Henry's law constant for the ozone-water system

War. Res. Vol. 23, No. 10, pp. 1239-1246, 1989 Printed in Great Britain. All rights reserved

0043-1354/89 $3.00+0.00 Copyright © 1989 Pergamon Press pie

HENRY'S LAW CONSTANT FOR THE OZONE-WATER SYSTEM J. L. SOTELO1, F. J. BELTRA.N2., F. J. BENITEZ2 a n d J. BELTRAN-HEREDIA2 IDepartamento de Ingenieria Quimica, Facultad de Quimicas, Universidad Complutense, 28040 Madrid and 2Departamento de Ingenieria Quimica y Energetica, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz, Spain

(First received July 1988; accepted in revised form March 1989) Abstract--Ozone absorption in water in the presence of several salts has been studied in an agitated tank. The influence of the operating variables: ionic strength, temperature, pH, gas flow rate, ozone partial pressure and agitation speed, on the dissolved ozone concentration has been investigated. From an ozone balance in the reactor, the liquid phase volumetric mass transfer coefficient and the equilibrium ozone concentration were calculated. Finally, equations for the Henry's law constant as a function of temperature, pH and ionic strength for every salt have been deduced. These equations reproduce the experimental results with deviations less than _+15%. The equations allow us to know the ozone solubility for a given operating condition.

Key words--ozone, ozone solubility, absorption, ionic strength, water ozonation

NOMENCLATURE [A] = concentration of dissolved gas (M) a = specific interracial area (m -I ) DA = diffusivity of gas (m 2 s - i ) E = enhancement factor H = Henry's law constant (kPa mol frac- ~) H A = heat of absorption (J tool- i ) Ha = number of Hatta defined by equation (1) I = ionic strength (M) k = mth order gas decomposition reaction rate constant (1m- i mop - " s-t ) k c = liquid side mass transfer coefficient (m s- ~) m = order of reaction with respect to the gas N = agitation speed (rpm) N ^ = gas absorption rate (tool s -~ m -2) [03] -- ozone concentration (M) [O~'] = ozone solubility (M) Po3 = ozone partial pressure (kPa) Q = gas flow rate (1 h - t ) R = gas constant (J mol- i K - t ) r = ozone decomposition rate (tool 1-~ s- ~) IS] = hydroxyl radical scavenger concentration (M) T = temperature (K) t = t i m e (s).

INTRODUCTION O z o n a t i o n o f organic p o l l u t a n t s dissolved in water is being used as a n alternative way to chlorination. This is preferred because o f the m a n y d r a w b a c k s t h a t c h l o r i n a t i o n presents, mainly due to the incompatibility with m e m b r a n e processes (Applegate, 1984) a n d the f o r m a t i o n of o r g a n o c h l o r i n a t e d c o m p o u n d s ( U r a n o et al., 1983). T h e global rate in such a process depends o n the diffusion o f ozone in water, the ozone d e c o m p o s i t i o n a n d the chemical reaction with the dissolved pollu*Author to whom correspondence should be addressed.

tant. So, it is necessary to k n o w every one o f these stages individually a n d the influence of operating variables to evaluate this rate. Several papers have been published in the literature regarding the ozone d e c o m p o s i t i o n in water (Hewes a n d Davidson, 1971; Sullivan a n d Roth, 1980; T e r a m o t o et al., 1981; G u r o l a n d Singer, 1982; Sotelo et al., 1987, etc.). Likewise, ozone a b s o r p t i o n in water has been treated in previous works as depicted in Table 1. However, there are i m p o r t a n t disagreements a m o n g them. The m a i n sources of these discrepancies are: some a u t h o r s neither consider the reaction d e c o m p o sition n o r the ionic strength influence; others carried o u t their experiments in unbuffered systems or studied the process in a n a r r o w range o f variables. The work o f R o t h a n d Sullivan (1981) seems to be the m o s t enlightening, b u t few expriments were carried out a n d m o s t o f them being d o n e at low p H levels a n d temperatures. So, it has been considered necessary to study the a b s o r p t i o n o f ozone in water in the presence o f several salts, in order to deduce a n expression for the ozone solubility involving the influence o f the operating variables: temperature, p H a n d ionic strength. Table 1. Works on ozone absorption in water from literature Temperature Investigators Year pH (°C) Kawamura 1932 -0-60 Briner and Perrottet 1939 -3.5-19.8 Rawson 1953 -9.6-39 Stumm 1958 -5-25 Mailfert 1970 -0--60 Li 1977 2.2-7.1 25 Nebel 1981 -0-50 Roth and Sullivan 1981 0.65-10.2 3.5--60 Caprio et aL 1982 -0.5-41 Morris 1988 7 0--60

1239

1240

J.L. SOTELOet al. GAS PHASE

LIQUID PHASE

Interface

~

,,

~

[A] t

I

..~. film_,...~ Liquid thickness

bulk - - - ~

Absorption

(O) Physical GAS PHASE LIQUID PHASE Interface

GAS PHASE LIQUID PHASE Interface

I

i

I':'".':.:': :':: : : : : : : . . : . . ' . : Reaction Zone ~: ..": ..'., .. "-'. :"

\,-.-.....,'...........

/

x~::.-.ii.r.A]

".'.'::: ":.."'a

"-...'.'..:, "...;-.:.

