Ind. Eng. Chem. Res. 1996, 35, 1467-1471
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Ozone Solubility in Phosphate-Buffered Aqueous Solutions: Effect of Temperature, tert-Butyl Alcohol, and pH Roberto Andreozzi,*,† Vincenzo Caprio,‡ Ilio Ermellino,‡ Amedeo Insola,† and Vincenzo Tufano§ Istituto di Ricerche sulla Combustione, CNR, p.le V. Tecchio, 80125 Napoli, Italy, Dipartimento di Ingegneria Chimica, Universita` di Napoli Federico II, p.le V. Tecchio, 80125 Napoli, Italy, and Dipartimento di Ingegneria e Fisica dell’Ambiente, Universita` della Basilicata, v. della Tecnica 3, 85100 Potenza, Italy
Ozone solubilities in aqueous solutions containing phosphate buffers and tert-butyl alcohol have been measured in the ranges 0 < I < 0.48 M, 18 °C < T < 42 °C, and 2 < pH < 6. The experimental method adopted accounts for the reaction of ozone self-decomposition, by evaluating the relevant rate constant for each experiment. The results obtained at constant pH can be coherently explained in terms of a salting-out effect. In contrast, a rather complex behavior has been observed when changing the pH. This effect can be tentatively explained when accounting for the detailed composition of the solutions and for the activity coefficients of the ionic species. Introduction When studying the ozonolysis of organic compounds in aqueous solutions, the quantitative evaluation of the rate constants requires, inter alia, the knowledge of the ozone solubility in the liquid phase. Buffered solutions are employed in these studies, because the pH markedly affects the reaction mechanism. Moreover, when the research is focused on the study of the ionic mechanism of reaction, the competing radicalic mechanism must be inhibited by the addition of a radical scavenger. The usual choices are represented respectively by phosphoric acid and related salts (KH2PO4 and Na2HPO4) and by tert-butyl alcohol. The scarcity of ad hoc literature data and the complexity of these solutions recommend an experimental measurement of the ozone solubility. In fact, the extrapolation of data referring to “similar” solutions can give unreliable results because of several not wellknown effects (salting-out in mixed electrolyte solutions and effects of tert-butyl alcohol and of pH). The paper discusses the results of an experimental study on this subject. Experimental Apparatus and Procedure The reaction of ozone self-decomposition cannot be completely eliminated by the use of the radical scavenger (Roth and Sullivan, 1981; Kosak-Channing and Helz, 1983; Sotelo et al., 1989). When the experiments are carried out in a semibatch gas-liquid reactor operated at steady state, the rate of this reaction (which can be assumed to be first order with respect to ozone) equals the flux of ozone entering the liquid phase:
kDC ) kLa(C° - C)
(1)
Consequently, the liquid-phase ozone concentration at the gas-liquid interface, C°, which is in equilibrium with the gas concentration, is larger than the concentration in the liquid bulk, C, which is measured when sampling the liquid phase. It results in * Author to whom correspondence should be addressed. † Istituto di Ricerche sulla Combustione. ‡ Universita ` di Napoli Federico II. § Universita ` della Basilicata.
0888-5885/96/2635-1467$12.00/0
Figure 1. Scheme of the experimental apparatus: (1) oxygen cylinder; (2) flowmeter; (3) ozonizer; (4) UV spectrophotometer; (5) ozone decomposition unit; (6) stirred vessel; (7) thermostat, (8) thermometer; (9) stirrer; (10) optoelectronic probe; (11) gas sparger; (A,B) valves.
