unfortunately not considered by refs 10, 46, 96, and 99, seem to disagree with the recommendation by Small et al.,157 especially at lower temperatures, where the difference can amount up to several tens of percent (see Figure 6). p,p′-Dichlorodiphenyltrichloromethylmethane (p,p′DDT). The temperature-dependent vapor pressures of p,p′-DDT (CAS RN 50−29−3) obtained by direct methods have been published by Balson,166 Kuhn and Massini,167 Dickinson,168 Spencer and Cliath,169 Rothman,170 Webster et al.,171 and Wania et al.172 The gas-saturation method was used by all of the authors except for Balson166 (the effusion method). It seems that the results by Kuhn and Massini167 and by Webster et al.171 are outliers and will not be discussed any further. Some authors168,170 have reported problems with p,p′-DDT decomposition catalyzed by iron. The vapor pressures reported at a single temperature and/ or determined by the indirect method are not quoted here and can be found in Shen and Wania128 and Mackay et al.4 p,p′-DDT was used as a reference compound by Eitzer and Hites,49 Hinckley et al.,60 van Haelst et al.,53 Drouillard,63 Lei et al., 64 Wong et al., 66 Tittlemier and Tomy, 67

Figure 6. A. Relative deviations {p0(lit) − p0(rec)}/p0(rec) of the literature vapor pressures p0(lit) for dibutylphthalate from the values recommended by Small et al.157 p0(rec). B. Comparison of vaporization enthalpies Δgl H of dibutylphthalate. Δ, Gardner and Brewer153 (partially displayed); ■, Hickman et al.;154 ◮, Verhoek and Marshall;155 □, Burrows;156 ☆, Small et al.;157 ★, Small et al. (redistilled sample);157 ◐, Birks and Bradley;158 ∗, Perry and Weber;159 ⬠, Hammer and Lydersen;160 ▼, Franck;161 ●, Hales et al.162 (large saturator); ○, Hales et al.162 (small saturator); ◆, Hales et al.162 (large and small saturator); ·····, absolute deviations.

Tittlemier et al.,68,72 Bidleman et al.,70 Vetter et al.,73 Goel et al.,79 Zhang et al.,80 and as one of calibration compounds by Bidleman,11 and Hinckley et al.60 Eitzer and Hites49 as well as Bidleman11 and Hinckley et al.60 employed data by Balson,166 Dickinson,168 Spencer and Cliath,169 and Rothman170 for establishing the recommended data with slightly different results. The recommendation of Eitzer and Hites49 was used by van Haelst et al.,53 whereas that of Hinckley et al.60 was retained by Drouillard et al.63 and Tittlemier and Tomy.67 Lei et al.64 used data by Balson,166 Spencer and Cliath,169 Rothman170 (i.e., Dickinson168 was not considered), and Wania et al.172 to establish a new recommendation, which was later used by Tittlemier et al.,68 Zhang et al.,80 Goel et al.,79 and presumably by Wong et al.66 (with the parameter B of eq 6 used by Wong et al. 66 slightly differing from that reported by Lei et al.64). Bidleman et al.70 extended the recommendation of Hinckley et al.60 by including the data by Wania et al.172 It is not clear whether the recommendation by Bidleman et al.70 or Lei et al.64 or their combination was used by Tittlemier et al.72 and by 1358



Review

Vetter et al.73 The last recommendation is from Shen and Wania.128 Both Bidleman et al.70 and Shen and Wania128 however have published parameters of eq 6 for the liquid state only without ΔlsS and Tfus needed for recalculation to sublimation pressure. A comparison of the direct data is presented in Figure 7,

