gas partition coefficients of volatile organic compounds by a headspace gas chromatography technique

gas partition coefficients of volatile organic compounds by a headspace gas chromatography technique

Fluid Phase Equilibria 213 (2003) 139–146 Graphical method for the determination of water/gas partition coefficients of volatile organic compounds by...

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Fluid Phase Equilibria 213 (2003) 139–146

Graphical method for the determination of water/gas partition coefficients of volatile organic compounds by a headspace gas chromatography technique Anna-Maria Bakierowska∗ , Jerzy Trzeszczy´nski Institute of Organic Chemical Technology, Technical University of Szczecin, Aleja Piastów 42, 71-160 Szczecin, Poland Received 1 November 2002; accepted 2 June 2003

Abstract Water/gas partition coefficients have been determined for hydrocarbons and chlorinated derivatives of hydrocarbons. In this paper a graphical method based on a static headspace gas chromatography technique is described. This technique relies on the linear dependence of the phase volume ratio in the vial and the ratio of the concentration of the solute in two phases. The partition coefficients were determined at four temperatures ranging from 10 to 25 ◦ C. The temperature dependence of the partition coefficients is described by the classical van’t Hoff equation. © 2003 Elsevier B.V. All rights reserved. Keywords: Vapour–liquid equilibria; Volatile organic compounds; Experimental method; Henry’s law constant; Headspace analysis

1. Introduction Static headspace analysis is a very useful tool for qualitative and quantitative analysis of substances with high vapor pressure present in the liquid phase or a condensed matrix. The method is not limitated to trace analysis, but also allows to obtain biological data, e.g. a physiological media–air partition coefficient [1], a leaf essential oil–air partition coefficient [2] or physicochemical data [3–6]. Equilibrium headspace is based on the partitioning of volatile compounds between a solid or a liquid phase and an equilibrium gas phase. In the equilibrium step the analyte is transferred from condensed phase to gas phase. After reaching the equilibrium state a sample of gas phase is taken for gas chromatographic analysis. In the case of the determination of partition coefficients as function of temperature, the equilibrium static headspace technique is convenient, since only the water bath temperature has to be controlled. In contrast with the stripping methods the alterations of both the inert gas temperature and the water-bath should be checked. The relationship between partition coefficient and temperature is poorly described in ∗

Corressponding author. Tel.: +48-91-449-49-61; fax: +48-91-449-43-65. E-mail address: [email protected] (A.-M. Bakierowska). 0378-3812/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0378-3812(03)00286-3


A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146

literature. The effect of temperature on partition coefficients in the higher temperature range (298–353 K) was studied previously by various authors [7–10]. Instead, the earlier-mentioned relationship in the lower temperature range (275–303 K) is rarely found and is difficult to obtain at laboratory conditions [11–13]. In literature two main types of experimental techniques for determination of partition coefficients based on the headspace method are described. First, dynamics methods are described, e.g. stripping techniques [14,15]. In the dynamic methods stripping gas is used to extract the volatiles from the solution. The partition coefficient is calculated from the results of a dynamic process rather than from a data for a system at equilibrium. Among different methods described in literature the most accurate methods seems to be based on the equilibrium technique. The equilibrium state can be reached in one step or in multiple extraction steps [16]. The equilibration step can be carried out at constant pressure in a glass syringe at the desired temperature and then the headspace is recovered by transfer into another syringe and analyzed by gas chromatography [3]. Next, the EPICS technique can be applied. It was first developed by Lincoff and Gossett [12] and further applied with modifications by Gossett [17] and Dewulf et al. [6]. Another static technique is the vapor phase calibration method VPC [7] where an external vapor standard is used to determine the concentration of the volatile analyte in the headspace, while the concentration in the sample is found from the difference in the total amount in the vial. 2. Phase ratio variation method There is another possibility to measure the partition coefficient in a gas-liquid system without the need for an external standard. This method was described by Ettre et al. [18] and it is called the phase ratio method PRV. The PRV method is based on the relationship between reciprocal peak area and the phase ratio in the vial containing the sample solution. Robbins [8] developed this method further. Trzeszczy´nski [19] used the PRV method to determine the solid/air partition coefficient of volatile organic compounds evolved from polymers.The purpose of this paper was to describe the theory and using PRV method to determine partition coefficients by the static headspace method for some volatile organic compounds in the temperature range from 283 to 298 K without calibration and knowledge of substance concentration in the gas phase. 3. Equations The PRV method was further developed for determination of the partition coefficient of volatile organic compounds. This method is based on the relationship of the phase volume ratio and the concentrations ratio in gas and liquid phase, respectively. The partition coefficient K is defined through the following equation K=

cL cg


where cL is the equilibrium concentration of the solute in the liquid phase, cg the equilibrium concentration of the solute in the gas phase. According to the mass balance, the total mass of the solute added to the vial is given by V L c0 = V g cg + V L cL


