Dilute Vapor Absorption: A New Accurate Technique for Measurement

Article pubs.acs.org/jced

Dilute Vapor Absorption: A New Accurate Technique for Measurement of the Limiting Activity Coefficient of Water in Hydrophobic Solvents of Lower Volatility Jan Haidl and Vladimír Dohnal* Department of Physical Chemistry, University of Chemistry and Technology, Prague 6, 166 28, Czech Republic ABSTRACT: An accurate experimental method for the determination of the limiting activity coefficient of water in hydrophobic solvents was described theoretically; the pertinent apparatus was built and its performance was duly verified. The method is based on continuously saturating the solvent by a gas stream of a constant and known humidity up to the attainment of the steady state and subsequent determination of the water content in the solvent by Karl Fischer titration. Using this new method, accurate values of the limiting activity coefficient of water were determined in eight selected solvents. The measurements were carried out at several temperatures and from these data the infinite dilution dissolution enthalpy and entropy of water in the solvents were evaluated. They both exhibit highly positive values reflecting the breakage of the hydrogen bonding network of water upon its dissolution in the solvents. Prediction of the water limiting activity coefficients was further attempted using the Modified UNIFAC method and found to fail dramatically, the calculated values being lower than the experimental ones by a factor ranging from 2 to 10. General lack of reliable limiting water activity coefficient data and their unreliable prediction indicate the significance of both the new method and the acquired data.

1. INTRODUCTION To cope with increasing demand for highly pure solvents in the chemical industry, intensification of separation and purification technologies is needed. Among severe impurities to be eliminated, the ubiquitous and often the major one is water. The drying of solvents is required for a number of applications, in particular when moisture-sensitive reagents are involved. The use of anhydrous solvents is vital to many syntheses, for instance the Grignard, Wurtz, and Witting reactions. To separate water from organic solvents in industry, distillation is usually the primary method of choice, possibly being followed by further more sophisticated and expensive separation techniques.1 Unfortunately, reliable design of the distillation processes to separate minute water contents is hindered by insufficient data on the water activity coefficient at high dilution in these media. Compared to relatively abundant data on limiting activity coefficients of (semi)hydrophobic volatile organic compounds in water, those on the limiting activity coefficient of water in these compounds are very fragmentary and less reliable. This unfavorable situation results partly from a weak portfolio of suitable experimental techniques to determine the infinite dilution activity coefficient of water, especially in hydrophobic solvents. For instance, gas−liquid chromatography retention measurements are limited only to truly nonvolatile solvents and can be easily distorted due to the susceptibility of water to adsorption. Another possible procedure for the purpose is to evaluate the infinite dilution activity coefficient from liquid− liquid solubility measurements; however, experience shows that © 2017 American Chemical Society

results obtained in this way are usually of lower accuracy, causes being, for example, improper equilibration producing dispersions and errors in sampling or sample handling. It is just the objective of this paper to present an accurate experimental technique of a novel principle that we have recently designed, developed, and successfully tested in our laboratory. The proposed technique, denoted by us as the dilute vapor absorption (DVA), stems from those of exponential saturator (EXPSAT) 2 and saturated vapor absorption (SVA)3 which we have developed previously. Nevertheless, the present method differs distinctly from both EXPSAT and SVA in various aspects including principle, instrumentation, and target applicability. The essence of the DVA method consists in absorbing water from a stream of an inert gas of constant and known humidity which is continuously passed through a given solvent until the attainment of the steady state and subsequent assay of the highly dilute solution thus prepared. Here we give the theoretical background of the DVA method, describe its implementation and validation and report quite a number of reliable data acquired by applying this technique. Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 31, 2017 Accepted: March 15, 2017 Published: March 28, 2017 2713

DOI: 10.1021/acs.jced.7b00114 J. Chem. Eng. Data 2017, 62, 2713−2720

Journal of Chemical & Engineering Data

Article

Figure 1. Principle of the DVA method. Material balance scheme.