Pyrene. The temperature-dependent vapor pressures of solid pyrene (CAS RN 129-00-0) obtained by direct methods have been published by Bradley and Cleasby,173 Hoyer and Peperle,174 Malaspina et al.,175 Smith et al.,176 Sonnefeld et al.,177 Sasse et al.,178 Oja and Suuberg,179 and Siddiqi et al.180 Data for the liquid phase have been published by Tsypkina,181 and by Smith et al.176 There are other papers not considered in this review.182−184 The data by Inokushi et al.182 are apparently wrong as noted already by Smith et al.176 Pupp et al.183 did not report the temperature range of their measurements and published only the parameters of eq 6 derived by the combination of the author’s data with that by Bradley and Cleasby.173 Nass et al.184 measured data over an extended temperature range from (313 to 453) K but published a single (extrapolated) value at 298.15 K. The vapor pressures reported at a single temperature and/or determined by the indirect method are not quoted here and can be found in Mackay et al.4 and Ma et al.129 Pyrene was used as a reference compound by Lei et al.,69 Odabasi et al.,75,76 and by Hanshow et al.107 and also as one of the calibration compounds by Bidleman11 and Hinckley et al.60 All of the measurements prior to 1980 were found to be in serious error by Smith et al.,176 while “generally reasonable agreement” with the same literature data was claimed by Oja and Suuberg.179 These two rather different statements can serve as an illustration of the (un)usefulness of ln(p0) vs 1/T plot used by Oja and Suuberg179 in contrast to the deviation plot used by Smith et al.176 The recommendations for pyrene are from Smith et al.,176 extended to lower temperatures by means of thermodynamically controlled extrapolation (SimCor, see “Extrapolation of Vapor Pressures toward Lower Temperatures” section) by Růzǐ čka et al.44 Lei et al.69 omitted these papers and used four data sets173,177−179 for the evaluation of the parameters A and B in eq 6 (there is a newer recommendation from the same laboratory,129 which is, however, in serious disagreement with all of the previous recommendations). Odabasi et al.75,76 retained the recommendation by Lei et al.69 Bidleman et al.11,60 used data by Bradley and Cleasby,173 Sonnefeld et al.,177 and Pupp et al.183 while rejecting Inokuchi182 and overlooking the remaining data sets.174−176 The recommendation by Růzǐ čka et al.44 was used by Hanshow et al.107 A comparison of the direct vapor-pressure data for solid pyrene is presented in Figure 8, where the deviations from the recommendation by Růzǐ čka et al.44 based on the data from the Bartlesville laboratory176 are shown. Although individual data sets173,177−179 exhibit significant scatter and/or deviate from Růzǐ čka et al.,44 the recommendation by Lei et al.69 based on these data sets is by chance close to that by Růzǐ čka et al.44 As a final conclusion of the section devoted to the reference/ calibration p0 data, it must be stated that in most cases the selected data were either of insufficient accuracy or not the best available or had been evaluated in an unacceptable way. Using more carefully selected and treated data would place significantly higher confidence on any conclusions derived from the p0 data used by most authors.

Figure 7. A. Relative deviations {p0(lit) − p0(rec)}/p0(rec) of the literature vapor pressures p0(lit) for p,p′-DDT from the values recommended by Lei et al.64 p0(rec). B. Comparison of sublimation enthalpies Δgs H of p,p′-DDT. ■, Balson;166 Δ, Dickinson;168 ◮, Spencer and Cliath;169 □, Rothman170 (partially displayed); ☆, Wania et al;172 −, recommendation by Lei et al.;64 --, former recommendation by Hinckley et al;60 ·····, absolute deviations.

where deviations from the recommendation by Lei et al.64 are shown. From Figure 7A, it is apparent that the data by Rothman170 exhibit a trend differing from all of the remaining data sets. This difference is more pronounced when a comparison of the sublimation enthalpies is made; see Figure 7B. It should be emphasized that Rothman170 reports large corrections to his experimental data, which were (prior to the corrections) close to Kuhn and Massini.167 In view of these facts, the inclusion of Rothman’s data170 in any recommendation is questionable. There are several reasons for questioning p,p′-DDT as a reference/calibration compound. Besides the significant discrepancies in both vapor pressures and sublimation enthalpies reported in literature, an additional problem is the lack of reliable related thermophysical data (the heat capacities of both condensed and gaseous phases) which would enable the selection/rejection of inconsistent data sets.

