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Henry’s law constants derived from equilibrium static cell measurements for dilute organic–water mixtures
Fluid Phase Equilibria 185 (2001) 359–377
Henry’s law constants derived from equilibrium static cell measurements for dilute organic–water mixtures P. Chatkun Na Ayuttaya, T.N. Rogers, M.E. Mullins∗ , A.A. Kline Department of Chemical Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
Abstract The relationship of pressure and composition in the Henry’s law regime has been experimentally measured in an equilibrium static cell for a set of binary organic–water mixtures. The solutes range from hydrophilic materials, such as alcohol to extremely hydrophobic components, such as toluene and 1,2-dichloroethane. The goal of this study is to determine the effective concentration range over which Henry’s law reasonably approximates the gas–liquid partitioning. With the goal of obtaining accurate values of Henry’s law constant, several methodologies are critically compared for the aqueous solutes examined experimentally. The apparatus employed can determine gas–liquid partitioning coefficients through a variety of methods including direct phase concentration ratios, equilibrium partitioning in closed systems (EPICS), and application of the coexistence equation for γ ∞ . Results to date indicate a more complex dP/dx behavior in the dilute region than previously assumed; and Henry’s law constant may not strictly apply to hydrophobic materials until the solute concentration is so low that analytical detection is problematic. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Activity coefficient; Henry’s law constant; Air–water partitioning; Hydrophobic chemicals; Organic–water mixtures
1. Introduction The activity coefficient at infinite dilution is a key parameter for predicting the phase partitioning of a solute. It is also one of the basic thermodynamic properties used to obtain the adjustable parameters in various activity coefficient models of multi-component systems. It is generally used to characterize the behavior of a single solute molecule completely surrounded by solvent molecules, which corresponds to the maximum non-ideality of the solute behavior in solution [1]. Therefore, the activity coefficient at infinite dilution (γ ∞ ) for the solute gives specific information about the molecular interactions between the solute and solvent, eliminating solute–solute interactions. As a consequence, single-solute experiments at infinite dilution to determine activity coefficient model parameters (e.g. binary solute–solvent interaction parameters) can be extrapolated to mixtures at higher solute concentrations. The activity coefficient ∗ Corresponding author. Tel.: +1-906-487-2736; fax: +1-906-487-3213. E-mail address: [email protected] (M.E. Mullins).
0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 4 8 4 - 8
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at infinite dilution is also a particularly important indicator of partitioning of dilute contaminants in the environment. Accurate experimental values and an appropriate model for activity coefficients at infinite dilution (γ ∞ ) form the basis for predicting partitioning properties related to environmental fate assessment, such as Henry’s law constant, n-octanol/water partition coefficient, and water solubility. In this work, we examine several methodologies for measuring Henry’s law constants and activity coefficients at infinite dilution for binary solute–solvent mixtures. The representative solute–solvent systems are binary mixtures of pure water and the following pure chemical solutes: isopropyl alcohol, acetone, 1,2-dichloroethane, and toluene. These binary mixtures represent several important functional groups covering a wide range of hydrophobicity, typical of that found in industrial hazardous wastes. A equilibrium static cell apparatus has been constructed that permits examination of several experimental methodologies: equilibrium static cell, equilibrium partitioning in closed systems (EPICS), and direct phase concentration ratios for the direct measurement of Henry’s law constant. These experiments were conducted over a range of solute concentrations at isothermal conditions. Analysis of the results can be used to recommend the measurement techniques that are suitable for each type of chemical mixture and are used to bridge the ‘gap’ from experiments to a predictive model. 2. Background 2.1. Experimental methodologies 2.1.1. Equilibrium static cell This methodology [2–4] is based on the isothermal measurement of pressure differences between the vapor pressure of the very dilute solution (at several compositions) and the pure solvent. This methodology depends upon the volumetric determination of the liquid phase composition, and highly accurate pressure measurements under stable temperature conditions. The disadvantages of this methodology [5] are the long times needed in order to reach equilibrium between the vapor and liquid phases, and the need for complete degassing of all liquid solutes and solvents. The accuracy of this methodology is mainly dependent on precise vapor phase pressure determinations. The applicable form of the Gibbs–Duhem equation for a binary system is sometimes called the coexistence equation as follows: γ1∞ =
[P2S + (∂PT /∂x)x→0 ] T S P1
(1)
where PiS is the vapor pressure of pure component (atm), ‘1’ and ‘2’ refer to the solute and solvent, respectively, PT the total pressure (atm), x the mole fraction of organic solute, and (∂PT /∂x)x→0 the T limiting slope of pressure versus mole fraction as the mole fraction approaches zero. The calculations for this method require the pure component vapor pressures of the solute and solvent as a function of temperature, and also the limiting slope [(∂PT /∂x)x→0 ] of the total pressure versus mole fraction. This T information is introduced into Eq. (1) in order to find the infinite dilution of activity coefficient for the solute in water. 2.1.1.1. Limiting slope (∂PT /∂x)x→0 of the equilibrium static cell. A set of total pressure measurements T of each binary mixture for vessels A and B were initially plotted as a function of mole fraction. The
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experimental data were fitted with several analytical equations in order to find the limiting slope (dP/dx), where the mole fraction (x) approaches zero (e.g. infinite dilution). The two equation forms that result in the best correlation coefficient, R2 , are a simple linear equation, and a non-linear (2nd order polynomial) equation. These correspond to two general assumptions that were made in this study to acquire a limiting slope, (∂PT /∂x)x→0 . T By assuming a linear relationship between the total pressure exerted in a closed system and the solute mole fraction, the limiting slope (∂PT /∂x)x→0 of each experiment is approximately equivalent to the T difference in total pressure and solvent vapor pressure over the mole fraction range of that experiment ∂PT x→0 PT − P2S ≈ (2) ∂x T x−0 where PT(actual) is the actual total pressure which equals to Pinert + P2S + Porganic solute . The variability of this limiting slope value corresponds closely to the accuracy of the total pressure measurement. The second approach for obtaining (∂PT /∂x)x→0 is derived from Pividal et al. [6,7]. The limiting slope T is obtained by fitting a 2nd degree polynomial equation to experimental data of equilibrium total pressure versus mole fraction. Here PT(actual) = Pinert + P2S + Porganic solute = Ax2 + Bx + C (assumed)
(3)
According to Eq. (3) the total pressure, which is measured in this study for an equilibrium static cell, accounts for the pressure of inerts (such as dissolved air present in the liquid solution), as well as the water and organic solute partial pressure. The presence of inerts (dissolved air) is caused by the degassing effect of the liquid mixture to the system and is a function of the liquid volume delivered to each equilibrium static cell. This leads to differential offset (C) for the polynomial equation for dPT /dx for each equilibrium static cell experiment, and each initial liquid volume. However, only the partial pressure of the organic solute is a function of mole fraction. Hence, the effect of the pressure offset, and the dPT /dx curvature that occurs, does not influence the limiting slope (∂PT /∂x)x→0 . The derivative of total pressure is, therefore, T equal to the derivative of the organic solute pressure, and can be determined as the second coefficient of the polynomial equation (Eq. (3)) ∂PT x→0 =B (4) ∂x T The second polynomial coefficient B, is therefore, the limiting slope as shown in Eq. (4) above. According to this assumption, a single limiting slope is obtained as a constant applied to the regression of PT versus x data for all experiments in this study. This results in much more consistent values of Henry’s law constants over the composition range. The pressure versus solute mole fraction is plotted, and the best fit to Eq. (3) is determined. Fig. 1 shows the plot of equilibrium total pressure versus mole fraction in vessels A and B for a binary system of 1,2-dichloroethane in water and the two best equations fitted which are used to obtain the limiting slope of a non-linear dPT /dx assumption. The equilibrium static cell methodology utilizes two equilibrium static cells, each containing a dilute mixture with different liquid volumes. Each cell is connected to a highly accurate pressure transducer, and each measurement is made isothermally at constant volume. The pressure, temperature, volume measurements may also be combined with liquid or gas phase solute concentration measurements to allow the determination of the infinite dilution activity coefficient via two different calculations.