C° ) RC ) (1 + kD/kLa)C
(2)
Since the self-decomposition reaction is very sensitive even to very small amounts of impurities, it is advisable to measure kD for each single experiment. Moreover, the use of a well-designed mass exchange apparatus (i.e., of large values of kLa) gives values close to 1 for the correction factor R and produces more accurate results. The mechanically agitated gas-liquid reactor (V ) 1 L) sketched in Figure 1 (Andreozzi et al., 1991) and the experimental procedure used in this study fit the above requirements. An oxygen stream containing ozone (up to 4% by volume) is bubbled into the liquid solution (V ) 800 cm3). Once steady state is attained, as indicated by the constancy of the ozone concentration CG measured in the exit gaseous stream by a Varian DMS 90 spectrophotometer operated at λ ) 253 nm, solution samples (3 cm3) are taken in a quartz cell which is completely filled with liquid and rapidly closed. In these samples, the reaction of ozone self-decomposition produces a decrease of the ozone concentration, which is monitored by an HP diode array spectrophotometer (Model 8452A). For each sample, the C(t) data are used to evaluate the relevant value of the rate constant kD. Subsequently, the ozone concentration C © 1996 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 Table 1. Best Fit Parameters phosphate solutions linear model -∆H0, kcal mol-1 -∆S0, cal mol-1 K-1 h1, K M-1 k1, K M-2 σ%
phosphate-tert-butyl alcohol solutions: linear model
quadratic model
5.34 ( 0.06
5.33 ( 0.06
5.26 ( 0.05
35.08 ( 0.21
35.06 ( 0.21
34.93 ( 0.18
67.8 ( 1.371
2.2a
8.2b
79.0 ( -22.8 ( 16.1 1.363
a
46.3 ( 2.1c 1.480
M-1
Corresponding to h ) 0.231 ( 0.008 at T ) 20 °C and to h ) 0.216 ( 0.007 M-1 at T ) 40 °C. b Corresponding to h ) 0.269 -1 ( 0.028 M at T ) 20 °C and to h ) 0.252 ( 0.026 M-1 at T ) 40 °C. c Corresponding to h ) 0.158 ( 0.007 M-1 at T ) 20 °C and to h ) 0.148 ( 0.007 M-1 at T ) 40 °C.
1983). In fact, from the parameters of the model:
log(H) ) BI + AI/T
Figure 2. Ozone solubility in phosphate-tert-butyl alcohol solutions (pH ) 4.71 ( 0.33, 0 < I < 0.48 M): I ) (0) 0, (9) 0.06, (4) 0.12, (2) 0.24, (O) 0.35, (b) 0.48 M.
at the sampling time is computed by extrapolating the C(t) curve with the measured value of kD. This value also represents the ozone concentration C in the main reactor. Thus, it can be substituted into eq 2, together with the values of kD and of kLa (kLa ) 4.4 ( 0.4 min-1, as measured in a previous study (Tufano et al., 1994), to compute the ozone liquid-phase concentration C° at the gas-liquid interface and consequently the mole fraction x. The Henry constant H is obtained as the ratio of the ozone partial pressure in the bubbles, yP, to the mole fraction x. Three different sets of experimental data are discussed in the next sections. First, solutions containing KH2PO4 at different ionic strengths (0 < I < 0.48 M) are considered. The pH of these solutions is adjusted with small amounts of Na2HPO4 at a constant value (pH ) 4.75 ( 0.19). The composition of these solutions is computed from the equations of mass conservation, electric neutrality, and acid-base equilibrium. The values of pH result from these computations and are confirmed by experimental measurements performed with a 960 Orion pH meter. A second set of data is obtained by including in the solutions (800 cm3) constant amounts of tert-butyl alcohol (4 cm3), while keeping constant the pH (pH ) 4.71 ( 0.33) and the examined range of I. Finally, the effect of pH (adjusted in the range 2-6 with H3PO4 or Na2HPO4) is studied at two values of I (I ) 0.24 and 0.48 M). The temperature is controlled by a thermostat and measured with a standard accuracy of 0.1 °C. All the experiments have been performed in the range 18 °C < T < 42 °C. Correlation Models Figure 2 shows, as a function of reciprocal temperature, the experimental Henry constants measured in solutions containing KH2PO4 and tert-butyl alcohol at different ionic strengths. The linear behavior observed at constant ionic strength is also supported by theory (Kosak-Channing and Helz,
