137
Ind. Eng. Chem. Fundam. 1981, 20, 137-140 Lefebvre du Prey, E. SOC. Pet. Eng. J . 1973, 13, 39. Lehner, F. K. I d . Eng. Chem. Fundsm. 1979, 18, 41. Leverett, M. C. Trans. AIME1939, 132, 149. Morrow, N. R.; Songkran, B., presentation to the 3rd Internatlonal Conference on Surface and Colloid Science, Stockholm, Sweden, Aug 20-25. 1979. Melrose, J. C.; Brander, C. F. J . Can. Pet. Techno/. 1974, 13(4), 54. Mungan, N. J . Pet. Techno/. 1965, 17, 1449. Muskat, M. ”Physlcal Principles of Oil Productlon”, McGraw-Hill: New York, 1949. Naar, J.; Wygal. R. J.; Henderson, J. H. SOC. Pet. Eng. J . 1962, 2 , 13. Weh, A. S. Trans. AXME 1956, 216, 346. Rlchardson, J. G.; KeNer, J. K.; Hafford, J. A.; Osuba, J. Trans. AIME1952, 195, 187.
R u m , R. R., Jr. In “Flow Through Porous Medla”, Dewiest, R. J. M., Ed.; Academlc Press: New York, 1989. Scheidegger, A. E. “The Physlcs of Flow Through Porous Medla”, 3rd ed.; University of Toronto Press, 1974. Slattery, J. C. A I C M J. 1969, 15, 888. Tek, M. R. Trans. A I M l 9 5 7 , 210, 378. Weinbrandt, R. M.; Ramey, H. J.; Cassa, F. J. Soc. Pet. €ng. J . 1975, 15, 376. Whltaker, S. Ind. Eng. Chem. 1969, 67(12), 14. Wlssler, E. H. Ind. Eng. Chem. Fundam. 1971, 10, 411
Received for review September 15, 1978 Accepted December 30,1980
Solubility of Ozone in Water John A. Roth’ and Danlel E. Sulllvan Vanderbitt University, Nashville, Tennessee 37235
A methodology is given for determinlng the solubility of ozone, a reactlng, gaseous solute, in water. The resultlng calculated solubilii data are presented In the form of Henry’s law constants. The experimental measurements needed are the ozone uptake data, steady-state ozone concentration for the experimental system, and the ozone decomposition data. The Henry’s law constants are found to be a function of temperature and pH over the conditions investigated. The literature ozone solubility data are reviewed critically. These data are analyzed in light of the results of this study.
Introduction Ozone in aqueous solution has great environmental importance both for water treatment and waste water treatment. Ozone is a strong oxidizer and has been used since the turn of the century as a disinfectant in Europe. It can also oxidize a wide range of organic and inorganic pollutants, making ozonation a viable alternative technically for meeting stringent environmental limitations. Ozone is typically generated by passing a dry air or an oxygen stream between electrodes across which an electrical discharge is generated. A wide variety of gas-liquid contactors are used to adsorb the ozone into solution. Since the ozone spontaneously undergoes decomposition upon absorption, saturation is not achieved when the rate of mass transfer of the gaseous ozone is less than the rate of decomposition, and a steady state concentration is reached. To determine the solubility characteristics of ozone in a typical laboratory ozonation system, the following phenomena are significant: the mass transfer of the gaseous ozone into the aqueous phase and the rate of autodecomposition of the ozone absorbed into solution. Because the ozone is unstable in the liquid phase, the observable steady-state aqueous ozone concentration is not the same as the solubility concentration in the regions where mass transfer is limiting and will be less than the saturation (equilibrium) concentration. While the autodecomposition of ozone has been extensively studied (Peleg, 1976; Sullivan, 1979),the proposed mechanisms for ozone decomposition are not in agreement. The decomposition species resulting from ozone decomposition are not clearly established. Henry’s law for a nondissociating solute in a dilute, isothermal solution states that the fugacity of the solute is proportional to the mole fraction at equilibrium, or
fj
= KXj
where f( = fugacity of the solute, j , in the gas phase; K = proportionality constant for Henry’s law, atm/mole fraction; and, x j = mole fraction of the solute, j , in the liquid phase. At conditions where the gas is an ideal solution Pj = H x ~
(2)
where Pj = partial pressure of the solute, j , in the gas phase and H = Henry’s law constant, atm/mole fraction. Most of the existing gas-liquid solubility data reported in the literature were determined from pure solute-solvent experiments. Deviations from Henry’s law which occur must be accounted for when a species dissociates or reacts in solution. To obtain the Henry’s law constants for gas-liquid systems in which reactions are OcCuTTing, the true solubility concentration is calculated from a material balance about a completely mixed gas-liquid contactor system. The Henry’s law constant can then be calculated from the true solubility concentration and the gaseous solute partial pressure. The steady-state concentration is reached by contacting the liquid with the gas for a period of time until the solute concentrations in the gas and the liquid are constant. Additional problems are often encountered in obtaining the correct Henry’s law constant for gas-liquid simultaneous mass transfer-reaction systems. One of these is caused by the effect of impurities on equilibrium. Correlations relating Henry’s law constant and ionic strength have been developed (Dankwerta, 1970). Secondly, when a species dissociates, the equilibrium of the dissociation reaction in the liquid is often used to determine the solute concentration. The true Henry’s law constants are then determined using the calculated concentration.