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Fig. 1. Equilibrium total pressure vs. mole fraction in vessels A and B for a binary system of 1,2-dichloroethane in water.
2.1.2. Equilibrium partitioning in closed systems (EPICS) The EPICS [8–10] method utilizes a pair of closed systems containing different liquid volumes of the same concentration solution mixture. It requires measurement of the solute concentration ratios of the two closed systems for one phase (liquid or gas phase) at equilibrium. The concentrations may be determined via gas chromatography (GC) peak areas, but absolute solute concentrations may not needed. Henry’s law constant is then determined by combining the mass balances for the two closed vessels into a single equation in terms of Henry’s law constant as follows: HC =
VL2 − βVL1 βVG1 − VG2
(5)
and β=
M2 /M1 CL2 /CL1
where CL , CG are the liquid and gas phase concentration of closed system, M the total organic mass in system, VL , VG the liquid and gas phase volume of closed system, ‘1’ and ‘2’ refer to closed systems 1 and 2, respectively, HC the Henry’s law constant (dimensionless), ρ w the liquid density of water, R the
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ideal gas constant, T the equilibrium temperature (K).Division by the pure solute vapor pressure yields the infinite dilution activity coefficient, γi∞ , as: γi∞ =
HC ρw RT PiS
The advantages of this method include a simple apparatus, and elimination of mass transfer problems. The major disadvantage of this method is the error introduced by imprecise addition of solute, system leakage, or error in the volumetric measurement of solute. 2.1.3. Direct phase concentration ratio This methodology requires measurement of both the liquid–phase concentration and the gas–phase concentration in each equilibrium cell. The liquid–phase and gas–phase concentrations are obtained by GC, and checked with the mass balances on the solute chemical in vessels A and B both before and after the experiment is run. Subsequently, Henry’s law constant is obtained directly by dividing the solute gas phase concentration (CG ) by the liquid phase concentration (CL ) HC =
CG CL
(6)
2.2. Aqueous binary systems In this research work, the infinite dilution activity coefficient (γi∞ ) for four single solute chemicals (isopropyl alcohol, acetone, 1,2-dichloroethane, and toluene) in water are measured. These four chemicals have different solubility and volatility characteristics, and may be broadly classified in four categories as shown in Fig. 2. Group I is the alcohol group, characterized by high solubility (difficult to strip) and low volatility, and is represented by isopropyl alcohol. Group II is the ketone group, characterized by high solubility (difficult to strip) and high volatility, and is represented by acetone. Group III is the chlorinated hydrocarbon group, characterized by low solubility (easier to strip) and moderate volatility, and is represented
Fig. 2. The classifications of solute chemicals based on their thermodynamic property.
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by 1,2-dichloroethane. Group IV is the aromatic group, characterized by low solubility (easier to strip) and high volatility, and is represented by toluene. These solute chemicals are used to examine both the operating limitations of the apparatus, and to determine which methodology is best suited to each solute chemical category. 3. Experimental procedure 3.1. Apparatus The concept of our equilibrium static cell apparatus is to measure Henry’s law constants based on total pressure, operating temperature, liquid volume, and composition measurements. However, the apparatus is designed with the capability to determine gas–liquid partitioning coefficients of binary mixtures via a variety of methods including equilibrium static measurements, EPICS, and direct phase concentration ratios. Accurate pressure, liquid volume, temperature, and composition data are the core of determining Henry’s law constants and infinite dilution activity coefficients for each methodology. The experiments with this apparatus are performed with highly accurate measuring equipment to control and measure these key parameters (pressure, liquid volume, and temperature). An apparatus that permits examination of several experimental methodologies has been constructed and shown schematically in Fig. 3. The equilibrium static cell apparatus is composed of two customized five-neck round glass vessels, each with an approximately interior volume of 1300 ml. Each vessel is connected to an absolute pressure transducer, precision RTD thermometers for temperature measurement, a liquid sampling port, a highly accurate pressure transducer, and a three-way valve for liquid injection and evacuation with vacuum pump. The liquid sampling port consists of a vacuum tight valve sealed with a Teflon® septa on the inlet side. Each connection uses an o-ring joint to maintain vacuum conditions. The absolute pressure transducer is an OMEGA® PX811 high accuracy wet absolute pressure transducer, Model PX811-015AV, with a 0–15 psia range. The pressure transducer is connected to a high performance process indicator (Model DP41-V) readout, and is inturn connected to the twin vessel using an o-ring joint welded with a Kovar® to glass seal 1/4 in. connection and a Swagelok® fitting. The apparatus also connected to a highly accurate absolute pressure transducer, a Digiquartz® pressure transducer 2000 series absolute, Model 230A-101, with 1 × 10−8 resolution, a 0–30 psia and an accuracy 0.01%. The pressure transducer is connected to a Digiquartz® intelligent display (Model 730) readout. The transducer is connected to the vessels via a stainless steel 1/16 in. three-way valve, which is manually switched to measure the total pressure from each vessel. The three-way valve is connected to the twin vessels neck by stainless steel 1/16 in. tubing conjoined with an o-ring joint welded with a Kovar® to glass seal 1/4 in. connection and a Swagelok® fitting. For the temperature measurements, two Azonix® Laboratory Grade Probes, Model A12001 with an accuracy of 0.007◦ C at 0◦ C and with −183 to +480◦ C ranges, are used. These resistance temperature detector (RTD) probes are connected to the twin vessel by a Swagelok® fitting with Teflon® ferrules for Kovar® to glass seal 1/2 in. connections. They are connected to an Azonix® precision RTD thermometer readout, Model A1011 with 0.001◦ C resolution, 0.01◦ C accuracy, and −200 to +800◦ C measurement range. The last neck of the test flask is connected to a three-way valve, which is conjoined to the adapter for evacuation of vessels, and for degassing by a vacuum pump. The other side of the three-way valve is
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Fig. 3. Schematic diagram of an equilibrium static cell.
connected to an adapter, which is joined to a 1 litre separatory funnel, for introducing the liquid mixture into the system. The bottom portion is filled with a coolant mixture up to the necks of the twin vessels, and the entire apparatus is covered with an insulated temperature control chamber. The coolant mixture is a mixture of ethylene glycol and water in the ratio of 1:3. The container is connected to a high capacity controlled temperature water bath, which has −45 to 200◦ C range and ±0.01◦ C temperature stability, for controlling temperature and circulating the coolant mixture. Additional coolant circulation in the bath is provided by two stirrers in order to provide a more homogeneous temperature between the two vessels. The apparatus was vacuum tested by applying 0.01 mmHg vacuum pressure to both vessels, and maintains a complete vacuum for at least 20 h with 0.0070 ± 0.0023 atm pressure inside both vessels.