A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146


where VL is the volume of the liquid phase (ml), Vg the volume of the gas phase (ml), c0 the initial concentration of compound in the liquid phase. By combining the Eqs. (1) and (2) we obtain Vg c0 = −K VL cg


Since the concentration of the solute in the headspace is proportional to the area A of the GC peak, for a given volume of gas phase VG cg = αA


where α is a GC calibration coefficient. By combining the Eqs. (3) and (4) we obtain c0 Vg −K = VL αA


4. Analytical reagents and stock solutions All compounds used in this study were chromatographically or analytically pure. The liquid solvents were purchased from Merck or Fluka. Stock solutions were prepared for each substance separately, except for a pair of isomers of 1-chloro-2-butene that were analyzed in the same solution. All single organic component stock solutions were prepared for each of selected solute at concentration 10% (v/v) in ethanol (Merck), except cyclohydrocarbons that were 1% (v/v). Gossett [17] investigated the possible effect of presence of methanol on partition coefficient of a typical, volatile organic solute. He has concluded that a methanol concentration under 1% (v/v) did not influence significantly the data obtained. 5. Headspace sampling The 1, 1.5, 2, 3, 10 and 20 ml of redistilled water was pipetted into six dry headspace vials (Alltech), of 35 ml volume, respectively. Thus, each vial represented a different phase ratio: 34.00, 22.33, 16.50, 10.67, 2.50 and 0.75, respectively. Exactly 1 ␮l of the stock solution was added to each vial with a microsyringe (Hamilton). The syringe content was added to the vial under the water surface and then the vial was immediately closed with a silicone septum and aluminium cap. After this the vials were equilibrated while gentle shaking in a thermostatic water bath (at ±0.1 K) for 30 min. When the equilibrium state was achieved the headspace was sampled for GC analysis with a 0.5 ml sample loop. 6. Instrumental conditions The analysis were carried out using a Carlo Erba gas chromatograph (model Fractovap 2450) equipped with a flame ionization detector FID and a stainless-steel column (2000 mm × 5 mm) fitted with 10% XE-60 on chromosorb W NAW, 60–80 mesh. The oven temperature was maintained constant in range


A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146

60–100 ◦ C, depending on the type of organic compound. The temperature of injection and detector was held at 125 ◦ C. The flow rate of nitrogen carrier gas was 37 ml/min, and that of hydrogen and air were 25 and 200 ml/min, respectively. 7. Results and discussion 7.1. Static headspace method Eight volatile organic compounds in redistilled water have been investigated: cyclopentene, cyclohexene, 2,2-dichloropropane, cis-1-chloro-2-butene, trans-1-chloro-2-butene, benzene, toluene and chlorocyclohexane. The measurements have been carried out at four different temperatures. At each temperature the aqueous solution was analyzed in six vials with different phase ratios. The partition coefficient was calculated from Eq. (5) using linear regression analysis. The curves obtained for every studied compound were all highly linear with correlation coefficients close to 1.00 in each case. Each plot consisted of six points. Fig. 1 shows an example for cyclopentene. Table 1 contains the values of partition coefficients obtained for studied compounds and results of linear regression analysis at four temperatures. 7.2. Dependence partition coefficient on temperature The temperature dependence of partition coefficients can be described with the classical van’t Hoff equation for the temperature effect on an equilibrium constant [20] ln K = a +

b T


where a and b are the empirical regression coefficients from which the slope b is a direct function of the heat of solution of the solute. The results from a linear fit of the natural logarithm of the partition coefficient K versus the reciprocal temperature are shown in Table 2. It is clear from the correlation coefficients R2 shown in Table 2 that this model fits the obtained data very well. From this fit, the 40

y =106.46x - 0.7957 R2 = 1

35 30 Vg/VL

25 20 15 10 5 0 0

0 .1

0. 2

0 .3

0. 4


Fig. 1. Linear dependence between concentration ratio and phase volume ratio for cyclopentene at 283 K.