0196-4313/81/1020-0137$01.25/0 0 198 1 American Chemical Society
138
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
Model for Determining the T r u e Solubility Concentration Consider the case where a gas species is absorbed into a liquid and simultaneously undergoes reaction. For a completely mixed semi-batch reactor, a mass balance about the reactor on the reacting species yields dC kLa(Ci- C)V = rV V(3) dt where C = concentration of the solute in the bulk liquid, g-mol L-l; Ci = concentration of the solute at the interface, g-mol L-’; kL = liquid film mass transfer coefficient, cm-2 min-’; a = interfacial area, cm2;r = rate of reaction, g-mol L-’ min-’; t = time, min; and V = volume, L. When the solute concentration reaches steady state, the accumulation term, dC/dt, goes to zero. Assuming nth order kinetics for the reaction, eq 3 becomes
+
(4) (Ci - CsJ = kcss” where k = specific rate constant, min-’ (g-mol L-l)’-n and C , = steady state concentration of the solute, g-mol L-I. Subtracting (4) from (3) Ul
It has been shown (Sullivan, 1979; Sullivan and Roth, 1980) that the autodecomposition of ozone in aqueous solutions can be satisfactorily represented by frrst-order kinetics with respect to ozone and that the specific rate constant, k, is a function of temperature and the hydroxide ion concentration. The intrinsic reaction rate expression for ozone, then, is -r = kC (6) where k, the intrinsic kinetic rate constant, is a function of [OH-] and temperature. When kinetics for ozone decomposition are applied, eq 5 becomes
_ dC - (kLa + k)(C,, - C)
(7) dt By monitoring the concentration of ozone as a function of time upon continuously contacting the air-ozone mixture into the aqueous, completely mixed, isothermal, constant pH sytem, the unsteady-state rate of change of ozone concentration, dC/dt, can be determined by numerical differentiation. Equation 7, then, provides a linear relationship through the origin which can be used to evaluate the slope, (kLa k). This slope is evaluated by linear regression. The specific rate constant, k, is determined from the decomposition rate data and the liquid film mass transfer coefficient, kLa,is then calculated from the value of the slope. Since the system is liquid-film controlled, the interfacial concentration, Ci, is assumed equal to the equilibrium concentration, C*. Substituting into eq 4 for first-order kinetics and rearranging
+
c,, =
(A+* =
qc*
where Da = Damkohler number for first order reaction, k / k L a and q = interphase effectiveness factor for a firstorder reaction. Rewriting eq 3 using the applicable assumptions for ozone autodecomposition in an aqueous system dC = kLa(C*) - ( ~ L u+ k)C (9) dt This equation can be integrated, assuming the ozone concentration is zero a t time equal to zero, to yield
C = Cs,[l - exp(-kLa/q)t] (10) Existing Ozone-Water Solubility Data Previous investigators who have experimentally determined the solubility of ozone in aqueous solution have bubbled gaseous ozone into an aqueous solution until it reached a steady state concentration. The Bunsen absorption coefficient,P, or the solubility ratio, S, is typically reported for their experimental conditions. It is important to note that only a few of these investigations recognized the impact of the simultaneous reaction occurring during the adsorption process, thereby inherently assuming incorrectly that c* = c,, (11) Comparing this with eq 8 the interphase effectiveness factor, q, which accounts for the simultaneous reaction, is omitted. Their reported “solubility constants” are based on the measured steady-state concentration. This is valid only when Da N 0, which occurs when the specific rate constant, k, is small compared to kLa. This condition is approximately true for the ozone-water system at low temperatures and pH’s. Table I summarizes the reported ozone-aqueous system solubilities reported in the literature. One of the early investigators