dimensionless Henry's law coefficient, H vs. tempera- ture. They cover the temperature range from 0 to ca. 60°C. The straight line corresponds to the so-called ...
Ozone: Science and Engineering, 28: 67–75 Copyright # 2006 International Ozone Association ISSN: 0191-9512 print / 1547–6545 online DOI: 10.1080/01919510600558635
Ozone Solubility in Liquids Andrzej K. Bin´ Faculty of Chemical and Process Engineering, Warsaw University of Technology, Warszawa, Waryn´skiego, Poland
A comprehensive and critical survey of the available data on ozone solubility in different liquids—in water and aqueous solutions, as well as in organic solvents has been made. Apart of comparing the data published by the various authors after 1981 for water and aqueous solutions, special attention has been paid to the effects of pH and the composition of the liquid phase (salt effect). The published data on ozone solubility in organic liquids have been compiled and the listing of such data given by Battino (1981) has been supplemented by the more recent ones. Special interest has been given to perfluorinated organic solvents, which exhibit high solubility for both oxygen and ozone. More formal thermodynamic approach has also been attempted. Special attention has then been paid to the predictive methods developed for oxygen solubility in non-polar and polar solvents. Keywords
Ozone, Solubility, Thermodynamic Approach
INTRODUCTION The data on solubility of gases in liquids are of great theoretical and practical interest. In modeling processes that involve dissolution (absorption) of gases in liquids such data are of primary importance. In general, gas solubility in liquids represents a special case of the phase equilibria between gas and liquid phases where the gaseous component is either above its critical temperature or has a vapor pressure above 1.013 bar at the system temperature. The other component will exist as a liquid and is referred to as the solvent. Typically, the dissolved gas is much diluted in the liquid solution, so a number of
simplifications are possible when the formal thermodynamic treatment of the phase equilibrium is considered. Since Battino’s survey of the data on ozone solubility in liquids, not much more can be found in the available references. Most of them refer to water and aqueous solutions of inorganic compounds (salts and acids). Very little information can be found on ozone solubility in organic liquids (solvents). Typically, the data due to different authors are very scattered and differ considerably when compared each other. The reasons of such a situation can on one hand be attributed to ozone decomposition in the aqueous environment, and on the other—on the applied experimental techniques and the experimental data treatment. The aim of the present paper is to make a comprehensive and critical survey of the available data on ozone solubility in different liquids—in water and aqueous solutions, as well as in organic solvents. Apart of comparing the data published by the various authors after 1981 for water and aqueous solutions, special attention has been paid to the effects of pH and the composition of the liquid phase (salt effect). The data on ozone solubility in organic liquids compiled by Battino (1981) has been supplemented by the more recent ones. Special interest has been given to perfluorinated organic solvents, which exhibit high solubility for both oxygen and ozone. A more formal thermodynamic approach has also been attempted. Special attention has then been given to the predictive methods developed for oxygen solubility in non-polar and polar solvents.
THEORETICAL BACKGROUND Received 09/15/2005; Accepted 12/06/2005 This paper is presented in order to start a discussion on the very important, but very complicated, issue of ozone solubility. It is hoped this these discussions will lead to a special workshop on ozone solubility at the next Ozone World Congress. Address correspondence to Andrzej Bin, Faculty of Chemical and Process Engineering, Warsaw University of Technology, Warszawa, ul. Warynskiego 1, 00-645, Poland. E-mail: bina@ ichip.pw. edu.pl
Two phases of a system are in equilibrium when each component has the same fugacity in both phases. In the case of equilibrium between the gas and liquid phases at temperature T and pressure P, this equality expressed for each component, i, is as follows (cf. e.g., (2)):
Ozone Solubility in Liquids
G L f i;ðT;P;yÞ ¼ f i;ðT;P;xÞ
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½1 67
G f i;ðT;P;yÞ ¼ yi PLi;ðT;P;xÞ
½2
L f i;ðT;P;xÞ ¼ i xi Hei
½3