A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146


Table 1 Water/gas partition coefficients K of different solute calculated using Eq. (5), where Sb is standard deviation of partition coefficient, R2 is a correlation coefficient Sb


0.796 0.703 0.631 0.567

0.058 0.184 0.040 0.064

1.0000 0.9999 0.9999 0.9999

283.15 288.15 293.15 298.15

1.138 0.971 0.931 0.836

0.053 0.031 0.221 0.141

1.0000 0.9996 0.9995 0.9999


283.15 288.15 293.15 298.15

3.914 3.105 2.451 2.065

0.235 0.080 0.073 0.223

0.9989 0.9999 0.9999 0.9997


283.15 288.15 293.15 298.15

4.798 4.088 3.510 3.078

0.231 0.436 0.260 0.261

0.9997 0.9965 0.9983 0.9991


283.15 288.15 293.15 298.15

8.173 6.699 5.219 4.048

0.670 0.406 0.406 0.211

0.9916 0.9990 0.9988 0.9995


283.15 288.15 293.15 298.15

8.017 6.777 5.535 4.444

0.351 0.380 0.118 0.301

0.9993 0.9991 0.9999 0.9992


283.15 288.15 293.15 298.15

12.545 10.707 8.535 7.924

0.427 0.374 0.366 0.726

0.9993 0.9993 0.9993 0.9971


283.15 288.15 293.15 298.15

12.155 9.167 8.206 7.172

0.255 0.214 0.265 0.264

0.9996 0.9998 0.9996 0.9997


T [K]


283.15 288.15 293.15 298.15



liquid–gas partition coefficient of a solute can be extrapolated within a reasonable range to other temperatures. 7.3. Comparison with literature data Table 3 contains the literature data and the values of the partition coefficients obtained in this work. The literature data listed in Table 3 have been obtained by different analytical methods using a headspace technique, except for a case where the data have been predicted from a bond contribution method [22].


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Table 2 Temperature dependence of natural logarithm of partition coefficient K according to Eq. (6), where a, b are empirical parameters of linear regression and R2 is correlation coefficient Compound




Cyclopentene Cyclohexene 2,2-Dichloropropane Benzene Toluene trans-1-Chloro-2-butene cis-1-Chloro-2-butene Chlorocyclohexane

1915 1691 3637 3920 3977 2707 2503 2982

6.989 5.860 11.496 11.663 11.926 7.045 7.282 8.069

0.9948 0.9527 0.9969 0.9963 0.9954 0.9724 0.9993 0.9602

Table 3 Comparison of water/gas or gas/water partition coefficient K with literature data Compound

T [K]

K (water/gas)

K (gas/water)

K (gas/water literature data)

Benzene Toluene Benzene Toluene Benzene Toluene

298 298 293 293 283 283

4.444 4.048 5.535 5.219 8.017 8.173

0.225 0.247 0.181 0.192 0.125 0.122

0.216 [5]; 0.235 [21]; 0.194 [6]; 0.110 [22] 0.263 [5]; 0.272 [21]; 0.224 [6]; 0.240 [22] 0.180 [10] 0.196 [10] 0.097 [6] 0.106 [6]

14 12 10


8 6 4 2 0 282









T [K]

Fig. 2. Temperature dependence of partition coefficient of investigated compounds: (×) trans-1-chloro-2-butene; ( ) chlorocyclohexane; ( ) toluene; (䊐) benzene; (+) cis-1-chloro-2-butene; (䉫) 2,2-dichloropropane; ( ) cyclohexene; (䊊) cyclopentene.

A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146


3 2,5 2

ln K

1,5 1 0,5 0 -0,5 -1 0,00333





1/T [K-1]

Fig. 3. Linear dependence natural logarithm of partition coefficients versus reciprocal temperature for the analyzed compounds: (×) trans-1-chloro-2-butene;( ) chlorocyclohexane; ( ) toluene; (䊐) benzene; (+) cis-1-chloro-2-butene; (䉫) 2,2-dichloropropane; ( ) cyclohexene; (䊊) cyclopentene.

8. Conclusions The value of water/air partition coefficients of eight volatile organic compounds was measured between 283 and 298 K using a developed headspace GC method, the so-called PRV technique. The present method is suitable for the accurate determination of the water/gas partition coefficients for a wide variety of chemical compounds. The PRV method allows to determine even small differences in the partition coefficient values, e.g. for isomers or compounds with similar molecular structure. The linear dependence of the natural logarithm of partition coefficient versus reciprocal temperature has been verified (Figs. 2 and 3). List of symbols A peak area a, b empirical parameters of linear regression cg gas phase equilibrium concentration of the solute cL liquid phase equilibrium concentration of the solute c0 solute initial concentration in the liquid phase K water/gas partition coefficient R2 correlation coefficient Sb standard deviation of partition coefficient Vg gas phase volume L V liquid phase volume Greek letter calibration coefficient


A.-M. Bakierowska, J. Trzeszczy´nski / Fluid Phase Equilibria 213 (2003) 139–146

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