■

RECALCULATION FROM SOLID TO SUBCOOLED LIQUID AND VICE VERSA The GLC−RT methods yield the vapor pressure of the subcooled liquid directly, but if the reference and/or calibration compound is a solid, recalculation of the p0solid to the p0liquid is necessary. The same holds for the comparison of the GLC−RT results with the values obtained by the direct methods. The first paper dealing with such recalculation in connection with vapor-pressure 1359



Review

and Hearing188 or by Acree and Chickos130 reveals that the entropy of fusion can differ from the average value significantly, e.g., from about 8.4 J·mol−1·K−1 (cyclooctane) to 220 J·mol−1·K−1 (n-eicosane). The experimental values of the fusion entropies were then used by Falconer and Bidleman,62 Koutek et al.,55,74Lei et al.,64 Paasivirta et al.,97,98 Wong et al.,64,66 Lei et al.,69 Bidleman et al.,70 Lei et al.,71 Odabasi et al.,75,76 and Haftka et al.89 Several other papers explicitly or presumably used equations for subcooled liquids obtained by the above-mentioned authors but in many papers the recalculation is not described and mostly not even mentioned. No matter whether the average or experimental value of the entropy of fusion was used, it should be noted that the equation ⎛ p 0 (T ) ⎞ l liquid ⎟ = ΔsS ⎜⎛ Tfus − 1⎞⎟ ln⎜⎜ 0 ⎟ ⎠ R ⎝ T ⎝ psolid (T ) ⎠

(14) 16

(mentioned also in the reviews by Delle Site and with typographical error by Letcher and Naicker6) is merely an approximation and assumes a constant value of ΔlsS over the temperature range from Tfus to T. This assumption is certainly not valid when Tfus and T are 100 K (or more) apart. As early as in 1969, Prausnitz 189 used basic and well-known thermodynamic relations and derived the equation (retained in the second190 and third191 editions of his book) ⎛ p 0 (T ) ⎞ l Δl C liquid ⎟ = ΔsS ⎜⎛ Tfus − 1⎟⎞ − s p (T − T ) ln⎜⎜ 0 fus ⎟ ⎠ R ⎝ T RT ⎝ psolid (T ) ⎠ +

Figure 8. A. Relative deviations {p (lit) − p (rec)}/p (rec) of the literature vapor pressures p0(lit) for pyrene from the values recommended by Růzǐ čka et al.44 p0(rec). B. Comparison of sublimation enthalpies Δgs H of pyrene. ■, Bradley and Cleasby;173 ○, Hoyer and Peperle;174 ◮, Malaspina et al.;175 □, Smith et al.;176 ▼, Sonnefeld et al.;177 ☆, Sasse et al.;178 ⬠, Oja and Suuberg;179 ●, Siddiqi et al.;180 ⊞, Lei et al;69 −, values recommended by Růzǐ čka et al;44 ·····, absolute deviations. 0

0

0

⎛ ln⎜⎜ ⎝

= 6.8

(Tfus − 298) 298

R

ln

Tfus T

(15)

Even this equation represents a simplified case, as it assumes that ΔlsCp is constant over the temperature range from Tfus to T. It can be shown (see e.g. Allen et al.,192 van Noort et al.193) that recalculation should be done by means of the equation ⎛ p 0 (T ) ⎞ liquid ⎟=− ln⎜⎜ 0 ⎟ p ( T ) ⎝ solid ⎠

determination by GLC−RT is due to Bidleman,11 who used the equation 0 pliquid (T ) ⎞ ⎟ 0 psolid (T ) ⎟⎠

ΔslCp

T

∫T

T

fus

ΔslH(Tfus) + ∫ ΔslCp(T ) dT T fus

RT 2

dT (16)

