Limiting Activity Coefficients of Nonelectrolytes in Aqueous Solutions

Chapter 16

Limiting Activity Coefficients of Nonelectrolytes in Aqueous Solutions

Downloaded by UNIV MASSACHUSETTS AMHERST on October 10, 2012 | http://pubs.acs.org Publication Date: October 27, 1992 | doi: 10.1021/bk-1992-0509.ch016

D. L. Bergmann and C. A. Eckert

1

School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0100

Infinite dilution activity coefficients of non-electrolytes in water are very useful for the economical design of both separation systems for specialty chemicals and for environmental control. However, the unique properties of water result in very large nonidealities and present special challenges in measurement, correlation, and prediction. A number of measurement techniques that exist specifically for determining limiting activity coefficients are reviewed. They provide a modest base of reasonably reliable data. Current estimation techniques are limited. Certainly more good data are needed for both design and correlation development. Almost every process in the chemical industry revolves around separations of materials, and the majority of the capital cost and as much as 90% of the energy costs go toward separations. Most separation processes are multistage processes and require an accurate representation of the phase behavior involved for both process feasibility and economics. Dilute Aqueous Solutions In today's market, with the rising costs of imported feed stocks, high purity, high value, low volume specialty chemicals such as pharmaceuticals are becoming increasingly important. Another area of burgeoning interest is in environmental separations. Both of these trends involve separations of dilute solutions. For specialty chemicals, high purity is often necessary, requiring the removal of dilute contaminants. In some cases, as in the biochemical industry, the dilute species may be the product of interest. Environmental separations such as treatment of hazardous wastes and pollution control often involve the concentration and removal of dilute contaminants. Thus we need a better understanding of the phase behavior of these dilute solutions to facilitate design of such separations. Aqueous solutions are of special interest for several reasons. Because of its unique properties and its great availability, water is the most commonly used solvent in industry. Water is a complex solvent which hydrogen bonds extensively; the actual 1Corresponding author

0097-6156/92/0509-0218S06.00/0 © 1992 American Chemical Society

In Environmental Remediation; Vandegrift, G., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

16.

BERGMANN & ECKERT

Limiting Activity Coefficients of Nonelectrolytes


structure of liquid water is not well understood (I). Due to its complexity, many aqueous solutions of non-electrolytes exhibit highly nonideal behavior, often resulting in regions of immiscibility. Water is also important in the new trends of the chemical industry. Most biochemical recovery processes are fed with a dilute stream of products which is almost exclusively water (2). Treatment of agricultural run-off waters and purification of drinking water are examples of environmental separations. One could hardly deal with the problem of cleaning up the environment without involving aqueous solutions. Thus, the ability to represent phase behavior of aqueous solutions is imperative. Limiting Activity Coefficients Activity coefficients are a means of representing the phase behavior of a system containing a liquid phase. For example, consider a liquid phase in equilibrium with a vapor phase. The equilibrium equation for component 1 in this system is given by:

RT

(D In this expression χ and y are the mole fractions of component 1 in the liquid and vapor phase respectively. Ρ is the system total pressure and P i is the vapor pressure of component 1. φ ι is the vapor phase fugacity coefficient representing the nonideality in the vapor phase. It can be calculated from an appropriate equation of state, and at low pressures has a value close to unity. The terms φι * , the fugacity coefficient at the saturation pressure, and the exponential term, known as the Poynting correction, are small corrections that are often negligible, v i is the molar volume of liquid 1, Ris the gas constant and Τ the temperature, γι is the activity coefficient of component 1 in the liquid phase, representing the nonideality of the liquid phase, and has a value of unity for pure liquid 1. In typical aqueous solutions of interest, the vapor phase nonidealities are negligible, but the liquid γ often deviates from unity by orders of magnitude. If one has a way of determining the value of this activity coefficient the phase equilibrium of the system can be correlated using equation 1. s a t

5

1

The activity coefficient of a component in a mixture is a function of the temperature and the concentration of that component in the mixture. When the concentration of the component approaches zero, its activity coefficient approaches the limiting activity coefficient of that component in the mixture, or the activity coefficient at infinite dilution, γ~. The limiting activity coefficient is useful for several reasons. It is a strictly dilute solution property and can be used directly in equation 1 to determine the equilibrium compositions of dilute mixtures. Thus, there is no reason to extrapolate equilibrium data at mid-range concentrations to infinite dilution, a process which may introduce enormous errors. Limiting activity coefficients can also be used to obtain parameters for excess Gibbs energy expressions and thus be used to predict phase behavior over the entire composition range. This technique has been shown to be quite accurate in prediction of vapor-liquid equilibrium of both binary and multicomponent mixtures (5). The limiting activity coefficient is also of great theoretical interest. At infinite dilution each solute molecule is surrounded by only solvent molecules, and the most nonideal conditions are represented. y\°° is in fact an excess property, so like-pair interactions are normalized out. Since only unlike-pair interactions are involved, any composition dependence of the solute on the properties of the mixture are removed, In Environmental Remediation; Vandegrift, G., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