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3.2. Analytical procedure The solution concentrations are measured by GC on a HP 5890 Series II GC (Hewlett-Packard) equipped with a flame ionization detector (FID), connected to an HP 3396 Series II Integrator (Hewlett-Packard), and an HP 7673 automatic sampler (Hewlett-Packard) for analyzing liquid sample. A stainless steel GC column packed with 3% SPTM -1500 on 80/100 Carbopack (Supelco Inc.) is used with all chemicals in this research (inject temperature is 200◦ C; detector temperature is 250◦ C; carrier flow (He) is 30 ml/min, hydrogen and air flows are 30 ml/min and 400 ml/min, respectively). The following programming sequences are used: 120◦ C (7 min) with 2 min equilibrium time for analyzing isopropyl alcohol and acetone; 120◦ C (5 min) and 10◦ /min to 200◦ C (with 2 min equilibrium time) for analyzing toluene; and 140◦ C (10 min) with 2 min equilibrium time for analyzing 1,2-dichloroethane. Retention times for the solute chemicals are as follows: 2.6 min for isopropyl alcohol; 2.1 min for acetone; 4 min for 1,2-dichloroethane; and 16 min for toluene. The peak areas for each chemical are applied to its standard chemical calibration curve to estimate concentration. 3.3. Experimental procedure The overall experiment setup for the equilibrium static cell apparatus is shown in Fig. 4. For each solute chemical in water, a set of experiments is performed as a function of solute mole fractions at a constant temperature. Each solute chemical composition range is based on its solubility limit and volatility, which are recommended by Kojima et al. [3]. Both solubility and volatility data for all chemical groups are obtained from the AIChE — DIPPR Project 911 database [6]. Prior to each experiment, the glassware parts and vessels are washed with water and dried in an oven for 2–3 h in order to eliminate undesired chemicals in the system. Each vessel is connected to a degassing manifold with a liquid nitrogen cold-trap (Fig. 4., Item 7) to prevent contamination of the vacuum pump (Fig. 4., Item 8). The measurements begin with evacuating the entire apparatus and the manifold to 0.1 mmHg vacuum pressure until the pressure transducer readouts achieve a constant value (usually about 2 h.). Valves (Fig. 4., Item V1, V4 and V3, V6) are closed before the evacuation process stops. The pressure and temperature readings are then noted. The liquid solution is delivered to each of the separatory funnels (Fig. 4., Item 3A, 3B) connected to the twin vessel apparatus (at valves V2 and V5 of the three-way valves). The vacuum pump is used to evacuate the connection parts between the separatory funnels (Fig. 4., Item 3A, 3B) and valves (Fig. 4., Item V2, V5) until the pressure readout reaches the initial vacuum readings. Valves (Fig. 4., Item V3, V6, V10, and V11) are closed, isolating the vessels and the vacuum pump is shut down. The liquid solution is introduced to both vessels by opening valves (Fig. 4., Item V7 and V9) until a volume ratio of 1:2 is reached in vessels A and B, respectively. Consequently, the valves (Fig. 4., Item V2, V5, V7, and V9) are shut, and the separatory funnels (Fig. 4., Item 3A, 3B) disconnect from the experimental setup. The initial temperatures (Fig. 4., Item TA3, TB3) and pressure (Fig. 4., Item PA3, PB3) from both vessels are recorded and the water bath (Fig. 4., Item TC1) circulators start. The setpoint temperature is then set, and the coolant mixture takes about 3 h to reach stability. The experiment is run for 10 h to assure equilibrium conditions. The temperatures and pressures are continuously monitored. Liquid solutions from both vessels are sampled into small vials, and subsequently analyzed by GC to obtain liquid phase concentration ratios. At the conclusion of each experiment, the vacuum is released and the liquid mixtures inside both vessels are withdrawn for sampling. The next experiment is performed by changing the mole
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Fig. 4. Experimental setup and support equipment for the equilibrium static cell apparatus: (1A, 1B) twin vessels; (2A, 2B) high performance process indicators for absolute pressure measurements; (3A, 3B) separatory funnels for introducing mixture to system; (4) a highly accurate absolute pressure transducer; (5) pressure indicator; (6) precision RTD thermometer readout; (7) liquid trap; (8) vacuum pump; (9) a high capacity controlled temperature water bath (TC1); (10) temperature control chamber.
Table 1 Operating conditions of binary systems for an equilibrium static cell apparatus Set
Solute
Solvent
Liquid volume ratioa
No. of experiments in a setb
Temperature setpoint (◦ C)
Mole fraction range (%)c
1 2 3 4
Isopropyl alcohol Acetone 1,2-Dichloroethane Toluene
DD, water DD, water DD, water DD, water
1:2 1:2 1:2 1:2
8 8 11 16
25 25 25 25
0.002–0.1 0.002–0.5 0.00073–0.073 0.00022–0.0096
a
Liquid volume ratio is the ratio of liquid volumes that are delivered to flasks A and B. The liquid volumes in vessels A and B are approximately 400 ± 30 and 800 ± 30 ml in flask B, respectively. b The experiments of some mole fractions are replicated. c The increment of mole fraction in each range is varied differently for each solute chemical.
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fraction of the solute chemical and repeating the same experimental procedure. The range of operating conditions of the binary systems examined is shown in Table 1.
