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## Journal of the Chilean Chemical Society

##
*versión impresa* ISSN 0717-9324*versión On-line* ISSN 0717-9707

### J. Chil. Chem. Soc. v.48 n.3 Concepción sep. 2003

#### http://dx.doi.org/10.4067/S0717-97072003000300001

J. Chil. Chem. Soc., 48, N 3 (2003) ISSN 0717-9324

**DETERMINATION OF THE HENRY'S CONSTANT OF VOLATILE AND SEMI-VOLATILE ORGANIC COMPONUDS OF ENVIRONMENTAL CONCERN BY **

THE BAS (BATCH AIR STRIPPING) TECHNIQUE:

A NEW MATHEMATICAL APPROACH.

THE BAS (BATCH AIR STRIPPING) TECHNIQUE:

A NEW MATHEMATICAL APPROACH.

*Roberto Bobadilla ^{1}, Tom Huybrechts^{2}, Jo Dewulf^{2} & Herman Van Langenhove^{2}.*

^{1 }Departamento de Prevención de Riesgos y Medio Ambiente. Facultad de Ciencias de la Construcción y Ordenamiento Territorial. Universidad Tecnológica Metropolitana. Chile.

^{2 }Research Group of Environmental Organic Chemistry and Technology. Department of Organic Chemistry. Faculty of Agricultural and Applied Biological Sciences. University of Ghent. Belgium.

(Received: May 15, 2002 - Accepted: January 2,2003)

**ABSTRACT**

Chemical transfer between environmental compartments plays a key role in an adequate command and control of pollutants. The gas-liquid partitioning equilibrium constant, better known as the Henry's constant (K_{H}) represents a crucial parameter in order to determine the environmental fate of chemicals and therefore, an accurate determination at ambient conditions is extremely important to assess the mentioned process.

Within the experimental dynamic methods, the batch air stripping technique (BAS) has as major drawback the equilibrium condition among phases, which is hardly achieved in open natural systems.

The present work, based on previously published mathematical models (4, 22), centers in the development of a new mathematical approach to determine K_{H} by means of the BAS in non-equilibrium conditions through experimental and theoretical determinations of volumetric mass transfer coefficients (K_{L}a) for volatile (1,1-DCE, ethylbenzene, p-xylene and toluene) and semivolatile (1,1,2-TCE, 1,2-DCP, penhylmethylether (anisole) and naphthalene) organic compounds of environmental concern.

In order to validate the approach, values obtained were compared to the K_{H} determined through the static EPICS (Equilibrium Partitioning in Closed Systems) method, confirming the calculated K_{H} and ratifying the new approach.

**INTRODUCTION**

The determination of the fate and distribution of polluting chemical compounds in the different environmental compartments is an area of tremendous importance in the development of successful strategies for the solution of the problematic that entails environmental contamination.

The organic compound transfer between the atmosphere and water bodies and vice versa, constitute important routes in the dispersion of polluting agents. The balance of distribution of a compound between a liquid and a gas phase is a process governed first by the affinities of the substance for both phases and by factors such as concentration, temperature, pH, reactivity and solubility, being this process characterized by the Henry's constant (K_{H}). The determination of K_{H} has been made in theoretical and experimental forms through diverse approaches. Between the methods used to determine K_{H} a widely employed is the calculation through the ratio between the vapor pressure and the solubility based on the vapor pressure of the pure compound and on the activity coefficient, respectively, values that evidently vary in solution and which therefore transform the calculation into a rough approach. On the other hand, predictive theoretical methods developed with the use of data bases as well as semi-empirical relations like the UNIFAC method (8) or the use of continuum-solvation models (13, 20), presents the disadvantage to associate compound with different properties, generating a low correlation between the theoretical value and the experimental one and, in the specific case of UNIFAC, overestimating the dependency of the activity coefficient (g) with respect to temperature (14).

Between experimental determination procedures, there are the static and dynamic methods. Static techniques are based on the determination of K_{H} in closed systems. Diverse methodologies such as the method of Drozd & Novak (7) or the technique of multiple balance of Macaulife (17) have laid the foundation for the development of the more used static method, the EPICS (9). In general, static methods lose utility in the case of less volatile compounds due to detection limits. In the case of EPICS, studies have demonstrated a tendency to the overestimate K_{H} (3). On the other hand, dynamic methods use open-flow systems, promoting phase exchange until equilibrium. The most used dynamic method is the Batch Air Stripping (BAS) (15). This technique requires as a fundamental condition, equilibrium between the interacting phases. Nevertheless, equilibrium is hardly achieved due to the heterogeneity of the liquid phase and the short time of exchange at the interphase, being this dependent on the type of compound used.