2

22α

ENVIRONMENTAL REMEDIATION

thus allowing the unlike-pair interactions to be studied direcdy. An infinitely dilute solution is also much simpler to model when using a statistical mechanical approach. The investigation of aqueous systems is also of theoretical importance. Due to its hydrogen bonding characteristics, water often exhibits large nonideal behavior with other compounds. Understanding such extreme behavior will help in understanding less complex mixtures. Thus limiting activity coefficients are useful in understanding and representing dilute solution equilibrium behavior. Downloaded by UNIV MASSACHUSETTS AMHERST on October 10, 2012 | http://pubs.acs.org Publication Date: October 27, 1992 | doi: 10.1021/bk-1992-0509.ch016

Techniques For Measuring γ* For Aqueous Solutions Activity coefficients at infinite dilution can be measured by several techniques, each with its advantages and disadvantages. The most established techniques are dynamic or inverse gas chromatography and differential ebulliometry. Other methods include gas stripping, headspace chromatography, and liquid-liquid chromatography. Since many systems exhibit miscibility gaps in water solutions, solubility data have also been used to obtain y . These techniques have been used by several researchers to investigate a variety of binary water systems. The use of dynamic gas chromatography to make thermodynamic measurements was first proposed by Martin (4). The value of γ°° is found by measuring the retentiontimeof a solute injected into an inert carrier gas stream passing through a gas chromatographic column containing the solvent as the stationary phase. Details of the apparatus and procedure used in this technique are given by Pecsar and Martin (5) and Shaffer and Daubert (6). Equipment for such measurements can be found commercially, and the technique is well established. The method is quick and simple. The solute need not be of extreme purity and the detector need not be calibrated, since only retention time data are required. The technique is best suited for the study of highly volatile solutes in solvents of low volatility; it is inapplicable for systems where the solute has low relative volatility. The technique has been extended to systems with moderately volatile solvents by presaturating the carrier gas with the solvent (7), and correcting for solvent strippingfromthe column. The main source of error in this technique is adsorption of the solute at various interfaces within the column. The study of polar solutes in nonpolar solvents is hindered by adsorption on exposed solid support material (8-9). For solutes that are appreciably immiscible in a solvent, as in many aqueous systems, adsorption can occur on the vapor-liquid interface, and overloading the column where peak width, shape and position change may also become a problem. Several researchers have used gas chromatography to measure γ*» for solutes such as chlorohydrocarbons, oxygenated compounds, aromatics and hydrocarbons in water (5-7,10-16). Another technique for γ° is differential ebulliometry, first proposed by Gautreaux and Coates (17). In this method γ~ is found by measuring the change in the boiling point of a solvent with the addition of a dilute amount of solute under constant pressure. Descriptions of the apparatus and procedure involved are given by Scott (18) and Trampe and Eekert (19). The differential measurement negates the effects of pressure fluctuations that affect the temperature measurements and precludes the need for thermometer calibration. The technique has been tested extensively and found to be very accurate. Several solutes can be run simultaneously in the same solvent; however, it takes several hours to obtain a value of γ*. Since the experiment requires a heat sink, measurements are mostly made at higher than room temperatures. The technique is limited to measuring systems with relative volatilities between approximately 0.05 and 20. This upper volatility constraint has limited researchers to studying only alcohols and ketones in water. It has been more widely used to measure γ° for systems in which water is the dilute component (20-24).



16.

BERGMANN & ECKERT

Limiting Activity Coefficients ofNonelectrolytes

Headspace chromatography measures γ° by using gas chromatography as an analytical tool to measure the composition of a low-volume vapor phase in equilibrium with a dilute liquid solution. Great care is required in proper sampling and calibration of the detector. Thetechniquecan be used with nonvolatile or volatile solvents; the solute must be volatile enough to be measurable in the vapor phase. For solutes that are appreciably immiscible in the solvent, knowing the accurate composition of the liquid phase becomes the limitation. Once the detector has been calibrated accurately, the measurement is quick, and a series of solutes can be measured in the same solvent simultaneously. A detailed description of the apparatus and procedure involved is given by Hassam and Can* (25). This technique has only recently been explored as a way of measuring γ* for a variety of solutes in water (26-29). Gas stripping (50), sometimes called the dilutor method, involves bubbling an inert gas through a dilute solution to strip the solute. The limiting activity coefficient is related to the decay in concentration of the solute in the exit gas stream, normally measured by gas chromatography. Since a decay rate is measured and not a concentration, die gas chromatograph need not be calibrated, but a constant calibration factor must be assumed. A detailed description of the equilibrium cell and procedure used in this measurement is given by Richon et al (31) and Richon and Renon (52). The technique is applicable only for volatile solutes in low volatile solvents, and the solute must be volatile enough to be stripped in a reasonable amount oftime.When the relative volatility between the solute and solvent becomes very large, which is typical for systems with large γ* values, it becomes difficult to obtain equilibrium in the column. Limiting activity coefficients for some alcohols, ketones, acetates and benzene have been measured in water (33-37). Liquid-liquid chromatography (LLC) is a technique that can also be used to obtain ratios of γ~ values. The theory of LLC as a method to probe the thermodynamics of liquid solutions has been known for years (38). LLC takes advantage of the fact that a solute will distribute itself between mobile and stationary liquid phases in a column, leading to a specific retention time of the solute in the column. This retention time is related to the ratio of γ° of the solute in the mobile phase to γ°° of the solute in the stationary phase. Thus, to obtain γ~ of the solute in one phase requires a priori knowledge of y°° in the other phase. The mobile and stationary phases must be immiscible. If they are not, the ratio of y°° values measured is not that of γ°° in the pure solvents but the ratio of γ° values in the saturated mixtures which can be appreciably different. There are several organic liquids which are almost completely immiscible in water for which there are γ* data available through gas chromatography. The solute must be somewhat soluble in both liquid phases in order to be measurable (59). However, the main problem with this technique is avoiding the problems of adsorption on the liquid and solid interfaces in the column. It has been shown (Carr, P. W.,University of Minnesota, personal communication, 1990) that when the mobile phase has a large concentration of water, the history of the column greatly affects the retention of solutes in the column. Janini and Qaddora (39) and Djerki and Laub (40) have used this technique to measure γ° for various oxygenated hydrocarbon solutes in water. They used OV-1 polydimethylsiloxane (PDMS) and squalane as the stationary phase respectively. Comparison of data for similar solutes in water measured by these researchers yields a difference ranging from 20-100%. The oldesttechniquefor obtaining values of γ* for immiscible substances in water is actually an estimation relating γ°° of the component in water to the inverse of its solubility in water. For example, consider two liquid phases in equilibrium with