2. THEORETICAL BACKGROUND To explain the principle of the DVA method and formulate the mathematical description of the involved saturation process, we will make use of the scheme depicted in Figure 1. Consider an apparatus composed of two units, namely the controlled evaporator mixer (CEM) and an equilibrium cell (EC). The first unit (CEM) provides a stream of an inert gas (3) with a constant content of solute (1) vapor. The second unit (EC) is a vessel containing the solvent (2) through which the gaseous stream, dispersed in small bubbles, is continuously passed, the solute from it being thus partially absorbed by the solvent until its saturation is achieved. Assume that the experimental temperature T and pressure p in the equilibrium cell are kept constant, the gas stream leaving EC and the EC content are equilibrated and the gas phase behaves ideally. Also, all quantities involved in the scheme in Figure 1 and treated in subsequent exposition are considered at the experimental T and p unless explicitly noted. The CEM unit is fed by the pure liquid solute at a constant mass flow rate ṁ 1 and the inert gas at a constant volume flow rate V̇ 03 (measured at Tst = 273.15 K and pst = 101.325 kPa), so that the solute is totally vaporized and diluted by the inert gas. The flow rate of the inert gas is chosen such that the solute partial pressure p1′ in the gas leaving the CEM unit is well below its saturation vapor pressure ps1 at experimental temperature T. Since the gas flow produced by CEM is excessive for being passed through EC, it is split, and its major portion is vented. Because of the content of the solute, the flow rate of the gas entering the equilibrium cell V̇ ′ is higher than the respective flow rate of the neat carrier gas V̇ 3, their relation being readily obtained from respective mass balance considerations and the equation of state V̇ ′ =

V3̇ 1 − p1′ /p

dn1′ =

p1′V̇ ′ RT

dt

(2)

Some of the solute carried by the gas stream dissolves in the solvent, forming a highly dilute solution of a continuously increasing concentration. The gas equilibrated with the highly dilute solution formed exits EC. The partial pressures of the solute p1″ and of the solvent p2″ in the outlet gas are given by the equilibrium conditions p1″ = γ1∞x1p1s ,

p2″ = p2s

(3)

where γ∞ 1 is the solute limiting activity coefficient, x1 is the solute mole fraction in the highly dilute solution (x1 ≤ 10−3) and ps2 is the pure solvent vapor pressure. As before, the flow rate of the outlet gas can be related to the pure inert gas flow rate through material balance and equation-of-state considerations V̇ ″ =

V3̇ 1 − p1″ /p − p2″ /p

(4)

and, in analogy with eq 2, the amount of the solute dn″1 leaving EC per element of time can be expressed as follows

dn1″ = −

p1″V̇ ″ RT

dt

(5)

The rate at which the solute is accumulated in the equilibrium cell, dn1/dt, is then obtained as the algebraic sum of dn′1/dt and dn″1 /dt dn1 dn ′ dn ″ = 1 + 1 dt dt dt ⎞ p1′ x1γ1∞p1s V3̇ ⎛ ⎜⎜ ⎟ = − s ∞ s RT ⎝ 1 − p1′ /p 1 − x1γ1 p1 /p − p2 /p ⎟⎠

(1)

The amount of the solute dn′1 brought into the equilibrium cell per element of time dt can be expressed from the equation of state

(6)

The rate at which the solvent is depleted from the equilibrium cell can be expressed in analogic manner 2714



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p2s V3̇ dn 2 =− dt RT (1 − x1γ1∞p1s /p − p2s /p)

region (x(∞) ≤ 10−3). It is important to notice that x(∞) takes 1 1 the same value regardless of the initial value of x1. Thus, in case the initial solute content in the solvent is higher than x(∞) 1 , the solute is desorbed until the steady state is attained. When x(∞) is experimentally determined, the value of the 1 infinite dilution activity coefficient can be obtained from the following equation

(7)

Because of high dilution x1 ≅ n1/n2, the rate at which the solute mole fraction changes with time is obtained by combining eqs 6 and 7 as follows dx1 (dn1/dt ) − x1(dn2 /dt ) = dt n2 ⎛ p1′ x1·(γ1∞p1s − p2s ) ⎞ V3̇ ⎜⎜ ⎟ = − n2RT ⎝ 1 − p1′ /p 1 − x1γ1∞p1s /p − p2s /p ⎟⎠

γ1∞ =

p1′(1 − p2s /p) + x1(∞)p2s (1 − p1′ /p) p1s x1(∞)

(9)

which results from eq 8 on imposing the steady state condition dx1/dt = 0. Equation 9 constitutes the essential work relation to determine the value of γ∞ 1 from the DVA experiment.