reporting solubilities was Mailfert (1894). These results, converted to Henry’s law constants, are reported in the “International Critical Tables” (1928) and are commonly used today over a wide range of conditions. It is inferred that these solubilities are valid for “pure water”. In his original work, Mailfert also reported the solubilities obtained in weak sulfuric acid solutions and noted that the results were consistent with those for pure water at lower temperature. At increased temperatures (greater than 20 “C),he noted a substantial deviation from the values for pure water. Kawamura (1932) measured solubilities in pure water and in sulfuric acid solutions. His “observed” solubilities showed a definite decrease as the acid normality was increased. Briner and Perrottet (1939) determined the Bunsen absorption coefficient in water at 3.5 and 19.8 “C. They also reported values in a 3.5% salt solution and found a significantly lower solubility which was attributed to the increased ionic strength. Hoather (1948) noted that the saturation of water with ozone was not possible because of the simultaneous decomposition. He did not suggest a method to correct for this effect and reported his experimental steady-state concentrations. Stumm (1958) reported solubilitiesto be independent of pH up to 8.5 for solutions with an ionic strength of 0.05. Li (1977) clearly recognized the problem of obtaining the ozone solubility. He estimated the solubility at low p H s by extrapolation of experimental determinations at decreasing liquid volumes but did not fully account for the interaction between the mass transfer and reaction. He performed his experiments at 25 “C. Li did, however, report sufficient experimental data to allow calculations of the solubilities using eq 7. Experimental Section Ozone was bubbled through a ceramic fritted diffuser into an isothermal compeltely mixed, semi-batch vessel. Ozone demand free water was prepared by first taking deionized tap water and then distilling from an alkaline potassium permanganate solution. The distillate center fraction was then ozonated and subsequently boiled to remove the ozone. The pH of the ozone demand free water was maintained during an experimental run by a phosphate buffer, using either sulfuric acid or sodium hydroxide to obtain the desired pH. The total dissolved solids in the liquid resulting from the buffer are estimated to be between 0.3 and 0.5% for all experimental runs. The tem-
Ind. Eng. Chem. Fundam., Vol. 20, No.
Table I. Ozone-Water Solubilities in the Literature (Should Not Be Used to Represent Equilibrium) H, atm/ kopP, mole temp, investigator C P S fraction investigator “C P Schone (1873) Mailfert (1894)
Mailfert (1894)’ all values in weak H,SO, soln. Luther (1905) Rothmund (1912) Fischer and Tropsch (1917) Kawamura (1932)
Kawamura (1932)‘ 7.57 N H,SO, 2.02 N H,SO, 1.01 N H,SO, 0.18 N H,SO, 0.11 N H,SO,
18.2 0.366 0.0 6.0 11.8 13.0 15.0 19.0 27.0 32.0 40.0 47.0 55.0 60.0 30.0 33.0 42.7 49.0 57.0 0.0 20.0 0.0 18.0
3 400 0.641 1940 0.562 2 260 0.500 2 600 0.482 2 710 0.456 2 880 3 500 0.381 5 070 0.270 7 130 0.195 0.112 12 750 0.077 18 960 0.031 48 260 m 0.000 5 760 0.240 6 230 0.224 8 280 0.174 9 410 0.156 0.096 15680 0.44 2 830 0.23 5 810 0.487 2 560 2 890 0.460
5.0 10.0 20.0 30.0 40.0 50.0 60.0
0.44 0.38 0.29 0.20 0.15 0.11 0.08
Briner and Perrottet (1939) Briner and Perrottet.’ 3 5 g/L NaCl Meddows-Taylor (1948) Hoather (1948) Rawson (1953)
Stumm (1958)
Kirk-0thmer (1967)
2 880 3 400 4 610 6 910 9 520 13 390 18 980
H , atm/ mole fraction
S
0.480 0.323 0.24 0.17 0.49 0.34 0.173 0.39 0.29 0.21 0.17 0.14 0.12 0.07 0.45 0.41 0.37 0.34 0.30 0.49 0.44 0.375 0.285 0.2 0.145 0.105
2 590 3 860 5 190 7 320 2 570 3 930 7 590 3 300 4 520 6 370 8 010 9 890 11 710 20 330 2 820 3 150 3 550 3 930 4 530 2 530 2 820 3 330 4 370 6 210 8 550 11 770 7 840 7 600 9 000 9 400
25.0 25.0 25.0 25.0
20.0 20.0 20.0 20.0 20.0
‘Not shown in Figure 2.