Pure compound at system temperature (T) and pressure (P) has been taken as the reference state of the solvent while an infinite dilution for the solute. In Equations [2] and [3] xi and yi are the mole fractions of the ith component in the liquid and gas phase, respectively, fiG is the fugacity coefficient, gi–activity coefficient of the solute in the liquid phase, and Hei – the Henry’s law coefficient (cf. Appendix). After combining Equations [1]–[3]) the phase equilibrium can be expressed as follows. yi PG i;ðT;P;xÞ ¼ i xi Hei
½4
Under normal conditions, i.e., at moderate pressures, the gas phase can be assumed as a perfect one, so the fugacity coefficient, fiG, of each component practically equals 1. The values of the solute activity coefficient, gi, depend on temperature and composition of the liquid phase. For ozone dissolving in pure water gO3 = 1. In case of aqueous solutions containing salts or non-ionic compounds it will differ from 1. Hence, for ozone–water (solvent) systems Equation [4] will take the form yO3 P ¼ pO3 ¼ O3 xO3 HeO3
½5
In Equation [5] pO3 is the ozone partial pressure. The product gO3HeO3 is called the apparent Henry’s law constant. The experimental data on gas solubilities in liquids are most often reported in form of the Ostwald coefficients (L), the Henry’s law constants (different forms) or solubilities (x), so, if necessary, it is important to know how to calculate such data from one form to another (cf. Appendix). Typically, the tabulated values of xsolute are listed for the partial pressure psolute = 101.325 kPa. A more formal thermodynamic approach in predicting ozone solubility in organic solvents is of great practical interest. For this purpose a number of methods that have been developed mainly for non-polar gases, in particular for oxygen, could eventually be applied. Among them the following predictive methods of gas solubility in liquids can be mentioned: Regular solution theory (using solubility parameter, d, concept), Soave–Redlich–Kwong (PSRK) model, Scaled Particle Theory (SPT), Statistical Associating Fluid Theory (SAFT) equation of state. 68
A. K. Bin´
In general, application of these methods for ozone – different organic liquids is limited by the lack of the relevant parameters describing ozone or some solvent properties. Also, the amount of the experimental data for ozone systems is too scarce for the more extensive comparative attempts. However, from analyses of the available experimental data some general conclusions on the behavior similarity between two systems: oxygen— organic liquids and ozone—organic liquids can be drawn. DISCUSSION Ozone Solubility in Water The experimental data for ozone solubility in ‘‘pure’’ water are shown in graphical form in Figure 1 as a dimensionless Henry’s law coefficient, H vs. temperature. They cover the temperature range from 0 to ca. 60°C. The straight line corresponds to the so-called IOA standard data of ozone solubility in water and can be approximated by the following expressions (t in °C and T in K): H ¼ a exp ðbtÞ
½6
log H ¼ A þ B=T
½7
or
with a = 1.599 ± 0.0164; b = 0.0473 ± 0.0004 (R2 = 0.99988) and standard error of estimation 0.0405 (Eq. (6)) or A = 6.5987 ± 0.0591; B = –1752 ± 17.1 (R2 = 0.99971) (Equation [7]) within the temperature range from 0 to 35°C. Equation. [6] is slightly better in terms of statistics when analysis of the residues is performed. With a few exceptions the experimental data of different authors deviate from the IOA standard line max. by –40% to +25%.
100 90 80 70 60 50
Mailfert (1894) Rawson (1953) Matrozov (1975) Caprio (1982) Kosack-Channing (1983) Khadraoui (1988) Morooka (1986) Watanabe (1991) Miyahara (1994) Rischbieter (2000) Wu & Masten (2000) De Smedt (2000) IOA standard
40 30 20
H [-]
In a general case of T and P, the fugacities of the i-th component in the gaseous and the liquid phases can be given by:
109 8 7 6 5 4 3 2
1 0
10
20
30
40
50
60
t [oC]
FIGURE 1. Dimensionless Henry’s law constant vs. temperature for ‘‘pure’’ water.
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The reasons of these discrepancies are connected with the experimental techniques applied in determinations of the phase equilibrium during ozone absorption in the water. Probably the experimental procedure used by Caprio et al. (1982) seems to be the most reliable. In this procedure the batch system was led into a steady state identified with the phase (absorption) equilibrium with respect to the gas inlet concentration. Simple ozone mass balance allowed the Henry’s law constant to be calculated from the known volumes of both phases in the absorption vessel. The authors verified the accuracy of their method by changing the volume of water filling the absorber, which should provide a straight line of the overall ozone content and the water volume. Qiu (1999) has adopted a similar procedure. It is also evident from Figure 1 that extrapolation of the straight line beyond 50°C is doubtful. This means that there is lack of the experimental data on ozone solubility in this region.