(8)

Equations 7 and 8 form a set of differential equations describing the dependence of solute mole fraction in the solvent on the duration of its saturation. Specifying experimental parameters and a value of γ∞ 1 , the respective x1(t) dependence can be obtained by solving numerically this set of differential equations. Figure 2 illustrates

3. EXPERIMENTAL SECTION 3.1. Materials. Organic compounds used in this work as solvents were obtained from Sigma-Aldrich or other well established providers at the highest purity available. The commercial samples were used for measurements without further purification. Their declared purity was verified by gas chromatography using a DB-WAX capillary column and the flame-ionization detection. The content of water in the examined solvents is unimportant, as it does not affect the results of the DVA measurements. Water used in this work as the solute was distilled and subsequently treated by a Milli-Q water purification system (Millipore, USA). The chemical samples used are specified in Table 1. 3.2. Apparatus and Procedure. The DVA apparatus was built in our laboratory using commercial devices produced by Bronkhorst HI-TECH Co., Swagelok stainless steel valves and fittings, and ad hoc homemade glassware components. The dilute vapor was prepared by a Bronkhorst controlled evaporator mixer (CEM) by means of injecting a stream of liquid water into a stream of nitrogen in a heated chamber. Nitrogen, as an inert carrier gas, stimulates the vaporization process, dilutes the vapor, and transports it into the equilibrium absorption cell. A schematic diagram of our experimental setup is shown in Figure 3. Degassed water is propelled from a glass container (1) into the CEM by means of compressed helium at a gauge pressure of 100 kPa, water flow being accurately measured and controlled by a Bronkhorst mass flow controller (MFC), model L01-RAA (2) in conjunction with a control valve (3). This MFC allows the water flow rate to be controlled in the range from (5 to 110) mg·h−1 with an accuracy of ±2% of full scale. Nitrogen fed at 400 kPa inlet gauge pressure is metered, and its flow rate is accurately controlled by a Bronkhorst mass flow

Figure 2. Solute mole fraction x1 as a function of saturation time t. Model calculations using the set of eqs 7 and 8 with the following parameters T = 298.15 K, p = 100 kPa, ps1 = 3143 kPa (water), ps2 = 5 3 −1 ̇ and for kPa, γ∞ 1 = 400, p′1 = 1000 Pa, n2 = 0.2 mol, V′ = 20 cm ·min three different initial values of x1.

such a simulation for the absorption of dilute water vapor in a hydrophobic solvent with arbitrarily chosen, but realistic values of experimental parameters. As seen the rate of solute absorption is highest at the beginning of the process; then solute absorption continuously slows down to approach exponentially a steady state value x(∞) in the Henry’s law 1 Table 1. Specification of the Chemicals Used in This Work

a

chemical name

CAS registry number

source

initial puritya

purification method

final purity indicationb

trichloroethylene toluene anisole (methoxybenzene) phenetole (ethoxybenzene) p-bromoanisole (4-bromo-1-methoxybenzene) α,α,α-trifluorotoluene chlorobenzene bromobenzene water

79-01-6 108-88-3 100-66-3 103-73-1 104-92-7 98-08-8 108-90-7 108-86-1 7732-18-5

Fluka Penta Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Fluka Sigma-Aldrich tap water

0.995 0.995 0.997 0.99 0.99 0.99 0.995 0.995

none none none none none none none none distillation, Milli-Q

0.995 0.996 0.999 0.990 0.995 0.998 0.999 0.999 184 kΩ·mc

Mass fraction as declared by the provider. bMass fraction as determined by gas chromatography in this work. cElectrical resistivity. 2715



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h−1) and the desired value of p′1 was set by adjusting the value of V̇ 03 only, in order to minimize the uncertainty in p′1 and in turn also in γ∞ 1 . The nitrogen flow rates applied in this work varied from (200 to 600) cm3·min−1 corresponding to the mole fractions of water in the gaseous mixture y1 from 0.0037 to 0.011. In each experiment, the nitrogen flow rate was set so that the resulting partial pressure of water p1′ was well below the water saturation vapor pressure p1s at the experimental temperature, the respective relative humidity ranging from 0.06 to 0.65. The time for which the process of saturation was maintained, which ranged from (2 to 14) h, was dependent upon temperature, the solvent examined, and its initial water content. To be on the safe side, the duration of the saturation was always longer than the time estimated by the process simulation as necessary to attain 0.999 x(∞) 1 . As soon as the process of saturation was terminated, a sample of the liquid from the equilibrium cell was taken with a gastight syringe. The water content was determined by coulometric Karl Fischer titration using Metrohm KF Coulometer 831 and Hydranal Coulomat AG reagent. The size of the sample for the titration was chosen so that the mass of water determined was in the range from (100 to 500) μg. For each DVA experiment, the analysis of the sample was replicated three times. The relative standard uncertainty of the determination of x(∞) is 1 estimated to be within 0.5%.