4. Results and discussion Henry’s law constant results were obtained by applying the experimental data to the appropriate calculation for each technique: equilibrium static cell/coexistence equation (dPT /dx), EPICS, and direct phase concentration ratio. The liquid phase concentration ratios as determined from GC peak areas between vessels A and B were introduced to Eq. (5) for EPICS calculations. Direct phase concentration ratios were also used in Eq. (6) as yet another way to determine Henry’s law constants. Averages and standard deviations of Henry’s law constants determined for all of the techniques are presented in Tables 2 and 3. However, for 1,2-dichloroethane and toluene sufficient experimental results were available to apply a valid non-linear fit to the dPT /dx data for the coexistence equation. A comparison of the Henry’s law constant results (unitless) obtained for the binary systems of isopropyl alcohol, acetone, toluene, and 1,2-dichloroethane in water are presented in Figs. 5–8, respectively. For the binary system of isopropyl alcohol in water (group I), the average value of Henry’s law constants obtained via the EPICS method is about one order of magnitude higher than the literature values [11]. The EPICS results are quite reproducible and have a small standard deviation over the solute concentration range examined. On the other hand, the average values of Henry’s law constants derived from a linear assumption of dPT /dx behavior in the coexistence equation are about three orders of magnitude higher than the literature values. The results are scattered and have a high standard deviation over the solute mole fraction range. For this system, there is not sufficient data as a function of solute concentration to determine the Henry’s law constant from a non-linear dPT /dx assumption. For the direct phase concentration ratios, the average value of Henry’s law constant is in the same region as the literature value; however, the standard deviation is quite large. This results from analytical difficulties associated with absolute concentration measurements in the extremely dilute region. In fact, the standard deviation of the results increases greatly in the low mole fraction range. The somewhat better results of the EPICS method indicate that reliable Henry’s law constants results can be obtained in the dilute range, since concentration ratios, instead of absolute values, are required using this method. However, the measurements of this binary system are also ultimately limited by the detection capability of the gas chromatograph. Based on a comparison of the results obtained from these four methodologies, EPICS is the most suitable methodology for this binary system. Employing an extremely sensitive detector (e.g. ECD) in the gas chromatograph in order to obtain measurements in the extremely dilute region, results in more accurate Henry’s law constants. For the binary system of acetone in water (group II), the average value of the Henry’s law constant results from EPICS is approximately two times higher than the literature values, and has a small standard deviation from the average value. The average values of Henry’s law constant obtained from the linear dPT /dx assumption are about two orders of magnitude higher than the literature values and have large standard deviations over the solute mole fraction range. For the direct phase concentration ratios, the average value of Henry’s law constant are once again in the same region as the literature value; however, the standard deviation is also large. As before, the results obtained from the last two methodologies indicate a large standard deviation as the dilute region is approached due to analytical limitations. As with the measurements for isopropyl alcohol in water, there is not enough information to calculate the
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Henry’s law constant by extrapolation of a non-linear dPT /dx assumption for the equilibrium static cell data. The most suitable methodology for measuring the Henry’s law constants of acetone in water over the mole fraction range specified in this work is the EPICS method. For the binary system of 1,2-dichloroethane in water (group III), the Henry’s law constant results are determined using all four of the methodologies. For EPICS, the average value of the Henry’s law constant is approximately two times higher than the literature values. The results obtained by this methodology are very consistent and yield a small standard deviation over a wide solute concentration range, although like many of the other EPICS measurements, the results tend to be on the higher side of the literature values. For the linear dPT /dx fit to the equilibrium static cell data, the average values of Henry’s law constant determined are one to two orders of magnitude higher than the literature values. The results from both flasks A and B have large standard deviations, due to the considerable scattering of values in the low concentration region. The standard deviation decreases greatly as the solute concentration approaches the solubility limit. The results also seem to indicate a non-linear relationship between total pressure and solute concentration, which is more complex than previously assumed for the dilute region, may be appropriate. By applying a non-linear fit to the equilibrium static cell data, an average value of Henry’s law constant from both flasks may be determined from the limiting slope (dPT /dx). This methodology is determined based upon the limiting slope (dP/dx), which is obtained by fitting experimental data (total pressure) with a 2nd order polynomial equation, and the vapor pressure of the pure components (Eq. (3)). The average values of HC determined in this fashion are in the same range as the literature values, and have extremely small standard deviations over the solute mole fraction range. Because this methodology is based on a limiting slope obtained from numerous experimental points, a value for the limiting slope (dPT /dx) may be determined with greater statistical certainty. This is supported by the results, which yield regression correlation coefficient (R2 ) values of approximately 0.94 for both flasks. The Henry’s law constant determined via this method is in line with the literature values. For the direct phase concentration ratios, the average values of Henry’s law constant obtained from both flasks are in higher side of the literature value; however, the standard deviation is once again relatively large compared to the EPICS and a non-linear dPT /dx fit to the equilibrium static cell data. Thus, the recommended methodology for determining Henry’s law constant for this binary solution is application of a non-linear dPT /dx assumption to the equilibrium static cell data. Similar to the 1,2 dichloroethane–water system (group III), the Henry’s law constant results of toluene in water (group IV) are obtained using all four methodologies. For EPICS, the average value of the Henry’s law constant is in the same range, but on the higher side of the literature values. The Henry’s law constants obtained by this methodology also decrease slightly as the solubility limit is approached. For the linear dPT /dx analysis of the equilibrium static cell data, the Henry’s law constants determined are 3–10 times higher than the literature values. The results from both vessels have large standard deviations over the examined solute mole fraction range. For the direct phase concentration ratios, the average values of Henry’s law constant obtained from both flasks are on the higher side of the literature values; however, the standard deviation is once again relatively large compared to the EPICS and a non-linear dPT /dx fit to the equilibrium static cell data. For the non-linear assumption for dPT /dx behavior, the average values obtained from both vessels are slightly lower than the literature values, but have very small standard deviations over the solute mole fraction range. The correlation coefficient (R2 ) for the polynomial fit is approximately 0.85. Based on these observations, the most suitable methodologies to determine the Henry’s law constant for this binary mixture are the EPICS technique, and the non-linear dPT /dx assumption for the coexistence equation.
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5. Conclusions The conclusions of this study may be summarized as follows: 1. For chemicals with high solubility and low volatility (group I) and the chemicals with high solubility and high volatility (group II), the preferred methodologies for determining Henry’s law constant and the corresponding value for γ ∞ are the EPICS and non-linear coexistence equation, with both methods using extremely dilute liquid phase concentration data. 2. For chemicals with high volatility and partial miscibility (groups III and IV), the non-linear coexistence equation approach is the best methodology over the solute mole fraction range specified in this work. 3. The EPICS technique is a reasonable alternative methodology for measuring Henry’s law constant for these four binary systems. However, the Henry’s law constants determined this way are generally on the higher side of the literature range perhaps due to mass losses during the analytical procedure. 4. The mass balances obtained from the direct ratio measurements close to within 5% and the calculated Henry’s law constants are relatively close to literature values. However, the standard deviations of the results obtained from this methodology have large variation over mole fraction range specified in this work due to analytical limitations in the extremely dilute region. To support the conclusions and improve the efficiency of equilibrium static cell measurements, there are some future investigations required including: 1. Continued vapor–liquid equilibrium studies of additional representative binary systems of nonelectrolytes. 2. Investigation and refinement of the chemical and water degassing within this apparatus in order to minimize the effect of inerts on the total pressure measurement. List of symbols A the first coefficient of the polynomial equation B the second coefficient of the polynomial equation C the third coefficient or offset of the polynomial equation Ci concentration of closed systems HC Henry’s law constant (dimensionless) M total organic mass of closed systems P pressure (atm) PT total pressure (atm) R ideal gas constant T equilibrium temperature (K) V volume of closed systems Greek letters γ activity coefficient ρ liquid density Subscripts G gas phase i component indexes
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L T w 1 2 1,2
377
liquid phase constant temperature water solute component solvent component closed systems 1 and 2
Superscripts S saturate x → 0 infinite dilution ∞ infinite dilution Acknowledgements The authors wish to acknowledge continuing financial support from US Department Of Energy, Environmental Management Science Program (EMSP), and National Institute of Standards and Technology (NIST), Physical and Chemical Properties Division for collaboration. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
C.A. Eckert, B.A. Newman, G.L. Nicolaides, T.C. Long, AIChE J. 27 (1981) 33. P. Alessi, M. Fermeglia, I. Kikic, Fluid Phase Equilib. 29 (1986) 249. P. Alessi, M. Fermeglia, I. Kikic, Fluid Phase Equilib. 43 (1988) 355. P. Alessi, M. Fermeglia, I. Kikic, Fluid Phase Equilib. 70 (1991) 239. K. Kojima, S. Zhang, T. Hiaki, Fluid Phase Equilib. 13 (1997) 145. K. Pividal, A. Birtigh, S.I. Sandler, J. Chem. Eng. Data 37 (1992) 484. K.A. Pividal, S.I. Sandler, J. Chem. Eng. Data 33 (1988) 438. J.M. Gosset, Environ. Sci. Technol. 21 (1987) 202. A.H. Lincoff, J.M. Gosset, Gas Transfer Water Surf. (1984) 17. R.A. Ashworth, G.B. Howe, M.E. Mullins, T.N. Rogers, J. Hazard. Mater. 18 (1988) 25. T.N. Rogers, M.E. Mullins, A.A. Kline, C.R. Whitten, D.A. Zei, Environmental Safety, and Health Data Compilation, Design Institute for Physical Property Data, AIChE, New York, 1999.