0.18 7 420 5 810 0.23 5 350 0.25 4 770 0.28 4 770 0.28 Recalculated from Li’s experimental data (true solubilities).
perature range investigated varied from 3.5 to 60 “C,and pH was varied from 0.65 to 10.2. The ozone uptake was measured as a function of time and continued until steady state was reached and maintained. The gas-ozone stream was then stopped. The ozone composition was again measured at different times. Assuming minimal loss from the quiesent surface, the autodecomposition rate was then determined. The first-order autodecomposition specific rate constants were correlated as a function of pH and temperature (Sullivan, 1979; Sullivan and Roth, 1980). The equilibrium concentration, C*, was then calculated using eq 8. Ozone analyses were performed using a modified iodometric technique (Sullivan, 1979). Discussion of Results In this investigation both the steady-state concentration, C,,, for this experimental system and the calculated equilibrium concentration, C*, were converted to Henry’s law constants. The first Henry’s law constant, calculated from the steady-state concentration, is the apparent value. The second Henry’s law constant, based on the equilibrium concentration, is the true Henry’s law constant. Both sets of these constants were found to be satisfactorily modeled as a function of temperature and pH over the range of conditions investigated. The true Henry’s law constant, applicable to the interfacial equilibrium and fitted by multilinear regression, is
H
3.5 19.8 3.5 19.8 3.0 20.0 15.0 9.6 14.5 20.3 25.5 30.6 35.1 39.0 5.0 10.0 15.0 20.0 25.0 0.0 5.0 10.0 20.0 30.0 40.0 50.0
2, 1981 13g
= 3.84 X 107[OH-]0.035 exp(-2428/T)
(12)
where [OH-] = hydroxide concentration, g-mol L-l, and T = temperature, K. This correlation is shown in Figure
t 0
0
I
I
2
4
I
60.C I
I
6 8 p H OF SOLVENT
IO
I
12
Figure 1. Equiibrium Henry’s law constants for ozone-water. 1 with the experimental data. The index of determination is 0.84 and the standard error of estimate is 0.20. These results should not be extrapolated beyond the temperature and pH of the experimental work, as there is evidence of a shift in the Ozone decomposition mechanism (Hoigne and Bader, 1976; Sullivan, 1979) at higher pH and temperature values. To compare with the values reported in the literature, the experimentallydetermined steady-state concentrations of this investigation were also converted to apparent Henry’s law constants. These constants were correlated by a multilinear regression using an equation of the form of eq 12. These results, which neglect q, were determined only for comparison with the literature “steady-state” results. Regression lines for pH 1 and pH 7 are shown in Figure 2 along with the literature solubility data. Observe that the literature solubility constants fall almost entirely between the pH 1 and 7 regression lines from this study.
140
Ind. Eng. Chem. Fundam., Vol. 20, No. 2, 1981
c
c
TEMPERATURE, (‘C1
Figure 2. Apparent Henry’s law constants (for comparison with literature values; apparent ITS should not be used to represent equilibrium).
: d o g%
IO
20
30
43
TEMPERATURE *SOLVENT
50
Eo
P CI
Figure 3. Equilibrium Henry’s law constants compared to Mailfert’s data (from “International Critical Tables”, 1928).