Figure 3. Schematic diagram of the DVA experimental setup: 1, container with degassed water; 2, water MFC; 3, water flow control valve; 4, nitrogen MFC; 5, nitrogen flow control valve; 6, CEM; 7, heated splitter; 8, three-way valve; 9, equilibrium cell; 10, microfilter and degassing valve; 11, split vent; 12, gas outlet.

4. APPLICABILITY AND VALIDATION OF THE METHOD An a priori applicability analysis was carried out to delineate possibilities for the application of the DVA method. The results primarily showed that the developed technique is suitable only for solvents in which water exhibits rather enhanced values of the limiting activity coefficient. This constraint is imposed by technical possibilities to prepare gaseous streams with sufficiently low partial pressure of water so that the steady state water content in the solvent falls into the effective Henry’s law region. The concrete lowest borderline γ∞ 1 value depends on various experimental parameters, in particular on temperature, the highest allowable values of V̇ 03 and x(∞) 1 , and the maximum tolerable uncertainty of the measured γ∞ 1 value. To give an idea, Figure 4 shows the estimated lowest borderline γ∞ 1

controller, model F-201CV (4) and an associated control valve (5). The control range of the nitrogen MFC is from (20 to 1000) cm3·min−1 and its accuracy is ±0.5% of reading ±0.1% of full scale. The streams of water and nitrogen are mixed in the heated chamber of the Bronkhorst CEM unit, model W-101A (6) at a precisely controlled temperature, forming a stream of a homogeneous gaseous mixture of a desired composition. To obtain an appropriate flow rate (15−20 cm3·min−1) for feeding the equilibrium cell, the major portion of the prepared stream is subsequently shunted by a heated splitter (7), the split ratio of which is set by needle valves. While the excess is vented to atmosphere, the minor stream flows through heated stainless steel tubing toward the equilibrium cell. The three-way valve (8) allows the stream to be redirected from the cell in order to check the flow rate and/or set the split ratio. The equilibrium cell (9) is an all-glass jacketed vessel of 20 cm3 capacity thermostated to ±0.02 K by water circulating bath Lauda RC6CP. The gaseous stream enters the cell via its bottom Teflon sealed port, being dispersed by a capillary into small bubbles in the magnetically stirred liquid content, and exits via the upper port of the cell, heated tubing, and the cold trap to the atmosphere. The partial pressure of water vapor in the prepared gaseous mixture p1′ is determined from the set flow rates of water and nitrogen as follows: p1′ = py1 = p

n1̇ ṁ 1/M1 =p 0 n1̇ + n2̇ ṁ 1/M1 + pst V3̇ /(RTst)

(10)

V̇ 03

where M1 stands for molar mass of water and stands for the volume flow rate of nitrogen as measured by the MFC at the standard temperature Tst = 273.15 K and pressure pst = 101.325 kPa. In principle, the desired value of p′1 can be set by adjusting either the value of ṁ 1 or the value of V̇ 03 or both. However, since the flow rate of nitrogen could be determined more accurately than that of water, ṁ 1 was set to its full scale value (110 mg·

Figure 4. Lowest limiting activity coefficient values determinable by the DVA technique as estimated by its a priori applicability analysis ∞ (∞) 3 −1 ̇0 ≤ 0.003 considering u(γ∞ 1 )/γ1 ≤ 0.03, V3 ≤ 600 cm ·min , and x1 (∞) (solid line), or x1 ≤ 0.001 (dashed line). 2716



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(303.15 K) = 11.73 kPa).6 The reproducibility, as inferred from measurements performed at various experimental parameters, appears to be also very good, being about 2%. Figure 5 further

values for realistic experimental parameters. The temperature range is delimited by the water circulating thermostatization used. Finally, suitable solvents for the DVA measurements are only those having a lower vapor pressure (ps2 < 10 kPa at experimental T); more volatile solvents can be prohibitively depleted from the cell. Note that moderate solvent depletion from the equilibrium cell however does not bring problems and can be considered even beneficial because it speeds up the steady state attainment. The performance of the DVA method was further duly tested through methodical experiments examining measurement repeatability and reproducibility, the fulfillment of Henry’s law, and the agreement of the values measured with literature data. Trichloroethylene and toluene were chosen as test solvents because IUPAC/NIST-recommended water solubility values in these solvents are available for comparison.4,5 Table 2 Table 2. Testing Performance of the DVA Technique: Henry’s Law Constant KH,a Infinite Dilution Activity Coefficient γ∞ 1 , Steady State Water Liquid Mole Fraction x(∞) and Outlet Gas Water Partial Pressure p1″(∞) for Water 1 (1) in Trichloroethylene (2) as Determined at Various Temperatures T, Atmospheric Pressures p, and Inlet Gas Water Partial Pressures p1′b p/kPa