(3)
the (temperature-independent) entropy and enthalpy of solution can be derived respectively as ∆SI ) -2.303RBI and ∆HI ) 2.303RAI. At constant temperature, a marked decrease of ozone solubility is observed on increasing the ionic strength I. The H(I) relationship is usually described by the model:
log(H) ) log(H0) + hI + f(I)
(4)
where h is the salting-out coefficient and f(I) is a correction factor which accounts for the deviations from linearity usually observed at large ionic strengths (Bol’shov, 1991). As discussed in the following sections, several alternative models were tested, and the best results were obtained when setting f(I) ) 0 and considering the law of proportionality: h ) h1/T (Clever and Holland, 1968). Effect of Temperature and Ionic Strength The most significant results obtained with phosphate solutions (pH ) 4.75 ( 0.19 and 0 < I < 0.48 M) are reported in the first two columns of Table 1. The parameters A0 and B0 are expressed in terms of the corresponding enthalpies and entropies of solution in pure water (I ) 0). When the percent standard deviation on H, σ %, is considered as a quality yardstick, the linear model
A0 + h1I T
(5)
A0 + h1I + k1I2 T
(6)
log(H) ) B0 + and the quadratic model
log(H) ) B0 +
appear to be almost equivalent. Similar results were obtained with alternative models which assume h ) const or h ) h1/T + h2 and a corresponding expression for the function f(I). The larger value of h obtained with the quadratic model may be explained by the presence of the correction factor k1, which assumes negative values, as stated by theory (Bol’shov, 1991). The inspection of the isothermal data, plotted in Figure 3 as log(H) vs I, demonstrates that the correction
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1469
Figure 3. Ozone solubility in phosphate buffers (pH ) 4.75): T ) (9) 20, (2) 30, (b) 40 °C.
Figure 4. Ozone solubility in pure water at pH ) 4.75: (A) present work, pH ) 4.75; (B) data by Kosak-Channing and Helz (1983), pH ) 3.4 ( 0.1; (C) data by Roth and Sullivan (1981), pH ) 4.75.
for a nonlinear salting out, given by model (6), is in effect very small. The values of ∆H0 and ∆S0 (which refer to “pure” water at pH ) 4.75) can be compared with literature. Figure 4 shows this comparison in terms of log(H0) vs 1/T. The areas A and B respectively represent the values of log(H0) computed for the present work (linear model) and from literature data (Kosak-Channing and Helz, 1983) when accounting for the temperature range examined and for the standard deviation of the parameters A0 and B0. The difference between the results of the two models here discussed would be hardly appreciable with the adopted scale. The line C is obtained from the best fit values published by Roth and Sullivan (1981). In this case, the accuracies have not been reported by the authors. The three series of data fairly agree, both in terms of best fit values and of temperature dependence. The present results appear to be slightly more accurate. An alternative analysis of the experimental data makes use of a least-squares objective function defined on the liquid-phase molar fraction x. However, the more correct use of the effectively measured variable requires a nonlinear optimization procedure, since x ) yP × 10-log(H). The best fit values of the parameters are only slightly different from those obtained with the linear method, so that the difference in the values of log(H0) is not appreciable with the scale adopted in Figure 4. The following values of h can be reported: at T ) 20 °C, h ) 0.237 M-1 (linear model, to be compared with h
Figure 5. Ozone solubility at T ) 25 °C: (2) phosphate buffers; (9) phosphate-tert-butyl alcohol solutions.