Different authors have simplified the complex interactions that happen in two-phase systems through mathematical models such as the two-film model of Whitman (22) and the surface renewal model of Danckwerts (4). Both mentioned models gather the idea that the interaction of the phases happens through the creation of an interphase where concentration gradients are observed (Figure 1). In this interphase, a dynamic equilibrium establishes with a mass transfer proportional to the concentration gradient between the bulk phase and the interphase, giving place to mass transfer coefficients for each phase (k_{G} and k_{L} for the gaseous and liquid phases, respectively), proportional to molecular diffusion coefficients, D_{i} (4, 22) and dependent of the dimensions of the formed interphase, specifically the length of the interphase z_{i} and the exchange surface between phases, a. The main difference between both models lies in the definition of the mass transfer coefficients and particularly in the proportionality of these with the respective molecular diffusion coefficients. In the case of the two-film model, a direct proportionality between k_{i} and D_{i} exists. On the other hand, in the model of surface renewal is indicated that k_{i} is proportional to the square root of D_{i}. Recent studies indicate that depending on the limiting stage in the process of mass transfer, the relation varies between both models (16).

Fig. 1. Schematic representation of a compound transfer between a gaseous and a liquid phase, through a double interphase. Dotted lines show the concentration gradient between the interphase and the bulk phase, process governed by the molecular diffusion phenomenon. C_{G} : gaseous bulk phase concentration, C_{GI} : gaseous interphase concentration, C_{LI} : liquid interphase concentration, C_{L} : liquid bulk phase concentration, K'_{H} : dimensionless Henry's constant, relating C_{G} and C_{L}. k_{G} and k_{L} : mass transfer coefficients at the gaseous and liquid interphase, respectively, D_{i}: molecular diffusion coefficient, z_{i} : interphase length. |

Since it is experimentally impossible to determine the surface of exchange between phases in turbulent conditions, one resorts to volumetric mass transfer coefficients (k_{i}a). As well, the experimental determination makes very difficult the calculation of the individual mass transfer coefficients for each phase, reason why the determination of a total volumetric mass transfer coefficient is made (K_{L}a). Nevertheless, depending on the characteristics of the assayed compound (volatility and solubility, mainly) normally one of the processes of mass transfer, either the transfer at level of the gaseous or at the liquid interphase, constitutes the limiting critical stage in the process of mass transfer and therefore one of the mass transfer coefficients will dominate the whole transfer (k_{G} > > k_{L} or k_{L} > > k_{G}), giving rise to compounds whose transference is under gaseous or liquid control, directly associating the determination of K_{L}a, in many cases, with the limiting mass transfer coefficient. It is evident that in the case of some compounds, the two phases can have an important incidence in the transfer process being both stages important.

In the present work, a mathematical approach for the determination of K_{H} through the incorporation of volumetric mass transfer coefficients is presented, quantifying the variation in concentration of volatile and semi-volatile organic compounds of environmental interest in a system of dynamic exchange between a liquid and a gaseous phase, by means of the BAS method.

**Materials and Methods **

**Reactants. **

1,1-dichloroethane, 1,2-dichloropropane, p-dimethylbenzene (p-xylene) (Aldrich), methylphenylether (anisole), ethylbenzene, methylbenzene (toluene) (Fluka), 1,1,2-trichloroethane and naphtalene (Janssen) were investigated. Stock solution were prepared in methanol (purge and trap grade, Aldrich) stored in darkness at 20C. Trichloroethene was used as internal standard (Aldrich).

**Experimental design.**

Used system BAS consisted in air from a high-pressure cylinder passed through a low-pressure regulator at a constant flow rate and pre-saturated with water in order to keep the liquid volume in the stripping vessel constant. The gas was passed through a coil submerged into a thermostatic bath in order to ensure temperature equilibration between phases, then introduced into the bottom of the stripping vessel through a glass frit. The system was maintained at 25 ± 0.1°C. The exit gas flow rate was measured by a soap bubble flow meter (10-120 ml/min). Homogeneity of the liquid phase was maintained with a magnetic stirrer.

The general procedure consisted in the addition of a specific amount (between 25-200 ml) of a methanol stock solution containing one or more organic compounds to a fixed volume of ultrapure water (20-80 ml) in such a way that final concentration was below 10% of the water solubility of each added compound. Immediately after, air was bubbled through the vessel, at a constant flow rate, stripping the organic compounds out of the water phase.

**Sampling and Quantification.**

While stripping, 100 ml of the solution were sampled at regular time intervals. The obtained sample was placed in a 12 ml vial and 5 ml of internal standard were added. The vial was hermetically closed with a Teflon-faced rubber septum and placed overnight for equilibration, at a constant temperature (25 ± 1°C). Later, the concentration of the sample was quantified indirectly through the determination of the concentration of the gaseous phase of the vial by means of SPME (Solid-phase Microextraction) (2) using a 100 mm thickness non-bonded poly(dimethylsiloxane) coated fiber (SUPELCO), exposed during 30 min. Finally, the fiber was inserted into the injection port (5 min to 220C) of a gas chromatograph (VARIAN, model 3700) equipped with a column DB5 30 m x 0.53 mm, 1.5 micron (J&W Scientific) maintained at 40°C for 5 min and then ramped to 220°C at a rate of 10°C/min. The separated compounds were analyzed by a flame ionization detector (FID) maintained at 250C.