p′1/Pa

98.74

559

98.93 98.93

745 745

99.67 99.70

751 751

98.54 99.47 98.99 99.22 99.22

447 451 746 748 748

98.74 98.41 98.41 99.65 99.66 98.03 99.26

373 557 557 751 751 1104 1118

98.69 99.67 99.68

559 1122 1122

103 · x(∞) 1 T= 0.524 T= 0.601 0.602 T= 0.521 0.522 T= 0.271 0.275 0.447 0.449 0.450 T= 0.202 0.314 0.314 0.420 0.424 0.591 0.604 T= 0.271 0.520 0.534

p″1 (∞)/Pa 278.15 K 543 283.15 K 714 714 288.15 K 710 710 293.15 K 416 421 695 697 697 298.15 K 340 508 508 685 686 1006 1020 303.15 K 496 996 997

KH/kPa

γ∞ 1

1037

1200

1189 1187

978 978

1364 1361

806 805

1539 1530 1556 1552 1549

660 656 667 666 664

1686 1616 1617 1632 1616 1702 1687

546 511 511 516 511 538 533

1832 1917 1866

432 452 440

Figure 5. Demonstration of Henry’s law compliance for water in trichloroethylene. The equilibrium steady state partial pressure p″1 (∞) of water plotted against the steady state mole fraction of water x(∞) 1 : ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K. Corresponding values of the Henry’s law constant (KH ± u(KH))/kPa obtained by fitting the data are 1549 ± 4; 1663 ± 15; 1884 ± 22, respectively.

demonstrates that the measurements comply entirely with Henry’s law. The comparison of γ∞ 1 values measured by the DVA method with those inferred from the IUPAC/NISTrecommended water solubility values is shown for trichloroethylene and toluene in Figures 6 and 7, respectively. Note that

Figure 6. Limiting activity coefficient of water γ∞ 1 in trichloroethylene as a function of temperature T plotted in van’t Hoff coordinates: ■ and solid line, experimental values from this work and their fit by eq 11; dashed line and dotted lines, IUPAC/NIST recommended solubility data4 along with their demarked standard uncertainty.

s b KH = p1″(∞)/x(∞) = γ∞ 1 1 p1. Standard uncertainties are as follows: u(p) (∞) = 0.005, u(p1′)/p1′ = u(p1″(∞))/ = 0.05 kPa, u(T) = 0.02 K, u(x(∞) 1 )/x1 ∞ p1″(∞) = 0.02, u(KH)/KH = u(γ∞ 1 )/γ1 = 0.03. a

the recommended data and the estimates of their standard uncertainty are based on the best fits of selected critically evaluated experimental solubility data taken from original literature. The reciprocal mole fraction solubility was taken here as the value of γ1∞; this approximation introduces no appreciable error, since mutual solubilities (water in solvent, solvent in water) are for both these solvents sufficiently small. As seen, the present measurements agree with the recommended data within their demarked standard uncertainty,

reports in detail all measurements we carried out for trichloroethylene at various experimental conditions and parameters. As seen from this table, the repeatability of DVA measurements (based on replicated measurements) is excellent, being within 1%. The only larger difference between replicates observed at T = 303.15 K resulted probably from difficulties associated with the higher volatility of trichloroethylene (ps2 2717



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Table 3. Infinite Dilution Activity Coefficients of Water (1) γ∞ 1 in Eight Solvents (2) as a Function of Temperature Determined in This Work by the DVA Techniquea T/K

γ∞ 1

trichloroethylene 278.15 1200 283.15 978 288.15 807 293.15 663 298.15 524 303.15 441 anisole 298.15 95.3 303.15 84.4 308.15 75.8 313.15 68.8 318.15 61.7 323.15 55.9 328.15 50.0 p-bromoanisole 298.15 119.2 303.15 105.9 308.15 93.7 313.15 83.3 318.15 74.1 323.15 65.5 chlorobenzene 298.15 376 303.15 318 308.15 271 313.15 235 318.15 202 323.15 177

Figure 7. Limiting activity coefficient of water γ∞ 1 in toluene as a function of temperature T plotted in van’t Hoff coordinates: ■ and solid line, experimental values from this work and their fit by eq 11; dashed line and dotted lines, IUPAC/NIST recommended solubility data5 along with their demarked standard uncertainty.

except perhaps for trichloroethylene at the lowest temperatures, where however their difference is only slightly larger. Compared to our DVA measurements, the standard uncertainty of which was estimated to u(lnγ∞ 1 ) = 0.03, the IUPAC/NISTrecommended data are considerably more uncertain providing thus a rather weak validation test. Lack of more accurate data for comparison makes however more stringent verification tests hardly feasible. On the other hand, such a situation gives support to our present effort to bring a better experimental method and in turn also better data.