Henry’s law constants derived from equilibrium static cell measurements for dilute organic–water mixtures P. Chatkun Na Ayuttaya, T.N. Rogers, M.E. Mullins∗ , A.A. Kline Department of Chemical Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA
Abstract The relationship of pressure and composition in the Henry’s law regime has been experimentally measured in an equilibrium static cell for a set of binary organic–water mixtures. The solutes range from hydrophilic materials, such as alcohol to extremely hydrophobic components, such as toluene and 1,2-dichloroethane. The goal of this study is to determine the effective concentration range over which Henry’s law reasonably approximates the gas–liquid partitioning. With the goal of obtaining accurate values of Henry’s law constant, several methodologies are critically compared for the aqueous solutes examined experimentally. The apparatus employed can determine gas–liquid partitioning coefficients through a variety of methods including direct phase concentration ratios, equilibrium partitioning in closed systems (EPICS), and application of the coexistence equation for γ ∞ . Results to date indicate a more complex dP/dx behavior in the dilute region than previously assumed; and Henry’s law constant may not strictly apply to hydrophobic materials until the solute concentration is so low that analytical detection is problematic. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Experimental method; Activity coefficient; Henry’s law constant; Air–water partitioning; Hydrophobic chemicals; Organic–water mixtures
1. Introduction The activity coefficient at infinite dilution is a key parameter for predicting the phase partitioning of a solute. It is also one of the basic thermodynamic properties used to obtain the adjustable parameters in various activity coefficient models of multi-component systems. It is generally used to characterize the behavior of a single solute molecule completely surrounded by solvent molecules, which corresponds to the maximum non-ideality of the solute behavior in solution [1]. Therefore, the activity coefficient at infinite dilution (γ ∞ ) for the solute gives specific information about the molecular interactions between the solute and solvent, eliminating solute–solute interactions. As a consequence, single-solute experiments at infinite dilution to determine activity coefficient model parameters (e.g. binary solute–solvent interaction parameters) can be extrapolated to mixtures at higher solute concentrations. The activity coefficient ∗ Corresponding author. Tel.: +1-906-487-2736; fax: +1-906-487-3213. E-mail address: [email protected] (M.E. Mullins).
0378-3812/01/$20.00 © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 4 8 4 - 8
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at infinite dilution is also a particularly important indicator of partitioning of dilute contaminants in the environment. Accurate experimental values and an appropriate model for activity coefficients at infinite dilution (γ ∞ ) form the basis for predicting partitioning properties related to environmental fate assessment, such as Henry’s law constant, n-octanol/water partition coefficient, and water solubility. In this work, we examine several methodologies for measuring Henry’s law constants and activity coefficients at infinite dilution for binary solute–solvent mixtures. The representative solute–solvent systems are binary mixtures of pure water and the following pure chemical solutes: isopropyl alcohol, acetone, 1,2-dichloroethane, and toluene. These binary mixtures represent several important functional groups covering a wide range of hydrophobicity, typical of that found in industrial hazardous wastes. A equilibrium static cell apparatus has been constructed that permits examination of several experimental methodologies: equilibrium static cell, equilibrium partitioning in closed systems (EPICS), and direct phase concentration ratios for the direct measurement of Henry’s law constant. These experiments were conducted over a range of solute concentrations at isothermal conditions. Analysis of the results can be used to recommend the measurement techniques that are suitable for each type of chemical mixture and are used to bridge the ‘gap’ from experiments to a predictive model. 2. Background 2.1. Experimental methodologies 2.1.1. Equilibrium static cell This methodology [2–4] is based on the isothermal measurement of pressure differences between the vapor pressure of the very dilute solution (at several compositions) and the pure solvent. This methodology depends upon the volumetric determination of the liquid phase composition, and highly accurate pressure measurements under stable temperature conditions. The disadvantages of this methodology [5] are the long times needed in order to reach equilibrium between the vapor and liquid phases, and the need for complete degassing of all liquid solutes and solvents. The accuracy of this methodology is mainly dependent on precise vapor phase pressure determinations. The applicable form of the Gibbs–Duhem equation for a binary system is sometimes called the coexistence equation as follows: γ1∞ =
[P2S + (∂PT /∂x)x→0 ] T S P1
(1)
where PiS is the vapor pressure of pure component (atm), ‘1’ and ‘2’ refer to the solute and solvent, respectively, PT the total pressure (atm), x the mole fraction of organic solute, and (∂PT /∂x)x→0 the T limiting slope of pressure versus mole fraction as the mole fraction approaches zero. The calculations for this method require the pure component vapor pressures of the solute and solvent as a function of temperature, and also the limiting slope [(∂PT /∂x)x→0 ] of the total pressure versus mole fraction. This T information is introduced into Eq. (1) in order to find the infinite dilution of activity coefficient for the solute in water. 2.1.1.1. Limiting slope (∂PT /∂x)x→0 of the equilibrium static cell. A set of total pressure measurements T of each binary mixture for vessels A and B were initially plotted as a function of mole fraction. The
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experimental data were fitted with several analytical equations in order to find the limiting slope (dP/dx), where the mole fraction (x) approaches zero (e.g. infinite dilution). The two equation forms that result in the best correlation coefficient, R2 , are a simple linear equation, and a non-linear (2nd order polynomial) equation. These correspond to two general assumptions that were made in this study to acquire a limiting slope, (∂PT /∂x)x→0 . T By assuming a linear relationship between the total pressure exerted in a closed system and the solute mole fraction, the limiting slope (∂PT /∂x)x→0 of each experiment is approximately equivalent to the T difference in total pressure and solvent vapor pressure over the mole fraction range of that experiment ∂PT x→0 PT − P2S ≈ (2) ∂x T x−0 where PT(actual) is the actual total pressure which equals to Pinert + P2S + Porganic solute . The variability of this limiting slope value corresponds closely to the accuracy of the total pressure measurement. The second approach for obtaining (∂PT /∂x)x→0 is derived from Pividal et al. [6,7]. The limiting slope T is obtained by fitting a 2nd degree polynomial equation to experimental data of equilibrium total pressure versus mole fraction. Here PT(actual) = Pinert + P2S + Porganic solute = Ax2 + Bx + C (assumed)
(3)
According to Eq. (3) the total pressure, which is measured in this study for an equilibrium static cell, accounts for the pressure of inerts (such as dissolved air present in the liquid solution), as well as the water and organic solute partial pressure. The presence of inerts (dissolved air) is caused by the degassing effect of the liquid mixture to the system and is a function of the liquid volume delivered to each equilibrium static cell. This leads to differential offset (C) for the polynomial equation for dPT /dx for each equilibrium static cell experiment, and each initial liquid volume. However, only the partial pressure of the organic solute is a function of mole fraction. Hence, the effect of the pressure offset, and the dPT /dx curvature that occurs, does not influence the limiting slope (∂PT /∂x)x→0 . The derivative of total pressure is, therefore, T equal to the derivative of the organic solute pressure, and can be determined as the second coefficient of the polynomial equation (Eq. (3)) ∂PT x→0 =B (4) ∂x T The second polynomial coefficient B, is therefore, the limiting slope as shown in Eq. (4) above. According to this assumption, a single limiting slope is obtained as a constant applied to the regression of PT versus x data for all experiments in this study. This results in much more consistent values of Henry’s law constants over the composition range. The pressure versus solute mole fraction is plotted, and the best fit to Eq. (3) is determined. Fig. 1 shows the plot of equilibrium total pressure versus mole fraction in vessels A and B for a binary system of 1,2-dichloroethane in water and the two best equations fitted which are used to obtain the limiting slope of a non-linear dPT /dx assumption. The equilibrium static cell methodology utilizes two equilibrium static cells, each containing a dilute mixture with different liquid volumes. Each cell is connected to a highly accurate pressure transducer, and each measurement is made isothermally at constant volume. The pressure, temperature, volume measurements may also be combined with liquid or gas phase solute concentration measurements to allow the determination of the infinite dilution activity coefficient via two different calculations.