**Mathematical Approach.**

Based on the previous developed mathematical approach (21), homogeneity in the liquid phase is assumed and it is considered that the gaseous phase does not reach equilibrium before leaving the system. In that case, an expression that accounts for the mass transfer between phases must be incorporated in the traditional equation used to determine K'_{H} (15) so that:

(1) |

where dC/dt is the infinitesimal variation of the concentration as a function of time, V corresponds to the volume (ml), K'_{H} is the dimensionless Henry's constant, Q is the flow of an ideal gas (ml/s), C_{i} is the concentration of the compound (mol/ml) and K_{L}a is the total volumetric mass transfer coefficient (s^{-1}), that can be subdivided between K_{L},_{ }the mass transfer coefficient (cm/s) and a, the specific transfer area (cm^{2}/ml).

Integrating from initial conditions (t_{0} and initial concentration C_{0}) to a time t results:

(2) |

In the calculation of the previous formula all the variables are clearly known with the exception of K_{L}a. Scarce values of K_{L}a are found in literature for compounds of environmental interest. Some determinations have been made for highly volatile compounds (16) and rough approaches have been used to determine K'_{H} under non-equilibrium conditions (15).

**RESULTAS**

**Non-equilibrium conditions. **

Initially, ethylbenzene and anisole Henry's constant was determined experimentally assuming equilibrium conditions using the traditional approach (15). The obtained values named K'_{H} _{eq}, were compared with reference values obtained in different studies through the EPICS method, named K'_{H} _{EPICS} (5, 6). This comparison demonstrated the inaccuracy of the traditional approach, showing underestimations as high as 70% respect to the reference value. Results are shown in Table 1. Of the used parameters a volume of 40 ml and a 50 ml/min airflow were selected for accomplishment of later experiments. Depending on the degree of volatility of the assayed compounds, the sampling interval varied between 2 and 10 minutes.

**Table 1. **Comparison of K'_{H} experimental values.

* : slope from the curve ln(C_{0}/C_{t}) vs. time.
K' _{H eq} : dimensionless Henry's constant, determined experimentally through BAS assuming equilibrium. Y : Dewulf et al., 1995 # : Dewulf et al., 1999 |

**Determination of K _{L}a.**

Using the mathematical approach previously described (equation (2)) the total volumetric mass transfer coefficients (K_{L}a) for ethylbenzene and anisole were determined experimentally. To do so, the natural logarithm of the variation of the relative concentration ln(C_{t}/C_{0}) was plotted as a function of time (Figure 2), by means of experimental quantification, solving the slope equation using validated dimensionless Henry's constants (5, 6, 19). (Table 2).

Fig. 2. Linear semi-logarithmic relation of the concentration decrease with time obtained for anisole (A) and ethylbenzene (B). Mean values from three independent experiments are plotted. | |

**Table 2.** Experimental determination of K_{L}a.

* : slope from the curve ln(C |

**Correction of K _{L}a for volatile and semi-volatile compounds of environmental interest.**

Based on the relation between the molecular diffusion coefficients, D_{i}, and the mass transfer coefficient, k_{i}, the K_{L}a were calculated for different organic compounds. D_{i} was calculated theoretically using the approach of Hayduk & Laudie (10) for each compound to be analyzed. The experimental values of K_{L}a obtained for ethylbenzene and anisole were used as reference in the calculation of total volumetric mass transfer coefficients by means of the relation described for compounds under liquid control (16, 18):

(3) |

The calculated values are listed in Table 3.

**Table 3.** K_{L}a Corrected values.

**Determination of the dimensionless Henry's constant, K' _{H}.**

Keeping the same experimental conditions used for the determination of K_{L}a, quantifications of the variation of the relative concentration in time were made for the volatile organic compounds: 1,1-dichloroethane, 1,2-dichloropropane, p-xylene and toluene and semi-volatile: 1,1,2-trichloroethane and naphthalene, using again the mathematical approach (equation (2)), including the corrected value of K_{L}a for each compound and solving the slope equation for the dimensionless Henry's constant, named K'_{H} _{BAS}. The obtained value was compared with the one calculated through the traditional approach assuming equilibrium, K'_{H} _{eq}, and with the value of reference from other studies where the EPICS method was used (5, 6), K'_{H} _{EPICS} (Table 4).