It is straightforward to use eq 16 in combination with the linear or quadratic temperature dependence of ΔlsCp (see eq 17 in ref 192). Allen et al.192 showed on a group of PAHs that using eq 13 and eq 14 results in vapor pressures which are up to 35 times and 6 times higher, respectively, than using eq 16. To demonstrate this using recent high-quality data, recalculation was performed for several compounds. In the case of naphthalene, the vapor pressures (a temperature range of (384 to 539) K; a pressure range (4 to 270) kPa) and heat capacities of the liquid phase (a temperature range of (357 to 440) K) were measured by Chirico et al.194 and the heat capacities and entropy of fusion of crystalline naphthalene were later published by the same laboratory.195 The ideal-gas heat capacities of naphthalene were calculated from experimental vibrations by Chen et al.196 and fitted by a nonlinear equation by Frenkel et al.197 The vapor pressures of solid naphthalene were critically evaluated by Růzǐ čka et al.20 These data can be used to evaluate the difference between the calculations by using eqs 13 to 16. The results are shown in Figure 9, where the values obtained from eqs 13 to 16 are compared with the extrapolated vapor pressures by Chirico et al.194

(13)

where 6.8 stands for the ratio of the average entropy of fusion ΔlsS = 56.5 J·mol−1·K−1 divided by the universal gas constant R. The value 56.35 J·mol−1·K−1 found for “some hydrocarbons” by Mackay and Shiu185 was rounded in another study by Yalkowsky,186 who attributed this value to “rigid” compounds. The average value of ΔlsS/ R = 6.8 was later used by Kim et al.,58 Bidleman and Renberg,59 Foreman and Bidleman,100 Eitzer and Hites,49 Donovan,96 Kuo et al.,51 Tsuzuki,99 Povh et al.,78 and Van Roon et al.88 Van Roon et al.88 used a generic value for all of the compounds except for (+)-camphor with an entropy of fusion well below the average, namely 15.1 J·mol−1·K−1. He was not the first who questioned the use of the average entropy of fusion; Mackay187 stated that the constant 6.8 is an average empirical value and may be substantially in error for certain compounds already in 1982. Hinckley et al.60 found that the entropy of fusion for the reference compound p,p′-DDT is 71.2 J·mol−1·K−1. A brief look into the compilation by Domalski 1360



Review

been published recently,203 a new method for Csp estimation along with a comparison with the older method comes from Laštovka and Shaw.204 When no information is available on the heat capacities, one can use semiempirical equations for the p0liquid/p0solid recalculation derived for several groups of compounds by van Noort.205,206 To complete the overview, it must be mentioned that some authors use oversimplified relations for ΔlsCp (see refs 125 or 207 and the references therein).

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COMPARISON OF THE RESULTS OBTAINED BY GLC−RT FOR SELECTED COMPOUNDS The most frequently studied classes of compounds are halogenated aromatic compounds (pesticides, polychlorinated biphenyls, flame retardants etc.) and polyaromatic hydrocarbons. Polychlorinated biphenyls were studied using the GLC−RT technique and their properties were reviewed e.g. by Delle Site,16 Shiu and Ma,122 and Wania.124 Polyaromatic hydrocarbons were studied employing the GLC−RT technique by Bidleman,11 Yamasaki,48 Hinckley et al.,60 Donovan,96 Lei et al.,69 Odabasi et al.,75 Haftka et al.,89,107 and their properties were reviewed by Delle Site,16 Allen et al.,192 Shiu and Ma,126 Roux et al.,125 and Ma et al.129 The maximum differences in the p0 obtained from the abovementioned reports are illustrated for selected compounds in Table 7. It can be seen that reported p0 differ up to a factor of 8; also corresponding Δgl H as listed by Roux et al.125 for polyaromatic hydrocarbons differ significantly (e.g., by more than 30 % for compounds with more than four aromatic rings).

Figure 9. Relative deviations {p0(calc) − p0(Wag)}/p0(Wag) of the vapor pressures of naphthalene for subcooled liquid calculated using eqs 13 to 16 p0(calc) from values obtained by extrapolation from Wagner equation194 p0(Wag). −■−, eq 13; −▲−, eq 14; −●−, eq 15; −○−, eq 16.