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Fig. 1. Equilibrium total pressure vs. mole fraction in vessels A and B for a binary system of 1,2-dichloroethane in water.
2.1.2. Equilibrium partitioning in closed systems (EPICS) The EPICS [8–10] method utilizes a pair of closed systems containing different liquid volumes of the same concentration solution mixture. It requires measurement of the solute concentration ratios of the two closed systems for one phase (liquid or gas phase) at equilibrium. The concentrations may be determined via gas chromatography (GC) peak areas, but absolute solute concentrations may not needed. Henry’s law constant is then determined by combining the mass balances for the two closed vessels into a single equation in terms of Henry’s law constant as follows: HC =
VL2 − βVL1 βVG1 − VG2
(5)
and β=
M2 /M1 CL2 /CL1
where CL , CG are the liquid and gas phase concentration of closed system, M the total organic mass in system, VL , VG the liquid and gas phase volume of closed system, ‘1’ and ‘2’ refer to closed systems 1 and 2, respectively, HC the Henry’s law constant (dimensionless), ρ w the liquid density of water, R the
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ideal gas constant, T the equilibrium temperature (K).Division by the pure solute vapor pressure yields the infinite dilution activity coefficient, γi∞ , as: γi∞ =
HC ρw RT PiS
The advantages of this method include a simple apparatus, and elimination of mass transfer problems. The major disadvantage of this method is the error introduced by imprecise addition of solute, system leakage, or error in the volumetric measurement of solute. 2.1.3. Direct phase concentration ratio This methodology requires measurement of both the liquid–phase concentration and the gas–phase concentration in each equilibrium cell. The liquid–phase and gas–phase concentrations are obtained by GC, and checked with the mass balances on the solute chemical in vessels A and B both before and after the experiment is run. Subsequently, Henry’s law constant is obtained directly by dividing the solute gas phase concentration (CG ) by the liquid phase concentration (CL ) HC =
CG CL
(6)
2.2. Aqueous binary systems In this research work, the infinite dilution activity coefficient (γi∞ ) for four single solute chemicals (isopropyl alcohol, acetone, 1,2-dichloroethane, and toluene) in water are measured. These four chemicals have different solubility and volatility characteristics, and may be broadly classified in four categories as shown in Fig. 2. Group I is the alcohol group, characterized by high solubility (difficult to strip) and low volatility, and is represented by isopropyl alcohol. Group II is the ketone group, characterized by high solubility (difficult to strip) and high volatility, and is represented by acetone. Group III is the chlorinated hydrocarbon group, characterized by low solubility (easier to strip) and moderate volatility, and is represented
Fig. 2. The classifications of solute chemicals based on their thermodynamic property.
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by 1,2-dichloroethane. Group IV is the aromatic group, characterized by low solubility (easier to strip) and high volatility, and is represented by toluene. These solute chemicals are used to examine both the operating limitations of the apparatus, and to determine which methodology is best suited to each solute chemical category. 3. Experimental procedure 3.1. Apparatus The concept of our equilibrium static cell apparatus is to measure Henry’s law constants based on total pressure, operating temperature, liquid volume, and composition measurements. However, the apparatus is designed with the capability to determine gas–liquid partitioning coefficients of binary mixtures via a variety of methods including equilibrium static measurements, EPICS, and direct phase concentration ratios. Accurate pressure, liquid volume, temperature, and composition data are the core of determining Henry’s law constants and infinite dilution activity coefficients for each methodology. The experiments with this apparatus are performed with highly accurate measuring equipment to control and measure these key parameters (pressure, liquid volume, and temperature). An apparatus that permits examination of several experimental methodologies has been constructed and shown schematically in Fig. 3. The equilibrium static cell apparatus is composed of two customized five-neck round glass vessels, each with an approximately interior volume of 1300 ml. Each vessel is connected to an absolute pressure transducer, precision RTD thermometers for temperature measurement, a liquid sampling port, a highly accurate pressure transducer, and a three-way valve for liquid injection and evacuation with vacuum pump. The liquid sampling port consists of a vacuum tight valve sealed with a Teflon® septa on the inlet side. Each connection uses an o-ring joint to maintain vacuum conditions. The absolute pressure transducer is an OMEGA® PX811 high accuracy wet absolute pressure transducer, Model PX811-015AV, with a 0–15 psia range. The pressure transducer is connected to a high performance process indicator (Model DP41-V) readout, and is inturn connected to the twin vessel using an o-ring joint welded with a Kovar® to glass seal 1/4 in. connection and a Swagelok® fitting. The apparatus also connected to a highly accurate absolute pressure transducer, a Digiquartz® pressure transducer 2000 series absolute, Model 230A-101, with 1 × 10−8 resolution, a 0–30 psia and an accuracy 0.01%. The pressure transducer is connected to a Digiquartz® intelligent display (Model 730) readout. The transducer is connected to the vessels via a stainless steel 1/16 in. three-way valve, which is manually switched to measure the total pressure from each vessel. The three-way valve is connected to the twin vessels neck by stainless steel 1/16 in. tubing conjoined with an o-ring joint welded with a Kovar® to glass seal 1/4 in. connection and a Swagelok® fitting. For the temperature measurements, two Azonix® Laboratory Grade Probes, Model A12001 with an accuracy of 0.007◦ C at 0◦ C and with −183 to +480◦ C ranges, are used. These resistance temperature detector (RTD) probes are connected to the twin vessel by a Swagelok® fitting with Teflon® ferrules for Kovar® to glass seal 1/2 in. connections. They are connected to an Azonix® precision RTD thermometer readout, Model A1011 with 0.001◦ C resolution, 0.01◦ C accuracy, and −200 to +800◦ C measurement range. The last neck of the test flask is connected to a three-way valve, which is conjoined to the adapter for evacuation of vessels, and for degassing by a vacuum pump. The other side of the three-way valve is
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Fig. 3. Schematic diagram of an equilibrium static cell.
connected to an adapter, which is joined to a 1 litre separatory funnel, for introducing the liquid mixture into the system. The bottom portion is filled with a coolant mixture up to the necks of the twin vessels, and the entire apparatus is covered with an insulated temperature control chamber. The coolant mixture is a mixture of ethylene glycol and water in the ratio of 1:3. The container is connected to a high capacity controlled temperature water bath, which has −45 to 200◦ C range and ±0.01◦ C temperature stability, for controlling temperature and circulating the coolant mixture. Additional coolant circulation in the bath is provided by two stirrers in order to provide a more homogeneous temperature between the two vessels. The apparatus was vacuum tested by applying 0.01 mmHg vacuum pressure to both vessels, and maintains a complete vacuum for at least 20 h with 0.0070 ± 0.0023 atm pressure inside both vessels.