γ∞ 1

T/K toluene 283.15 293.15 303.15 313.15 318.15 323.15

620 423 300 214 184 155 phenetole

298.15 303.15 308.15 313.15 318.15 323.15

110.0 97.0 87.3 77.7 69.9 62.7

α,α,α-trifluorotoluene 298.15 362 303.15 302 308.15 256 313.15 218 318.15 181 323.15 155 bromobenzene 298.15 367 303.15 311 308.15 264 313.15 226 318.15 189 323.15 164

a

At atmospheric pressure p = 100 kPa. Standard uncertainties are as ∞ follows: u(p) = 3 kPa, u(T) = 0.02 K, u(γ∞ 1 )/γ1 = 0.03.

5. RESULTS AND DISCUSSION Using the DVA technique, systematic determinations of the infinite dilution activity coefficient of water were performed in eight more or less hydrophobic solvents. Apart from trichloroethylene and toluene mentioned above, the measurements were carried out for anisole, phenetole, p-bromoanisole, α,α,αtrifluorotoluene, chlorobenzene, and bromobenzene at six equidistant temperatures from 298.15 to 323.15 K typically. The results for all eight solvents are summarized in Table 3. The infinite dilution activity coefficient was evaluated from the primary DVA measurements using eq 9, the saturation vapor pressure of water being calculated from the reference equation of Wagner and Pruss7 and those of solvents taken from CDATA database,6 or (for phenetole and α,α,α-trifluorotoluene) from Knovel Critical Tables.8 It should be noted that the accuracy of ps2 values adopted for the evaluation of γ∞ 1 is of no concern here, since the value of γ∞ 1 , as obtained from eq 9, is quite insensitive to the ps2 variation (δ (ps2) = 1 kPa results in ∞ only δ (γ∞ 1 )/γ1 = 0.01). Data obtained are displayed for the aromatic ethers in Figure 8 and for the halogenated aromatics in Figure 9. As seen from these figures and the previous ones for trichloroethylene (Figure 6) and toluene (Figure 7), the temperature dependences of the limiting activity coefficient of water obey for all studied solvents fully linear van’t Hoff plots, the respective equation B ln γ1∞ = A + (T /K) (11)

Figure 8. The limiting activity coefficient of water γ∞ 1 in aromatic ethers as a function of temperature T plotted in van’t Hoff coordinates: ■, anisole; ●, phenetole (this work); ○, phenetole;9 ▲, pbromoanisole. Solid lines are fits of data from this work by eq 11.

thus fitting the measured values well within the measurement reproducibility. The values of the adjustable parameters of eq 11 optimized by the least-squares method, along with the 2718



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Table 5. Recommended Values of Activity Coefficient ln γ∞ 1 , Partial Molar Excess Enthalpy H̅ E,∞ 1 , and Partial Molar Excess Entropy SE,∞ of Water (1) at Infinite Dilution in 1̅ Eight Solvents (2) Together with Respective Standard Uncertainties at T = 298.15 K solvent trichloroethylene toluene anisole phenetole p-bromoanisole α,α,α-trifluorotoluene chlorobenzene bromobenzene

standard deviation of fit s, are listed in Table 4. The very small values of s indicate high precision and reproducibility of the measurements. Table 4. Parameters A and B of Equation 11 Fitted to Experimental Data from This Work, Together with Respective Standard Deviation of Fit and Temperature Range of Underlying Data solvent