It is obvious that eq 16 yields practically the same values as extrapolation from the liquid phase, whereas eq 13 can lead to an error in several tens of percents. A similar calculation can be performed also in the case of pyrene and benzo[a]pyrene. For pyrene, the high-quality data published by Smith et al.176 were thermodynamically extrapolated to ambient temperature using the heat capacity and entropy of fusion by Wong and Westrum,198 and the ideal gas heat capacities were taken from the TRC Tables.113,114 For benzo[a]pyrene, the vapor pressures were measured and critically evaluated by Růzǐ čka et al.44 along with the heat capacities and entropy of fusion. The heat capacities of ideal gas were taken from the TRC Tables.113,114 While Figure 9 shows the temperature trend of the errors associated with extrapolation in the case of naphthalene, Table 6 provides the

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CONCLUSIONS The present investigation was initiated by a number of questions related to the reliability of vapor pressure values determined by the GLC − RT technique. Since this technique is one of the indirect methods, the technique’s success depends (among other factors) on the quality of vapor pressure data of compounds to serve as reference and calibration standards. Therefore, before any attempts to evaluate the effect of factors related to the process of chromatography and in turn the validity of the GLC - RT model, it is extremely important to ensure that well-established p0 data of the standards are available as a function of temperature. Accordingly, the objective of this study was to examine the reliability of frequently used vapor-pressure data of standards and identify opportunities for both the best data selection and improvement of the methodological design. We have identified here the significant dependence of the reference vapor pressure data on four factors including (a) the data source, (b) the vapor-pressure equation used, (c) the extrapolation method from the GLC−RT temperature range to the required temperature, and (d) the method for the recalculation of the vaporpressure data from the solid state to the subcooled liquid state (or vice versa). The differences in the vapor-pressure values caused by these factors were found to reach even orders of magnitude for some compounds. In addition, we have shown that, regardless of usually correct trends found for compounds within specific classes, many authors who were previously using the GLC−RT techniques could probably generate results with significantly lower uncertainties provided that they select better data for the reference and/or calibration compounds and avoid some rather simplistic assumptions. However, our aim in this paper was not to comment critically on the previous efforts made in this area but rather to summarize our results as practical recommendations for future studies focusing

Table 6. Illustrative Errors Caused by Different Approximations in p0liquid to p0solid Recalculation ΔTexp compound 20

naphthalene pyrene44 benzo[a]pyrene44

σrb

Ka

eq 13

eq 14

eq 15

eq 16

55.2 125.7 151.5

10.7 138.5 533.7

4.2 8.4 89.0

1.7 1.7 22.0

0.5 −3.4 4.7

a

Length of extrapolation interval from the triple point temperature to 298.15 K. bRelative deviation σr = 100(p0(calc) − p0(rec))/p0(rec) where p0(calc) is the vapor pressure obtained by eqs 13 to 16 and p0(rec) is the literature vapor pressure value.

numbers corresponding to errors at 298.15 K for naphthalene, pyrene, and benzo[a]pyrene. From Table 6, it is apparent that (especially for long extrapolations) the temperature dependence of Δgl Cp should be taken into account; it is generally advisible to use eq 16. A large body of experimental data is available for ΔlsS,130,188 Clp,199−201 and Csp.188 If the necessary input data (ΔlsS, Clp, Csp) are not available, using the estimated values will probably yield better results than eq 15, 14 or even 13. It seems that much larger uncertainty is associated with the estimation of ΔlsS than of either Clp or Csp, and therefore the new experimental values of ΔlsS are especially valuable, but they can also be estimated according to Chickos et al.202 A review of the estimation methods for Clp has 1361



Review

Table 7. Comparison of Published GLC-RT Derived Vapor Pressures for Selected Compounds compound and CAS registry no. 4-chlorobiphenyl [2051-62-9] 2,2′-dichlorobiphenyl [13029-08-8] 2,5-dichlorobiphenyl [34883-39-1] 3,3′-dichlorobiphenyl [2050-67-1] 3,4-dichlorobiphenyl [2974-92-7] 4,4′-dichlorobiphenyl [2050-68-2] 2,2′,5,5′-tetrachlorobiphenyl [35693-99-3] 3,3′,4,4′-tetrachlorobiphenyl [32598-13-3] 2,2′,3,3′,5,5′,6,6′-octachlorobiphenyl [2136-99-4] naphthalene [91-20-3] fluorene [86-73-7] anthracene [120-12-7] phenanthrene [85-01-8] fluoranthene [206-44-0] pyrene [129-00-0] benz[a]anthracene [56-55-3] chrysene [218-01-9] benzo[b]fluoranthene [205-99-2] benzo[k]fluoranthene [207-08-9] benzo[a]pyrene [50-32-8]