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3.2. Analytical procedure The solution concentrations are measured by GC on a HP 5890 Series II GC (Hewlett-Packard) equipped with a flame ionization detector (FID), connected to an HP 3396 Series II Integrator (Hewlett-Packard), and an HP 7673 automatic sampler (Hewlett-Packard) for analyzing liquid sample. A stainless steel GC column packed with 3% SPTM -1500 on 80/100 Carbopack (Supelco Inc.) is used with all chemicals in this research (inject temperature is 200◦ C; detector temperature is 250◦ C; carrier flow (He) is 30 ml/min, hydrogen and air flows are 30 ml/min and 400 ml/min, respectively). The following programming sequences are used: 120◦ C (7 min) with 2 min equilibrium time for analyzing isopropyl alcohol and acetone; 120◦ C (5 min) and 10◦ /min to 200◦ C (with 2 min equilibrium time) for analyzing toluene; and 140◦ C (10 min) with 2 min equilibrium time for analyzing 1,2-dichloroethane. Retention times for the solute chemicals are as follows: 2.6 min for isopropyl alcohol; 2.1 min for acetone; 4 min for 1,2-dichloroethane; and 16 min for toluene. The peak areas for each chemical are applied to its standard chemical calibration curve to estimate concentration. 3.3. Experimental procedure The overall experiment setup for the equilibrium static cell apparatus is shown in Fig. 4. For each solute chemical in water, a set of experiments is performed as a function of solute mole fractions at a constant temperature. Each solute chemical composition range is based on its solubility limit and volatility, which are recommended by Kojima et al. [3]. Both solubility and volatility data for all chemical groups are obtained from the AIChE — DIPPR Project 911 database [6]. Prior to each experiment, the glassware parts and vessels are washed with water and dried in an oven for 2–3 h in order to eliminate undesired chemicals in the system. Each vessel is connected to a degassing manifold with a liquid nitrogen cold-trap (Fig. 4., Item 7) to prevent contamination of the vacuum pump (Fig. 4., Item 8). The measurements begin with evacuating the entire apparatus and the manifold to 0.1 mmHg vacuum pressure until the pressure transducer readouts achieve a constant value (usually about 2 h.). Valves (Fig. 4., Item V1, V4 and V3, V6) are closed before the evacuation process stops. The pressure and temperature readings are then noted. The liquid solution is delivered to each of the separatory funnels (Fig. 4., Item 3A, 3B) connected to the twin vessel apparatus (at valves V2 and V5 of the three-way valves). The vacuum pump is used to evacuate the connection parts between the separatory funnels (Fig. 4., Item 3A, 3B) and valves (Fig. 4., Item V2, V5) until the pressure readout reaches the initial vacuum readings. Valves (Fig. 4., Item V3, V6, V10, and V11) are closed, isolating the vessels and the vacuum pump is shut down. The liquid solution is introduced to both vessels by opening valves (Fig. 4., Item V7 and V9) until a volume ratio of 1:2 is reached in vessels A and B, respectively. Consequently, the valves (Fig. 4., Item V2, V5, V7, and V9) are shut, and the separatory funnels (Fig. 4., Item 3A, 3B) disconnect from the experimental setup. The initial temperatures (Fig. 4., Item TA3, TB3) and pressure (Fig. 4., Item PA3, PB3) from both vessels are recorded and the water bath (Fig. 4., Item TC1) circulators start. The setpoint temperature is then set, and the coolant mixture takes about 3 h to reach stability. The experiment is run for 10 h to assure equilibrium conditions. The temperatures and pressures are continuously monitored. Liquid solutions from both vessels are sampled into small vials, and subsequently analyzed by GC to obtain liquid phase concentration ratios. At the conclusion of each experiment, the vacuum is released and the liquid mixtures inside both vessels are withdrawn for sampling. The next experiment is performed by changing the mole
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Fig. 4. Experimental setup and support equipment for the equilibrium static cell apparatus: (1A, 1B) twin vessels; (2A, 2B) high performance process indicators for absolute pressure measurements; (3A, 3B) separatory funnels for introducing mixture to system; (4) a highly accurate absolute pressure transducer; (5) pressure indicator; (6) precision RTD thermometer readout; (7) liquid trap; (8) vacuum pump; (9) a high capacity controlled temperature water bath (TC1); (10) temperature control chamber.
Table 1 Operating conditions of binary systems for an equilibrium static cell apparatus Set
Solute
Solvent
Liquid volume ratioa
No. of experiments in a setb
Temperature setpoint (◦ C)
Mole fraction range (%)c
1 2 3 4
Isopropyl alcohol Acetone 1,2-Dichloroethane Toluene
DD, water DD, water DD, water DD, water
1:2 1:2 1:2 1:2
8 8 11 16
25 25 25 25
0.002–0.1 0.002–0.5 0.00073–0.073 0.00022–0.0096
a
Liquid volume ratio is the ratio of liquid volumes that are delivered to flasks A and B. The liquid volumes in vessels A and B are approximately 400 ± 30 and 800 ± 30 ml in flask B, respectively. b The experiments of some mole fractions are replicated. c The increment of mole fraction in each range is varied differently for each solute chemical.
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fraction of the solute chemical and repeating the same experimental procedure. The range of operating conditions of the binary systems examined is shown in Table 1.