substances can be found in the references (e.g., Charpentier (1986); Schumpe (1993); Weisenberger and Schumpe (1996); Rischbieter et al. (2000)). The more recent paper by Rischbieter et al. (2000) specifically refers to ozone and aqueous solutions of a number of inorganic salts. These authors proposed estimating the solubility of ozone in water and aqueous salt solutions from Equation (8) and suggested to calculate the Sechenov’s constant, KS, from the ions contributions given by Weisenberger and Schumpe (1996), while for gas-specific (ozone) contribution they gave a simple temperature dependence: hG ¼ hG;0 þ hT ðT 298:15Þ
with hG,0 = 0.00396 m3/kmol, and hT = 0.00179 m3/ (kmol K) valid for the temperature range from 278 to 298 K. So, the estimating expressions of the Rischbieter et al. (2000) method are as follows: X KS ¼ ðhi þ hG Þ xi ½10
i
Ozone Solubility in Aqueous Systems The available (published) reference data for aqueous systems concern limited number of solutions of inorganic acids and salts (cf. listings due to Battino (1981); Aleksandrov et al., (1983); Rieschbiter et al. (2000)). In a number of cases the researchers used buffered solutions containing relatively small amounts of ionic substances. Although at the first sight the ionic strength could be small and practically constant, the reported ozone solubilities vary quite significantly. This refers in particular to the data of Li (1977), Roth and Sullivan (1981), Gurol and Singer (1982), Ouederni et al. (1987), Sotelo et al. (1989), Qiu (1999) and de Smedt (2000). It is generally known that dissolved substances (ionic or non-ionic) affect gas solubility in a liquid (strictly speaking a solution of these substances) and commonly referred to as a salting-out effect. In practice an empirical approach has been suggested and this may be represented by the Sechenov formula describing reduction in gas solubility in electrolyte solutions of low concentration. Using the Bunsen’s coefficient, a, the Sechenov-type formula can be written as X Hel 0 log hi I i ½8 ¼ log ¼ Ks Cs ¼ H0 el n where a0 means the Bunsen’s coefficient for pure solvent, and el —refers to the electrolyte solution, Ks—a constant specific for the system under consideration, Cs—molar salt concentration, Ii and hi represent the ionic strength of the individual ion i, while hi is the ion-specific saltingout constant which is a function of gas type and still slightly dependent on temperature. A number of the Sechenov constants for different gas/ salt/temperature combinations, also including organic
½9
log
H ¼ KS CS H0
½11
where xi denotes the index of ion i in the formula of the salt (e.g., for Na2SO4 x(Na+) = 2 and x(SO42–) = 1), CS is the molar salt concentration, H and H0 are the Henry’s constants for the salt solution and for water, respectively. Tromans (2000) suggested a new method of modeling oxygen solubility in water and electrolyte solutions. The method is based on a generalization that involves a coefficient accounting for the presence of inorganic solutes (f). Tromans (2000) approximated this coefficient by an expression ¼ ½l ¼ k Cyl h
½12
In Equation [12] C1 is concentration of an inorganic solute (mol/kg H2O), k, y and h are the coefficients that are dependent on the solute but are independent of the temperature. The author listed the values of these coefficients for a number of inorganic substances (salts). Sotelo et al. (1989) determined the Henry’s law constant for a number of the ozone–water systems. They presented the obtained results typically in form of the following equation. A H / exp expðBIÞ ½OH C ½13 T
where the values of constants A, B, C are specific for a given salt and are valid within a range of temperature, ionic strength (I) and pH. With such a presentation of the experimental data one can only compare the results of predictions based on Equation [13] with those following from using one of the above mentioned methods. Such a comparison for the effect of temperature on the Sechenov
Ozone Solubility in Liquids
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69
1.7 Na2SO4 (S) 1.6
Na2SO4 (R)
1.5
NaCl (S) NaCl (R) Na3PO4 (S) Na3PO4 (R)
1.4
1.3
1.2
1.1
1.0 0.0
0.1
0.4
0.5
18 MgSO4 NaCl KCl Na2SO4 Ca(NO3)2 perfect agreement
16
HO3, calc
Na3PO4
0.3
FIGURE 3. Comparison of the ratio HA/HA0 calculated from the Rischbieter et al. (2000) method and that resulting from the Sotelo et al. (1989) equations.
1.2 Na2HPO4
0.2
I [M]
14
NaH2PO4
t = 20oC pH = 7
H/H0
constant, KS, calculated from the Rischbieter et al. (2000) method and that resulting from the expressions given by Sotelo et al. (1989) for two salts is shown in Figure 2. From this figure one can conclude that the expression suggested by Sotelo et al. (1989) for the mixed salts solution (sodium phosphate and sodium carbonate) agree well with the predictions based on the Rischbieter et al. (2000) method. In a similar way the effect of ionic strength (or salt molar concentration) on the ratio of the Henry’s law constant can be compared for both methods (cf. Figure 3). The latter comparison reveals greater differences amounting in the worst case (Na3PO4) up to 30%. The ion parameters (contributions) suggested by the various authors for oxygen solubility in such solutions (Barrett, 1966; Charpentier, 1986; Schumpe, 1993; Tromans, 2000; Weisenberger and Schumpe, 1996) have been checked for prediction of ozone solubility in aqueous ionic solutions. The contribution of Rischbieter et al. (2000) that concerns ozone and some aqueous salt solutions has also been more extensively tested. The results of this assessment are presented in Figures 4–7 in form of the parity graphs where experimentally determined dimensionless Henry’s law constants for ozone and different aqueous solutions are compared with those estimated using different authors’ ion contributions or methods. In general, good or reasonable agreement between the experimental data and predicted values can be observed. It can also be concluded that ion contributions suggested for oxygen are applicable in ozone systems.