Na 4 5 5 6 4 7 9 7 5 7 7 7 7 7 6 7 4 5 5 8

refs

p0(max)/p0(min)b

16 16 16 16 16 16 16 16 16 11,48,60,69,89,96 11,48,60,69,75,89,107 11,48,60,69,75,89 11,48,60,69,75,89 11,48,60,69,75,89 11,48,60,89,107 11,48,60,89,107 48,69,75,89 48,69,75,89,107 48,69,75,89,107 11,48,60,69,75,89,107

3.36 1.45 1.26 3.24 1.44 1.72 3.63 1.60 3.24 2.72 1.51 1.57 2.00 3.23 3.51 6.93 1.79 2.79 2.32 8.17

e

(p̅0 ± σ)/Pac (1.91 ± 1.14)·10−1 (1.55 ± 0.22)·10−1 (2.10 ± 0.21)·10−1 (6.81 ± 2.23)·10−2 (3.88 ± 0.64)·10−2 (4.38 ± 0.79)·10−3 (4.61 ± 1.49)·10−3 (5.76 ± 1.15)·10−5 (1.83 ± 0.81)·10−5 (3.16 ± 1.05)·101 (4.66 ± 0.62)·10−1 (8.38 ± 2.48)·10−2 (7.76 ± 1.60)·10−2 (7.88 ± 3.38)·10−3 (5.87 ± 2.78)·10−3 (4.70 ± 0.40)·10−4 (1.77 ± 0.36)·10−4 (1.36 ± 0.46)·10−5 (1.32 ± 0.44)·10−5 (3.03 ± 3.72)·10−5

σrd 59.7 14.2 10.0 32.7 16.5 18.8 30.3 20.0 44.3 33.4 13.4 29.6 20.6 43.0 47.4 77.3 20.5 34.0 33.4 122.4

a

Number of p0 data points reported. bRatio of the highest to the lowest value of GLC-RT derived p0(298.15 K) for a given compound. cAverage value of GLC-RT derived vapor pressure p̅0 = 1/N ∑ip0i (lit); standard deviation σ = (∑i(p0i (lit) − p̅0)2/N)1/2. dRelative standard deviation σr = 100/ p̅0(∑i(p0i (lit) − p0̅ )2/N)1/2. eValues for polychlorinated biphenyls were taken from Table 7 in Delle Site.16

to be filled before a conclusive analysis can be made. First, there is a lack of the published experimental retention times and their temperature dependences which preclude testing of many reports; in this respect, publishing more detailed experimental data may significantly assist in evaluating the reliability of future GLC−RT based vapor pressure results. Second, the activity coefficient ratio evaluation needs more detailed investigation. The work related to this topic is in progress in our laboratory.

on the use of the GLC−RT technique to determine the vapor pressures of organic compounds. Our contributions to the methodology of the GLC−RT method that should serve as a base for further studies include the following recommendations: (i) Literature on vapor pressures of reference compounds should be taken preferably from acknowledged original sources (e.g., from papers published in Journal of Physical and Chemical Reference Data; from papers by Bartlesville laboratory or obtained by thermodynamic extrapolation; see “Extrapolation of Vapor Pressures toward Lower Temperatures” section) in order to avoid a subjective bias in the process of selecting data and extrapolated, if necessary, using a reliable vapor-pressure equation. In the process of vapor-pressure data selection (or data comparison) plotting ln(p0) vs 1/T should be used with temperance as “it is too insensitive to be useful, and a plot of residuals from a fitting equation is preferable”.33 Such residual plots were accompanied by comparing enthalpies of vaporization/sublimation in present work. In many cases transformation of ln(p0) and 1/T to some other coordinates yields even clearer look onto differences between the respective datasources.208−210 (ii) Using a broad experimental temperature range with the low end of the temperature scale as close to 298.15 K as possible should be given priority in the experimental GLC setup to avoid the necessity of long-range temperature extrapolations. (iii) Consideration of the difference in the heat capacity between the liquid and solid states should be preferred in transforming the solid-state vapor pressures to subcooled vapor-pressure data (and vice versa). It must be emphasized that our study neither makes it feasible to quantify the overall uncertainty in the computation of p0x from eqs 2 to 5 nor to evaluate the reliability and correctness of the GLC− RT method derived vapor pressures. There are still important gaps in the baseline knowledge of the GLC − RT technique that need