A

B

s

(Tmin − Tmax)/K

−5.1652 −4.6959 −2.3949 −2.5229 −2.9342 −5.0679 −3.8150 −4.5714

3412.3 3150.6 2072.2 2153.2 2302.2 3268.7 2903.8 3125.4

0.018 0.008 0.007 0.004 0.006 0.009 0.005 0.009

278−303 283−323 298−328 298−323 298−323 298−323 298−323 298−323

6.280 5.871 4.556 4.699 4.787 5.895 5.924 5.911

± ± ± ± ± ± ± ±

0.010 0.006 0.006 0.004 0.005 0.007 0.005 0.006

H1̅ E, ∞ ± s(H1̅ E, ∞) kJ·mol−1

28.4 26.2 17.2 17.9 19.1 27.2 24.1 26.0

± ± ± ± ± ± ± ±

0.6 0.2 0.2 0.1 0.2 0.4 0.2 0.3

S1̅ E, ∞ ± s(S1̅ E, ∞) J·K −1·mol−1

42.9 39.0 19.9 21.0 24.4 42.1 31.7 38.0

± ± ± ± ± ± ± ±

2.1 0.6 0.6 0.5 0.8 1.1 0.7 1.1

highly positive values reflecting thus mainly the breakage of the hydrogen bonding network of water upon its dissolution in the solvents. The values of H̅ E,∞ and S̅E,∞ we obtained are quite 1 1 comparable to the hydrogen bonding enthalpy HHB = 23.3 kJ· mol−1 and entropy SHB = 37 J·K−1·mol−1 of neat water as calculated from dielectric constant data.13 A closer look at the values of water dissolution thermodynamic quantities given in Table 5 reveals that for aromatic ethers (anisole, phenetole, pbromoanisole) these values are all appreciably lower than those for the other solvents studied. The drop observed for aromatic ethers stems obviously from water−ether hydrogen-bond complex formation in which the oxygen atom of the ether is the proton accepting site. Finally, we explored the possibility of predicting the limiting activity coefficients of water in the solvents studied by the Modified UNIFAC method14 as implemented in the program ASPEN Properties incorporated in the process simulating software package ASPEN Plus, V8.6. We found out that for three of the solvents the prediction is not feasible due to missing interaction parameters for some of pairs of the groups involved. Predictions obtained for the remaining solvents are compared with experimental data from this work in Figures 10 and 11. As seen the predictions are very poor, the predicted γ∞ 1 values being lower than the experimental ones by a factor ranging from 2 to 10.

Figure 9. Limiting activity coefficient of water γ∞ 1 in aromatic halogenates as a function of temperature T plotted in van’t Hoff coordinates: ■, α,α,α-trifluorotoluene; ●, chlorobenzene (this work); ○, and dashed line, chlorobenzene;10 ⊕, chlorobenzene;11 ▲, bromobenzene (this work); △ and dashed line, bromobenzene.10 Solid lines are fits of data by eq 11.

trichloroethylene toluene anisole phenetole p-bromoanisole α,α,α-trifluorotoluene chlorobenzene bromobenzene

∞ ln γ∞ 1 ± s(ln γ1 )

6. CONCLUSIONS A new technique called dilute vapor absorption (DVA), based on the principle of continuous solvent saturation by water vapor from a gaseous stream of controlled humidity, was developed for the measurement of limiting activity coefficients of water in organic solvents. By means of an a priori analysis, inherent applicability of the DVA method was delimited to solvents of largely hydrophobic nature and lower volatility. Correct performance, high reliability and precision of the method were duly verified experimentally. The DVA measurement is simple and quite robust; there is no need for using anhydrous solvents or for knowing their water content. The DVA technique provides a preferable alternative to conventional liquid−liquid batch contacting which is in routine use for the determination of water−organic mutual solubilities; DVA is much faster, yet completely avoids aggregate formation which is the major problem of the shake flask method. Considering these favorable features, we believe that the DVA technique is the right experimental tool for the determination of limiting activity coefficients of water in hydrophobic solvents. Both the

Figures 8 and 9 display for comparison also some literature data that are available just for phenetole,9 chlorobenzene,10,11 and bromobenzene.10 The involved literature data originate from either single vapor−liquid equilibrium studies9,11 or a regression of critically evaluated solubility values from multiple sources.10 Because of rather high water solubilities in anisole, these were deemed inappropriate for the determination of γ∞ 1 ; hence, existing solubility data12 were disregarded in the comparison. Mutual agreement of the present data with those from the literature appears to be quite reasonable: the differences in the ln γ∞ 1 values are within 0.2 (about 20% in γ∞ 1 ), which we might consider to be also the level of probable uncertainty of the literature data (no uncertainty estimates provided in the source literature). As inferred from the fits of our γ∞ 1 data by eq 11, the partial molar excess enthalpy H̅ E,∞ = RB and entropy SE,∞ = −RA of 1 1̅ water at infinite dilution in each solvent, as well as the value of ln γ1∞ (298.15 K) along with their respective standard uncertainties are given in Table 5. Both H̅ E,∞ and SE,∞ take 1 1̅ 2719



Article

ORCID

Vladimír Dohnal: 0000-0001-8934-4667 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. P. Vrbka for his assistance with the construction of the apparatus.