2

222

ENVIRONMENTAL REMEDIATION

each other. The equilibrium expression for component 1 in this system is given by: (2) In this expression x i and x\t are the compositions of component 1 in the two phases. For most binary aqueous systems, when x i , the mole fractions of component 1 in water, is small, x\f and therefore γ ^ are both close to one. This results in the approximation γι = l/χχ. This approximation is valid at the solubility concentration xi. The question remains, however, of whether the solution is in fact infinitely dilute at a solute concentration of x i . Only if this is true is it valid to assume that γι = γ°°· Literature values of solubility data for several compounds in water were used to obtain parameters for the UNIQUAC and NRTL excess Gibbs energy expressions, and y°° values for these compounds were calculated. The calculated values are compared with inverse solubility data in Table I. The inverse solubility predicts lower values of y°° in all cases. However, the difference becomes smaller as the solubility decreases, and for compounds with solubility less than 0.5% the difference is less than 10%. It has been shown that these excess Gibbs energy expressions, while very useful, are not the exact representation of the composition dependence of activity coefficient; all expressions have difficulty in representing liquid-liquid equilibria (4344). Thus, extrapolating these expressions to infinite dilution may be in error. It is therefore inconclusive as to the correctness of using the inverse solubility to calculate


9

Direct measurement of y°° would confirm whether or not the solution is infinitely dilute at saturation. Lobien and Prausnitz (23) have attempted to measure this effect in a few systems by comparing the solubility limit with measurements of γ* from differential ebulliometry. The systems they studied all had solubilities of a few percent, and for these systems they found significant deviations from γι~ = 1/xi. It would be useful to have measurements for more dilute solubilities, but in this case the limiting activity coefficient becomes very large, and ebulliometry is inapplicable for high relative volatilities. Perhaps such data could be taken by ebulliometry for systems where the solute is much less volatile than water, or by chromatographic methods. Limiting activity coefficient data for a few water solvent systems measured by various researches using the techniques discussed are shown in Table II. The γ~ Table I. Comparison of Inverse Solubility to γ~ Calculated by the UNIQUAC and NRTL Expressions with Parameters Found from Mutual Solubility Data at 25 °C

7.56< >

15

15

4.74 3.9104) 3.92^ >

5

9.5^

S*™ (24)

96

2.67™

24

29

47

7. (29)

7.00< >

29

29

26

3.76< > 3.69< >

0.62< >

HS

(35)

12.25^

. 9(36) 7.70(37) 7 6

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GS

59

1

41

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Continued on next page

(39)

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39

(40)

LLC

2L1

•f Measured By Various Techniques

(24)

70

0.89

Ebul.

Las*

6.51

GC

3

60

50

25

Temp°C

Table Π. γ°° For Solutes in Water Measured by Several Researchers Using Various Techniques



1-Butanol

2-Butanone

Isopropanol (continued)

Solute in Water

20

(24)

(21)

90

55.5

(23)

21

23

46.5 57.2< >

21

80

59.3

60

20

14.00< >

59.3< > 67.8< >

u

20

13.68< >

70

49.5< >

5

14

50.5< > 51.6" >

40

25

20

30

25

100

90

11.6^

U

85

(15)

3

13.62< >

278

GC

9

2

4 . (29)

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41

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35

45.1< >

37

29.5< >

40

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72

39

41.2^ 66< >

Table II. Continued. γ~ Measured By Various Techniques LLC GS HS Ebul.

80

76

Temp°C


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16.

Limiting Activity Coefficients ofNonelectmlytes

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Limiting Activity Coefficients of Nonelectrolytes in Aqueous Solutions

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