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APPENDIX: CORRECT APPLICATION OF OTHMER’S EQUATION Othmer’s eq 4 is used incorrectly by many GLC−RT users. To demonstrate this, the calculations using n-hexadecane as a reference compound and n-eicosane as a target compound will be shown. Vapor pressures of the two compounds in the temperature range (398.15 to 448.15) K as recommended by Růzǐ čka and Majer43 are presented in Table A1. Least square fitting of p0 for n-hexadecane in this temperature range yields 0 ln(pC16 /Pa) = 26.29539 − 8064.74334/(T /K)

(A1)

and vapor pressure of n-hexadecane at 298.15 K is 0,extrap pC16 (298.15 K) = 0.471 Pa (recommended value43 is p0,lit (298.15 K) = 0.191 Pa). C16 Similarly, equation 0 ln(pC20 /Pa) = 28.58536 − 10011.075/(T /K)

(A2)

can be derived from vapor pressures of n-eicosane presented in Table A1; value calculated at 298.15 K is p0,extrap C20 (298.15 K) = 6.79·10−3 Pa (recommended value43 is p0,lit C20(298.15 K) = 2.09·10−3 Pa). Data from Table A1 can be also used for derivation of parameters of Othmer’s eq 4 resulting in 0 0 ln pC20 = 1.241348 ln pC16 − 4.056187

1362

(A3)



Review

Table A1. Vapor Pressures for n-Hexadecane and n-Eicosane as Recommended by Růzǐ čka and Majer43 n-hexadecane

n-eicosane

T/K

p0/Pa

p0/Pa

398.15 403.15 408.15 413.15 418.15 423.15 428.15 433.15 438.15 443.15 448.15

414.49 537.27 690.67 880.87 1114.93 1400.95 1748.09 2166.68 2668.30 3265.85 3973.61