) 0.231 M-1 from Table 1) and h ) 0.280 M-1 (quadratic model, to be compared with h ) 0.269 M-1 from Table 1). Taken as a whole, the above results show that the values computed for the salting out coefficient also depend on the (somewhat arbitrary) choice of the correlating model and of the optimality criterion. This residual uncertainity cannot be easily reduced, also because h is defined in terms of a derivative of the experimental data, so that small differences in the correlation of the data can result in nonnegligible differences in the best fit values of h. The values of h determined above cannot be directly compared with previous information, because of the scarcity of literature data for solutions containing both phosphate and ozone. Nevertheless, it can be observed that the present values are smaller than those reported for ozone in sodium sulfate solutions (Kosak-Channing and Helz, 1983) and that this difference does not contrast with literature (Charpentier, 1981; Pawlikowski and Prausnitz, 1983). Effect of tert-Butyl Alcohol A similar experimental campaign has been performed with solutions containing tert-butyl alcohol (Figure 2). In this case (Table 1, column 3), the best results were obtained with the linear model, because the correction for a nonlinear salting out effect produces an increase of σ %. However, the most interesting result is represented by the markedly smaller values obtained for the salting out coefficient. The existence of a measurable effect of tert-butyl alcohol on ozone solubility can be graphically appreciated from Figure 5, which shows, for the two data sets, the isothermal log(H) values at T ) 25 °C plotted against the ionic strength. It can be also reported that, when the different models are compared with all the experimental data (with and without alcohol), the standard deviation on H increases up to about 2%. The decrease of h observed when adding tert-butyl alcohol can be tentatively explained by an increase of the dielectric constant of the solutions produced by the slightly polar alcohol molecules. Effect of pH Contrasting information is reported in the literature. The experimental data of Roth and Sullivan (1981) and of Sotelo et al. (1989) show a nonzero effect of pH on
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996
Figure 6. Ozone solubility at T ) 25 °C in phosphate-tert-butyl alcohol solutions: I ) (9) 0.48 and (2) 0.24 M.
ozone solubility. Nevertheless, a law of general validity cannot be singled out from those data. In contrast, Kosak-Channing and Helz (1983) point out that the solubility of a weakly solvated nonhydrolyzing molecule such as ozone should be independent of pH at constant T and I. Thus, an attempt was made at evaluating the effect of pH in the solutions here considered. While keeping constant the ionic strength at two different values (I ) 0.24 and 0.48 M), the pH of phosphate-tert-butyl alcohol solutions was changed in the range 2-6 by the addition of suitable amounts of H3PO4 or Na2HPO4. Figure 6 shows the isothermal data at T ) 25 °C, which indicate a nonlinear dependence of log(H) on pH. This behavior is essentially produced by an increase of the solubility observed at pH > 5, which is also confirmed by few data measured at I < 0.24 M, not shown in the figure. When a linear model
A0 + h1I + β(pH - pH0) log(H) ) B0 + T
(7)
is used to correlate the data measured for pH < 5, very small values of β are obtained. In fact, when the reference value pH0 is set equal to the average pH of the previous experiments, carried out in phosphatetert-butyl alcohol solutions (i.e., pH0 ) 4.71), and the values of A0 (A0 ) -1150.6 K), B0 (B0 ) 7.6340), and h1 (h1 ) 46.38 K M-1) are fixed from those results (Table 1), 103β ) 10.3 ( 1.7 at I ) 0.24 M and 103β ) -8.14 ( 0.76 at I ) 0.48 M. These values of β are not significantly different from zero, because an alternative model based on the null hypothesis (β ) 0) fits those data well if the values of A0 and B0 are allowed to vary (which corresponds to considering the two sets of data independent). It should also be considered that the standard error on log(H), which amounts to about 0.01, is comparable with the overall variation observed for this variable in the pH range examined. On the contrary, the increase of solubility observed at the largest pH appears to be statistically significant. A few comments are tentatively proposed to interpret this result. It is well-known that, in a mixed electrolyte solution, the salting-out effect depends only as a first approximation on the ionic strength because the product hI results more correctly from the sum:
hI )
∑hjIj
(8)
where Ij is the fraction of the ionic strength attributable
to the jth electrolyte and hj is the relevant salting out coefficient (Charpentier, 1981). On the other hand, it should be considered that, in order to change the pH at constant I, it is necessary to change the composition of the solution. In the case under study, when the pH approaches the second dissociation constant of phosphoric acid (pKa ) 7.19) a nonnegligible fraction of H2PO4- dissociates to HPO42-. Thus, different solutions may be characterized by different effective values of h, and this effect can be mistaken for a pH effect or, at least, can bias the true effect of pH (if any). In the present case, attempts made at verifying this hypothesis have not been successful, since not all the values of hj are known (Onda et al., 1970; Charpentier, 1981). Moreover, the same mixture composition cannot be computed very accurately because of the nonideal behavior of the ions. In fact, the equations for the activity coefficients, such as the Davies formula here employed (Butler, 1964), are not completely reliable at large values of I. Conclusions Ozone solubilities in aqueous solutions containing phosphate buffers and tert-butyl alcohol have been measured at different temperatures and pH. The results obtained at constant pH have been coherently explained in terms of a salting out effect. In contrast, only a tentative hypothesis has been proposed in order to explain the rather complex behavior observed when changing the pH. Thus, at the moment, it is only possible to recommend the experimental measurement of the pH effect. Acknowledgment This work was supported by the Commission of the European Communities, EEC Contract EV5V CT93 0249. Nomenclature C° ) ozone concentration at gas-liquid interface, M C ) ozone concentration in the liquid bulk, M I ) 0.5∑CjZj2 ionic strength, M h ) salting out coefficient, M-1 H ) Henry’s constant, atm mol fraction-1 kD ) first-order rate constant of ozone self-decomposition, s-1 kLa ) volumetric gas-liquid coefficient of mass transfer, s-1 P ) pressure, atm T ) temperature, °C or K x ) liquid-phase mole fraction y ) gas-phase mole fraction ∆H0 ) enthalpy of solution in pure water, kcal mol-1 ∆S0 ) entropy of solution in pure water, cal mol-1 K-1 σ % ) percent standard deviation on H (referring to the average value of H)
Literature Cited Andreozzi, R.; Caprio, V.; D’amore, M. G.; Insola, A.; Tufano, V. Analysis of Complex Reaction Networks in Gas-Liquid Systems: the Ozonation of 2-Hydroxypyridine in Aqueous Solutions. Ind. Eng. Chem. Res. 1991, 30, 2098-2104. Bol’shov, L. A. Nature of the Deviations from Sechenov’s SaltingOut Law at High Concentrations of Electrolyte. Russ. J. Phys. Chem. 1991, 65, 1249-1252. Butler, J. N. Ionic Equilibrium; Addison-Wesley: New York, 1964.
Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1471 Charpentier, J. C. Mass-transfer Rates in Gas-Liquid Absorbers and Reactors; Advances in Chemical Engineering 11; Academic Press: New York, 1981. Clever, L.; Holland, C. J. Solubility of Argon Gas in Aqueous Alkali Halide Solutions. Temperature Coefficient of the Salting-out Parameter. J. Chem. Eng. Data 1968, 13, 411-414. Kosak-Channing, L. F.; Helz, G. R. Solubility of Ozone in Aqueous Solutions of 0-0.6 M Ionic Strength at 5-30 °C. Environ. Sci. Technol. 1983, 17, 145-149. Onda, K.; Sada, E.; Kobayashi, T.; Kito, S.; Ito, K. Salting-out Parameters of Gas Solubility in Aqueous Salt Solutions. J. Chem. Eng. Jpn. 1970, 3, 18-24. Pawlikowski, E. M.; Prausnitz, J. M. Estimation of Setchenow Constants for Nonpolar Gases in Common Salts at Moderate Temperatures. Ind. Eng. Chem. Fundam. 1983, 22, 86-90. Roth, J. A.; Sullivan, D. E. Solubility of Ozone in Water. Ind. Eng. Chem. Fundam. 1981, 20, 137-140.
Sotelo, J. L.; Beltra`n, F. J.; Benitez, F. J.; Beltra`n-Heredia, J. Henry’s Law Constant for the Ozone-Water System. Water Res. 1989, 23, 1239-1246. Tufano, V.; Andreozzi, R.; Caprio, V.; D’Amore, M. G.; Insola, A. Optimal Operating Conditions for Lab-Scale Ozonation Reactors. Ozone: Sci. Eng. 1994, 16, 181-195.
Received for review December 29, 1994 Revised manuscript received November 20, 1995 Accepted January 14, 1996X IE940778R
X Abstract published in Advance ACS Abstracts, March 1, 1996.