Figure 10. Prediction of the limiting activity coefficient of water γ∞ 1 in organic solvents by the Modified UNIFAC method (open symbols, dashed lines) in comparison with the experimental data from this work (closed symbols, solid lines): □ and ■, anisole; ○ and ●, phenetole; △ and ▲, toluene.

Figure 11. Prediction of the limiting activity coefficient of water γ∞ 1 in organic solvents by the Modified UNIFAC method (open symbols, dashed lines) in comparison with the experimental data from this work (closed symbols, solid lines): ○ and ●, chlorobenzene; △ and ▲, bromobenzene.

measurement principle of the DVA method and the respective apparatus are more versatile than the application presented in this work, and hence their adjustment can be envisaged for instance to measurements of finite concentration activity coefficients and/or to solutes other than water. Last, but not least the water limiting activity coefficient data acquired by the DVA technique represent a solid piece of reliable information which could be helpful for improving the performance of solvent drying technologies in general and relevant thermodynamic prediction methods in particular.

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REFERENCES

(1) Smallwood, I. Solvent Recovery Handbook; CRC Press: Boca Raton, 2002. (2) Dohnal, V.; Hovorka, Š. Exponential Saturator: A Novel GasLiquid Partitioning Technique for Measurement of Large Limiting Activity Coefficients. Ind. Eng. Chem. Res. 1999, 38, 2036−2043. (3) Dohányosová, P.; Fenclová, D.; Vrbka, P.; Dohnal, V. Measurement of Aqueous Solubility of Hydrophobic Volatile Organic Compounds by Solute Vapor Absorption Technique: Toluene, Ethylbenzene, Propylbenzene, and Butylbenzene at Temperatures from 273 to 328 K. J. Chem. Eng. Data 2001, 46, 1533−1539. (4) Horvath, A. L.; Getzen, F. W.; Maczynska, Z. IUPAC-NIST Solubility Data Series 67. Halogenated Ethanes and Ethenes with Water. J. Phys. Chem. Ref. Data 1999, 28, 395−627. (5) Maczynski, A.; Shaw, D. IUPAC-NIST Solubility Data Series 81. Hydrocarbons with Water and Seawater - Revised and Updated. Part 5. C7 Hydrocarbons with Water and Heavy Water. J. Phys. Chem. Ref. Data 2005, 34, 1399−1487. (6) CDATA: Database of Thermodynamic and Transport Properties for Chemistry and Engineering; Department of Physical Chemistry, Institute of Chemical Technology Prague; FIZ Chemie GmbH: Berlin, 1991. (7) Wagner, W.; Pruss, A. The IAPWS Formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (8) Calculated Properties of Common Organic Compounds. In Knovel Critical Tables [Online], 2nd ed.; Knovel Corporation: 2008; http:// app.knovel.com/hotlink/toc/id:kpKCTE000X/knovel-critical-tables/ knovel-critical-tables (accessed November 1, 2016). (9) Katal’nikov, S.; Nedzvetskii, V.; Voloshchuk, A. M. Solubility of water in phenetole and methods for drying phenetole. Zh. Prikl. Khim. 1969, 42, 1376−1382. (10) Horvath, A. L.; Getzen, F. W. Halogenated Benzenes, Toluenes and Phenols with Water; Pergamon Press: Oxford, 1985. (11) Cooling, M. R.; Khalfaoui, B.; Newsham, D. M. T. Phase Equilibria in Very Dilute Mixtures of Water and Unsaturated Chlorinated Hydrocarbons and of Water and Benzene. Fluid Phase Equilib. 1992, 81, 217−229. (12) Stephenson, R. M. Mutual Solubilities: Water-Ketones, WaterEthers, and Water-Gasoline-Alcohols. J. Chem. Eng. Data 1992, 37, 80−95. (13) Suresh, S. J.; Naik, V. M. Hydrogen bond thermodynamic properties of water from dielectric constant data. J. Chem. Phys. 2000, 113, 9727−9732. (14) Jakob, A.; Grensemann, H.; Lohmann, J.; Gmehling, J. Further Development of Modified UNIFAC (Dortmund): Revision and Extension 5. Ind. Eng. Chem. Res. 2006, 45, 7924−7933.

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Dilute Vapor Absorption: A New Accurate Technique for Measurement

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