30.70 42.40 57.94 78.40 105.06 139.49 183.59 239.60 310.16 398.38 507.87

of Petroleum, held at the Institution of Electrical Engineers, London, on 30th May-1st June, 1956); Desty, D. H., Ed.; Butterworth: London, 1957; pp 5−14. (8) Orbey, H.; Sandler, S. I. Relative Measurements of ActivityCoefficients at Infinite Dilution by Gas-Chromatography. Ind. Eng. Chem. Res. 1991, 30, 2006−2011. (9) Othmer, D. F. Correlating Vapor Pressure and Latent Heat Data. Ind. Eng. Chem 1940, 32, 841−856. (10) Hamilton, D. J. Gas chromatographic measurement of volatility of herbicide esters. J. Chromatogr., A 1980, 195, 75−83. (11) Bidleman, T. F. Estimation of Vapor-Pressures for Nonpolar Organic-Compounds by Capillary Gas-Chromatography. Anal. Chem. 1984, 56, 2490−2496. (12) Mader, B. T.; Pankow, J. F. Vapor pressures of the polychlorinated dibenzodioxins (PCDDs) and the polychlorinated dibenzofurans (PCDFs). Atmos. Environ. 2003, 37, 3103−3114. (13) Ambrose, D., Vapor pressure. In Experimental Thermodynamics of Non-reacting Systems, Le Neindre, B., Vodar, B., Eds.; Butterworths: London, 1975; pp 607−656. (14) Peggs, G. N. A Review of the Fundamental Methods for Measuring Gauge Pressures up to 1 kPa. J. Phys. E: Sci. Instrum 1980, 13, 1254−1262. (15) Carson, A. S., The measurement of vapor pressure. In Thermochemistry and Its Applications to Chemical and Biochemical Systems, Ribeiro da Silva, M. A. V., Ed.; D.Riedel Publishing Company: Dordrecht, The Netherlands, 1984; pp 127−41. (16) Delle Site, A. The vapor pressure of environmentally significant organic chemicals: A review of methods and data at ambient temperature. J. Phys. Chem. Ref. Data 1997, 26, 157−193. (17) Verevkin, S. P., Phase Changes in Pure Component Systems: Liquids and Gases. In Measurement of the Thermodynamic Properties of Multiple Phases; Weir, R. D., de Loos, T. W., Eds.; Elsevier: Amsterdam, 2005; pp 5−30. (18) Osborn, A. G.; Douslin, D. R. Vapor pressure relations of 36 sulfur compounds present in petroleum. J. Chem. Eng. Data 1966, 11, 502−9. (19) Steele, W. V. Fifty years of thermodynamics research at Bartlesville: The Hugh M. Huffman legacy. J. Chem. Thermodyn. 1995, 27, 135−162. (20) Růzǐ čka, K.; Fulem, M.; Růzǐ čka, V. Recommended Vapor Pressure of Solid Naphthalene. J. Chem. Eng. Data 2005, 50, 1956− 1970. (21) van Ekeren, P. J.; Jacobs, M. H. G.; Offringa, J. C. A.; de Kruif, C. G. Vapor-Pressure Measurements on Trans-Diphenylethene and Naphthalene Using a Spinning-Rotor Friction Gauge. J. Chem. Thermodyn. 1983, 15, 409−417. (22) Widegren, J. A.; Bruno, T. J. Vapor pressure measurements on saturated biodiesel fuel esters by the concatenated gas saturation method. Fuel 2011, 90, 1833−1839. (23) Sinke, G. C. Method for Measurement of Vapor-Pressures of Organic Compounds Below 0.1 Torr Naphthalene as a Reference Substance. J. Chem. Thermodyn. 1974, 6, 311−316. (24) van Ginkel, C. H. D.; de Kruif, C. G.; de Waal, F. E. B. Need for temperature control in effusion experiments. J. Phys. E: Sci. Instrum. 1975, 8, 490−2. (25) de Kruif, C. G.; van Ginkel, C. H. D. Torsion-weighing effusion vapor-pressure measurements on organic compounds. J. Chem. Thermodyn. 1977, 9, 725−730. (26) Zaitsau, D.; Kabo, G. J.; Kozyro, A. A.; Sevruk, V. M. The effect of the failure of isotropy of a gas in an effusion cell on the vapor pressure and enthalpy of sublimation for alkyl derivatives of carbamide. Thermochim. Acta 2003, 406, 17−28. (27) Zaitsau, D. H.; Verevkin, S. P.; Paulechka, Y. U.; Kabo, G. J.; Sevruk, V. M. Comprehensive Study of Vapor Pressures and Enthalpies of Vaporization of Cyclohexyl Esters. J. Chem. Eng. Data 2003, 48, 1393−1400. (28) Wahlbeck, P. G. Effusion. VII. The Failure of Isotropy of a Gas in an Effusion Cell and the Transition Region. J. Chem. Phys. 1971, 55, 1709−1715.

Value of n-eicosane vapor pressure at 298.15 K calculated by means of eq A3 strongly depends on value p0C16 used for calculation. With p0C16 = p0,lit C16(298.15 K) = 0.191 Pa one gets value 2.22·10−3 Pa, merely 6.1 % higher than recommended −3 p0,lit Pa. On the other hand using p0C16 = C20(298.15 K) = 2.09·10 0,extrap pC16 (298.15 K) = 0.471 Pa leads to value 6.79·10−3 Pa, exactly matching result obtained via eq A2 derived solely from n-eicosane vapor pressures. It can be shown that this is a general conclusion for a combination of any two compounds with data available in the same temperature range, in this case (398.15 to 448.15) K. To conclude, the successful application of Othmer’s equation (4) requires data for reference compound to be known over the entire temperature range of intended application.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone +420 220 444 116. Notes

The authors declare no competing financial interest. Funding

This work is supported by the Czech Science Foundation project 203/09/1327.

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REFERENCES

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