In unbuffered aqueous systems, the pH will drop considerably during ozonation. Prior investigators, most of whom do not report having buffered their systems or following their pH during the ozonation process, mainly operated with varying pH during an experimental run in a region below pH 7. The steady-state concentrations are specific for each experimental system as they are a function of kLa. These two factors can account for much of the scatter among various investigators. Ozone specific chemical analyses have evolved with considerable disagreement (Sullivan, 1979), and the discrepancies between different investigators studying this analytical chemistry problem add to the level of uncertainty in the literature work reported on the aqueous ozone system. In some cases, the analyses of past investigators have measured total oxidants, which would result in higher determined ozone concentrations and lower Henry’s law constants. It is concluded that the difficulties in analyses, the effect of mass transfer in different experimental systems, and the influence of pH expalin the wide variation of results reported in the literature. Table I gives the apparent ozone solubilities reported in the literature including those for “pure water” shown in Figure 2. Figure 3 shows “International Critical Table” (1928) values obtained from Mailfert’s (1894) “pure water” data compared to the true Henry’s law constant correlation of this investigation. The Henry’s law constants predicted by eq 12 are, again, only recommended for use within the temperatures and pH range from which they were obtained. General Discussion While the ozone-water reaction system was used as an example for which the equilibrium concentration, C*, of
a solute cannot be achieved in solution, the applicability of this experimental methodology and analysis is generally applicable to reacting systems in which the decomposition or reaction rates can be quantified. Since ozone autodecomposition exhibits linear kinetics, the analysis is greatly simplified, but more general equations for other reaction kintics can be developed following a similar methodology. Interestingly, for the first-order irreversible kinetics, the interphase effectiveness factor, q, can be used directly to relate the observable steady-state concentration to the solubility, C*. The experimental approach which is presented provides a technique by which the equilibrium solute concentration can be established in the presence of impurities and simultaneous reactions. Nomenclature a = interfacial area, cm2 C = concentration of the solute, g-mol L-’ Ci = concentration of the solute at the interface, g-mol L-’ Co = initial solute concentration, g-mol C, = steady-state solute concentration, g-mol L-’ C* = hypothetical equilibrium solute concentration, g-mol L-’ D a = Damkohler number (first-order kinetics), k / k l a f = fugacity, atm H = Henry’s law constant, atm/mole fraction k = specific rate constant, min-’ (g-mol/L)(’-”) kL = liquid film coefficient, cm-2min-’ n = order of reaction for power law rate expression [OH-] = hydroxide ion concentration, g-mol L-’ P, = partial pressure of solute, j , in gas phase, atm r = rate of reaction, g-mol L-’ min-’ S = Ostwalds’ coefficient of solubility, volume of absorbed gas/volume of absorbing liquid t = time, min T = temperature, K V = volume, L x = mole fraction /3 = Bunsen coefficient, volume of absorbed gas at standard temperature and pressure/volume of absorbing liquid x = generalized proportionality constant for Henry’s law, atm/mole fraction q = interphase effectiveness factor (first-order kinetics) Literature Cited Briner, E.; Perrottet Helv. Chem. Acta. 1939, 22, 397-404. Dankwetts, P. V. ”Gas-LiquM Reactions”, McQaw Hill: New York, 1970; pp 17-20.
Fischer, F.; Tropsch, H. Ber. Cbern. Ges. 1917, 50, 765-676. Hoather, J. J. Inst. Water Eng. 1948, 4 , 358-368. Hoigne, J.; Bader, N. Water Res. 1978, 70. 377-386. “International Critical Tables”, 1st Ed., Vol. III; McGraw-Hill: New York, 1928; p 257.
Kawamura, F. J. Chern. Soc. Jpn. PureChem. Secf; 1932, 53, 783-787. Kirk-Othmer, “Encyclopediaof Chemlcal Technology , 2nd Ed. Vol. 14, WC ley: New York, 1467; p 412. Li, K. Y. Ph.D. Dlssertatlon, Mtsslsslppi State Unhrerslty, 1977. Lutherleipzig, R. 2. EkWochern. 1905, 7 7 , 832-835. Maiifert, M. Compt. Rend. 1894, 779, 951-953. Meddows-Taylor J. Inst. Water Eng. 1947, 2 , 187-201. Peieg. M. Water Res. 1978, 70, 361-366. Rawson, A. E. Water WaferEng. 1953, 57, 102-111. Rothmund, V. “Nernsts’Festschrift”, 1912, p 391-4. Sullivan, D. E. W.D. Dissertation, Vanderbltl Unlverstty, Nashville, Tenn., Dec 1979.
Sullivan, D. E.; Roth, J. A. AICM Symp. Ser. 1980. 76, 142-49. Schone, E. Ber. Chern. Ges. 1873, 6 , 1224-1229. Stumm, W. J. Boston. Soc. Civil Eng. 1958, 45. 68-79.
Received for review May 1, 1980 Accepted January 26,1981 The work upon which this publication is based was supported in part by funds provided by the Office of Water Research and Technology (A-058-Ten), US.Department of the Interior.