4. Results and discussion Henry’s law constant results were obtained by applying the experimental data to the appropriate calculation for each technique: equilibrium static cell/coexistence equation (dPT /dx), EPICS, and direct phase concentration ratio. The liquid phase concentration ratios as determined from GC peak areas between vessels A and B were introduced to Eq. (5) for EPICS calculations. Direct phase concentration ratios were also used in Eq. (6) as yet another way to determine Henry’s law constants. Averages and standard deviations of Henry’s law constants determined for all of the techniques are presented in Tables 2 and 3. However, for 1,2-dichloroethane and toluene sufficient experimental results were available to apply a valid non-linear fit to the dPT /dx data for the coexistence equation. A comparison of the Henry’s law constant results (unitless) obtained for the binary systems of isopropyl alcohol, acetone, toluene, and 1,2-dichloroethane in water are presented in Figs. 5–8, respectively. For the binary system of isopropyl alcohol in water (group I), the average value of Henry’s law constants obtained via the EPICS method is about one order of magnitude higher than the literature values [11]. The EPICS results are quite reproducible and have a small standard deviation over the solute concentration range examined. On the other hand, the average values of Henry’s law constants derived from a linear assumption of dPT /dx behavior in the coexistence equation are about three orders of magnitude higher than the literature values. The results are scattered and have a high standard deviation over the solute mole fraction range. For this system, there is not sufficient data as a function of solute concentration to determine the Henry’s law constant from a non-linear dPT /dx assumption. For the direct phase concentration ratios, the average value of Henry’s law constant is in the same region as the literature value; however, the standard deviation is quite large. This results from analytical difficulties associated with absolute concentration measurements in the extremely dilute region. In fact, the standard deviation of the results increases greatly in the low mole fraction range. The somewhat better results of the EPICS method indicate that reliable Henry’s law constants results can be obtained in the dilute range, since concentration ratios, instead of absolute values, are required using this method. However, the measurements of this binary system are also ultimately limited by the detection capability of the gas chromatograph. Based on a comparison of the results obtained from these four methodologies, EPICS is the most suitable methodology for this binary system. Employing an extremely sensitive detector (e.g. ECD) in the gas chromatograph in order to obtain measurements in the extremely dilute region, results in more accurate Henry’s law constants. For the binary system of acetone in water (group II), the average value of the Henry’s law constant results from EPICS is approximately two times higher than the literature values, and has a small standard deviation from the average value. The average values of Henry’s law constant obtained from the linear dPT /dx assumption are about two orders of magnitude higher than the literature values and have large standard deviations over the solute mole fraction range. For the direct phase concentration ratios, the average value of Henry’s law constant are once again in the same region as the literature value; however, the standard deviation is also large. As before, the results obtained from the last two methodologies indicate a large standard deviation as the dilute region is approached due to analytical limitations. As with the measurements for isopropyl alcohol in water, there is not enough information to calculate the
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Henry’s law constant by extrapolation of a non-linear dPT /dx assumption for the equilibrium static cell data. The most suitable methodology for measuring the Henry’s law constants of acetone in water over the mole fraction range specified in this work is the EPICS method. For the binary system of 1,2-dichloroethane in water (group III), the Henry’s law constant results are determined using all four of the methodologies. For EPICS, the average value of the Henry’s law constant is approximately two times higher than the literature values. The results obtained by this methodology are very consistent and yield a small standard deviation over a wide solute concentration range, although like many of the other EPICS measurements, the results tend to be on the higher side of the literature values. For the linear dPT /dx fit to the equilibrium static cell data, the average values of Henry’s law constant determined are one to two orders of magnitude higher than the literature values. The results from both flasks A and B have large standard deviations, due to the considerable scattering of values in the low concentration region. The standard deviation decreases greatly as the solute concentration approaches the solubility limit. The results also seem to indicate a non-linear relationship between total pressure and solute concentration, which is more complex than previously assumed for the dilute region, may be appropriate. By applying a non-linear fit to the equilibrium static cell data, an average value of Henry’s law constant from both flasks may be determined from the limiting slope (dPT /dx). This methodology is determined based upon the limiting slope (dP/dx), which is obtained by fitting experimental data (total pressure) with a 2nd order polynomial equation, and the vapor pressure of the pure components (Eq. (3)). The average values of HC determined in this fashion are in the same range as the literature values, and have extremely small standard deviations over the solute mole fraction range. Because this methodology is based on a limiting slope obtained from numerous experimental points, a value for the limiting slope (dPT /dx) may be determined with greater statistical certainty. This is supported by the results, which yield regression correlation coefficient (R2 ) values of approximately 0.94 for both flasks. The Henry’s law constant determined via this method is in line with the literature values. For the direct phase concentration ratios, the average values of Henry’s law constant obtained from both flasks are in higher side of the literature value; however, the standard deviation is once again relatively large compared to the EPICS and a non-linear dPT /dx fit to the equilibrium static cell data. Thus, the recommended methodology for determining Henry’s law constant for this binary solution is application of a non-linear dPT /dx assumption to the equilibrium static cell data. Similar to the 1,2 dichloroethane–water system (group III), the Henry’s law constant results of toluene in water (group IV) are obtained using all four methodologies. For EPICS, the average value of the Henry’s law constant is in the same range, but on the higher side of the literature values. The Henry’s law constants obtained by this methodology also decrease slightly as the solubility limit is approached. For the linear dPT /dx analysis of the equilibrium static cell data, the Henry’s law constants determined are 3–10 times higher than the literature values. The results from both vessels have large standard deviations over the examined solute mole fraction range. For the direct phase concentration ratios, the average values of Henry’s law constant obtained from both flasks are on the higher side of the literature values; however, the standard deviation is once again relatively large compared to the EPICS and a non-linear dPT /dx fit to the equilibrium static cell data. For the non-linear assumption for dPT /dx behavior, the average values obtained from both vessels are slightly lower than the literature values, but have very small standard deviations over the solute mole fraction range. The correlation coefficient (R2 ) for the polynomial fit is approximately 0.85. Based on these observations, the most suitable methodologies to determine the Henry’s law constant for this binary mixture are the EPICS technique, and the non-linear dPT /dx assumption for the coexistence equation.
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5. Conclusions The conclusions of this study may be summarized as follows: 1. For chemicals with high solubility and low volatility (group I) and the chemicals with high solubility and high volatility (group II), the preferred methodologies for determining Henry’s law constant and the corresponding value for γ ∞ are the EPICS and non-linear coexistence equation, with both methods using extremely dilute liquid phase concentration data. 2. For chemicals with high volatility and partial miscibility (groups III and IV), the non-linear coexistence equation approach is the best methodology over the solute mole fraction range specified in this work. 3. The EPICS technique is a reasonable alternative methodology for measuring Henry’s law constant for these four binary systems. However, the Henry’s law constants determined this way are generally on the higher side of the literature range perhaps due to mass losses during the analytical procedure. 4. The mass balances obtained from the direct ratio measurements close to within 5% and the calculated Henry’s law constants are relatively close to literature values. However, the standard deviations of the results obtained from this methodology have large variation over mole fraction range specified in this work due to analytical limitations in the extremely dilute region. To support the conclusions and improve the efficiency of equilibrium static cell measurements, there are some future investigations required including: 1. Continued vapor–liquid equilibrium studies of additional representative binary systems of nonelectrolytes. 2. Investigation and refinement of the chemical and water degassing within this apparatus in order to minimize the effect of inerts on the total pressure measurement. List of symbols A the first coefficient of the polynomial equation B the second coefficient of the polynomial equation C the third coefficient or offset of the polynomial equation Ci concentration of closed systems HC Henry’s law constant (dimensionless) M total organic mass of closed systems P pressure (atm) PT total pressure (atm) R ideal gas constant T equilibrium temperature (K) V volume of closed systems Greek letters γ activity coefficient ρ liquid density Subscripts G gas phase i component indexes
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L T w 1 2 1,2
377
liquid phase constant temperature water solute component solvent component closed systems 1 and 2
Superscripts S saturate x → 0 infinite dilution ∞ infinite dilution Acknowledgements The authors wish to acknowledge continuing financial support from US Department Of Energy, Environmental Management Science Program (EMSP), and National Institute of Standards and Technology (NIST), Physical and Chemical Properties Division for collaboration. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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