**Table 4.** Comparison of K'_{H} experimentally determined *.

*: The results presented here were calculated using ethylbenzene as reference compound, only in the case of naphtalene anisole was used instead.
K' _{H BAS}: dimensionless Henry's constant, determined experimentally through BAS using the new mathematical approach (equation (2)). Results correspond to the experimental determination obtained from three independent experiments. ¥: arithmetic mean expressed with their standard deviation. § : Dewulf et al., 1995 # : Dewulf et al., 1999 + : Sander, 1999 |

**DISCUSSION**

Different methodologies are used for the determination of the Henry's constant, a crucial variable in the study of the dispersion of volatile and semi-volatile polluting agents between gaseous and liquid phases. This study focused on the validation of a new mathematical approach that incorporates the process of mass transfer in the traditional determination by means of the method of Batch Air Stripping (BAS).

It is evident, when comparing the values obtained experimentally by means of the BAS technique, assuming equilibrium conditions, respect to the values of different studies obtained by means of the EPICS method (5, 6) used as reference in this study (Tables 1 and 4), that depending on the analyzed compound and the experimental conditions in which the BAS is carried out, the resulting K´_{H} can be highly underestimated (until 70%), demonstrating why is necessary to incorporate in the traditional approach a mathematical expression who accounts for the mass transfer, which is an independent dynamic process of equilibrium between phases, doing feasible the determination of the Henry's constant for a wide range of semi-volatile organic compounds for which the static methods of determination are not useful (9) and where equilibrium in dynamic systems is evidently not reached. Nevertheless, this expression has the disadvantage to require the determination of mass transfer coefficients, highly specific variables that are dependent on system conditions and difficult to determine experimentally. In the present work, resorting on validated dimensionless Henry's constants (K'_{H}) (5, 6, 19) total volumetric mass transfer coefficients (K_{L}a) were experimentally determined. This determination was made for ethylbenzene (K'_{H} = 0.270) and anisole (K'_{H} = 0.015), organic compounds representative of the groups of whose mass transfer is under liquid or liquid and gaseous control, respectively. The total volumetric mass transfer coefficients experimentally obtained for ethylbenzene (K_{L}a = 0.5809 min^{-1}) and anisole (0.0201 K_{L}a = min^{-1}) are in the orders of magnitude previously described in other studies for organic compounds (18), adding them to the scarce published values. Later, the values of K_{L}a for organic compounds of environmental interest were corrected by means of theoretically calculated molecular diffusion coefficients (10). This correction threw a great difference in the corrected K_{L}a depending on the compound used as reference. In addition, close values for each compound were obtained respect to the value of reference (Tables 3) explained by the similarity of the calculated molecular diffusion coefficients. When incorporating the corrected values of K_{L}a in the experimental determination of K'_{H} (denoted as K'_{H} _{BAS}) by means of the mathematical approach proposed in this study (equation (2)), it was observed that the experimental determination of K'_{H BAS }approaches the reference K'_{H EPICS} value when the compound under study shares similar physical properties (volatility) with the reference compound. In the case of anisole, used as reference compound, it just allowed the calculation of naphthalene, which presents a similar volatility. In this particular case, a low exactitude in the determination of K´_{H} is observed, which is attributable to the great structural difference of both compounds, which makes the approach to loose soundness. On the contrary, when using ethylbenzene as reference compound, the results obtained for all compounds assayed, with the sole exception of naphthalene, approached the value of reference significantly (Table 4). From the before mentioned, it is possible to conclude that the relation of proportionality between k_{i} and D_{i} is only valid for compounds with similar physical properties, which is directly related to the control stages of the mass transfer process. Only those compounds that are under liquid control (where the limiting stage of the process of mass transfer is at the liquid interphase) will be representative and able to be used as reference in the K_{L}a correction for other compounds with equal limiting stage. On the matter, special interest presented the analysis of gaseous controlled compounds such as phenols and polycyclic hydrocarbons of greater complexity than naphthalene. Nevertheless, these compounds displayed disadvantages respect to the methodology used in this study in terms of their water solubility and sampling techniques.

It is important to mention that a more accurate mathematical expression that accounts for the phenomena of mass transfer between a liquid and a gas phase in a dynamic system as it is the BAS technique, requires to consider factors such as hydrophobicity and polarity among others. For example, polar compounds of low solubility can present an anomalous behavior accumulating at level of the liquid interphase and generating the phenomenon of "interphase partitioning" (11) where the interphase constitutes an independent phase in which these compounds accumulate reaching higher concentrations than those of the liquid phase and establishing a new equilibrium with the gaseous phase, generating overestimations of the Henry's constant (1, 11).

Finally, it is possible to conclude that the mathematical approach proposed in this study accounts for the process of mass transfer between phases extending considerably the use of BAS technique in the determination of the Henry's constant.

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