+20%
12 -20%
10
Na2CO3
1.0
Na2SO4
8
Ks(T)/Ks(298)
NaCl Sotelo (NaH2PO4) Sotelo (NaH2PO4+Na2CO3)
6
0.8
4
2 2 0.6
4
6
8
10
12
14
16
18
HO3, exper
FIGURE 4. Parity plot of the dimensionless Henry’s law constant for the data of Rischbieter et al. (2000). 0.4 270
275
280
285
290
295
300
305
T [K]
FIGURE 2. Comparison of the ratio KS(T)/KS(298) calculated from the Rischbieter et al. (2000) method and that resulting from the Sotelo et al. (1989) equations.
70
A. K. Bin´
An apparent effect of pH on ozone solubility has been examined by many authors (Andreozzi et al., 1996; Caprio et al., 1982; De Smedt, 2000; Kosack-Channing et al., 1983; Miyahara et al., 1994; Quderni et al., 1987; Qiu, 1999) and Figure 8 provides an illustration of the April 2006
10
20 Rothmund (1912), H2SO4 Brinner & Perrottet (1939), NaCl Kilpatrick (1956), HClO4 Tupalo et al. (1980), H2SO4 Tarunina et al. (1983), H2SO4 perfect agreement
8
HO3, calc
HO3, calc
15
Andreozzi et al. (1996) Gurol & Singer (1982) perfect agreement
+20%
10
-30%
+10% 6
-10%
4
5
2
0 0
5
10
15
2
20
4
6
HO3, exper
8
10
HO3, exper
FIGURE 5. Parity plot of the dimensionless Henry’s law constant estimated using the Rischbieter et al. (2000) procedure for different authors’ data.
FIGURE 7. Parity plot of the dimensionless Henry’s law constant calculated using Rischbieter et al. (2000) method for KH2PO4 and Na2SO4 (data of Andreozzi et al. (1996), and Gurol and Singer (1982)).
5.0
4.5
0.5
Barrett (1966) Schumpe (1978) Charpantier (1986) Tromans (2000) Weisenberger (1996) O3 perfect agreement
+10% Matrozov (1975)
o
t = 25 C
Caprio (1982) Kosack-Channing (1983) Ouderni (1987) Miyahara (1994) Andreozzi (1996)
0.4
4.0
Andreozzi (1996)
3.5
SR = 1/H
HO3, calc
Qiu (1999) IOA (1995)
-20%
3.0
0.3
0.2
2.5
2.0 2.0
Qiu (1999) Roth & Sullivan (1981) o de Smedt (2000), 26 C
2.5
3.0
3.5
4.0
4.5
5.0
0.1
HO3, exper
0
FIGURE 6. Parity plot of the dimensionless Henry’s law constant calculated using different authors’ methods for Na2SO4 (data of Kosack-Channing and Helz (1983)).
published data in form of a dependence of the solubility ratio (SR = 1/H) vs. pH. Two curves depicted in this figure correspond to the correlations suggested by Roth and Sullivan (1981) and by Qiu (1999). Li (1977) proposed an average value of 0.21 within pH range of 2 to 7 at 25°C for his data. The scatter of the
2
4
6
8
10
pH FIGURE 8. Apparent effect of pH on the solubility ratio SR of ozone in water.
experimental data on ozone solubility in buffered solutions is due to possible effects of liquid constituents or impurities such as salinity, ionic strength, and proper accounting for ozone decomposition in the liquid phase. In many cases ozone solubility has been estimated from measurements of the ozone concentration in the liquid
Ozone Solubility in Liquids
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71
phase when reaching a steady-state value in batch absorption experiments under fixed conditions. The asymptotic value of the ozone concentration, Css, can then be used to calculate an apparent Henry’s law constant (Happ). If ozone decomposition in the liquid phase can be approximated by the first order reaction with respect to the dissolved ozone concentration the true value of that constant (H) is related to the apparent (e.g., (Bin, 2004; De Smedt, 2000; Gurol and Singer, 1982; Roth and Sullivan, 1981)) as follows: 1 kd 1 ¼ 1 þ ½14 Happ kL a H where kd is the first-order reaction constant of ozone decomposition in the liquid phase, and kLa is the volumetric ozone transfer into the liquid phase. It is evident that Happ becomes practically equal to H when kd