"':".':'

I': "'.'.'.'." ". : ".

film thickness (b)

Chemical

Liquid bulk

film .~,.~ Liquid thickness bulk

Absorption

(c)

(SLow kinetic regime)

Chemical

Absorption

(Fast kinetic regime)

Fig. I. Concentration profiles of gas during its absorption. (Assuming there is no resistance in the gas phase.) Assuming that there is no resistance to mass transfer in the gas phase, and also according to the film theory, during the absorption of a gas into a liquid, the only resistance is found in a liquid film near the interface. If the absorption is accompanied by an irreversible chemical reaction in the liquid, this reaction will occur in the liquid bulk (slow kinetic regime), or in the film (fast kinetic regime), depending on the ratio between the maximum chemical reaction rate developed in the film and the maximum physical absorption rate. These possibilities are shown in Fig. 1 (Charpentier, 1981). The square root of this ratio is the dimensionless number of Hatta (1932), which is present in the kinetic equations derived from this theory for any type of chemical absorption. For a ruth irreversible reaction, it takes the form: Ha = ~ / ( 2 / m + 1)OAk [A*]"-I kL

(1)

where k is the kinetic rate constant, DA and [A*] the diffusivity and solubility of the gas A, m the gas kinetic order and k t the mass transfer coefficient. According to Charpentier (1981), the values of this ratio allow us to ascertain the type of kinetic regime: low values of Ha (less than 0.3) indicate that the reaction is slow, and hence the gas absorption rate will be: N A a = kLa ([A*] - [A]),

(2)

a being the specific interfacial area, and [A] the concentration of dissolved gas in the liquid bulk [see Fig. l(b)]. In this case, the absorption rate can be also

expressed as a function of both the chemical reaction and the accumulation rates of dissolved gas in the liquid bulk, that is: d[A] dt

NA a = r J r - -

(3)

If the reaction regime is fast (values of Ha higher than 3), the gas absorption is expressed as follows: NAa = kLa [A*]E

(4)

where E represents the factor by which the presence of a chemical reaction enhances the maximum physical absorption, equal to kL a [A*]. This factor involves both the physical mass transfer and chemical reaction contributions, the latter developing in the film region [see Fig. l(c)]. On the other hand, any gas absorption in water is affected by the presence of salts in the solution, due to the ionic strength as it is indicated below. The solubility of a gas A, that is the concentration of dissolved gas [A*], in equilibrium with its partial pressure, is given by: PA = n [A*]

(5)

where H is the Henry's law constant, which is an increasing function of temperature (Danckwerts, 1970): dlnH d (I/T)

--HA R

(6)

being R the gas constant and H A the heat of absorption (taken as positive) of the gas at the temperature considered.

Henry's law constant for ozone

1241 Stirrer

(J

Gas I N

Gas OUT

It

SampLe "1-

Ozone

181

Generator

10

4

Units (cm)

Agitated

Vessel

Fig. 2. Experimental set-up. In the case o f electrolyte solutions, the salt effect c a n be expressed by (Danckwerts, 1970): l o g ( H / H °) =

hL

(7)

where H ° is the value in water, I the ionic strength o f the solution a n d h the sum o f c o n t r i b u t i o n s referring to the species o f positive a n d o f negative ions present a n d to the species o f gas. EXPERIMENTAL

Figure 2 shows a scheme of the experimental set-up. Pure oxygen coming from a cylinder is fed into an ozone generator (Constrema SLO) which is able to produce a maximum mass flow rate of 6 g O3/h. The ozone-oxygen mixture can either be sent to the reactor or to a flask for analysis. The reactor is a 750 cm 3 Pyrex glass cylindrical vessel rounded at the bottom. The tap of the reactor has several inlets for gas feed, stirring, sampling, venting and temperature measuring. Stirring speed is adjusted by means of a photoelectronic measuring unit. Four baffles are located inside the reactor vessel. Before starting absorption, the ozone-oxygen stream is directed into a flask with a potassium iodide aqueous solution to analyze the ozone concentration in this gas. When the desired ozone percentage is reached, the gas stream is fed into the reactor. Five hundred em 3 salt aqueous solutions were prepared, adding the amount of salts needed to obtain the experimental conditions of pH, temperature and ionic strength shown in Table 4. High purity water was used (0.05 #S conductivity) taken from a Millipore Milli Q-Water System. Once the process had been started, several samples were taken out periodically and the dissolved ozone concentration was determined colorimetrically (Bader and Hoign6, 1981). The absorption process was carried out until a steady state concentration in the liquid was reached. In that moment, the gas stream was stopped. The ozone decomposition chemical reaction was then followed by determining the concentration of dissolved ozone using the method above mentioned. RESULTS

o n the a b s o r b e d ozone concentration. Figure 3 shows t h a t at a given pH, as time increases, the slope o f the a b s o r p t i o n curve reduces, reaching a n asymptotic value. Likewise, the dissolved ozone c o n c e n t r a t i o n decreases when the p H is increased, due to the fact t h a t high p H values are inducing the ozone decomposition. It c a n be n o t e d from Fig. 4 t h a t a n increase in t e m p e r a t u r e brings a b o u t a decrease in the dissolved ozone c o n c e n t r a t i o n . This occurs due to a d r o p in the liquid phase driving force a n d to a higher ozone d e c o m p o s i t i o n rate.

Effect of gas flow rate, ozone partial pressure and agitation speed These variables have a n i m p o r t a n t effect o n the global a b s o r p t i o n rate. T h e gas flow rate a n d the agitation speed influence o n the liquid a n d gass mass

T=IO *C P05=2 kPa 0=50 Lh-1N=3OOrpm i

Z =0.15M

pH=2.5

o

,. o---.

) ~0

~

o

o

~2

0

I 0.5

I 1,0

I 1.5

I 2.0

t x lO-~{s )

Effect of temperature and pH Figures 3 a n d 4 show the effect o f these variables

Fig. 3. pH influence on absorbed ozone concentration. Salt: sodium phosphate.

1242

J.L. SOTELOet al. pH=7 3

PO3=2 k Pa

pH=7

O =50 lh-lN =300rpm

Q=50 ti~ -~

6~T=10"C

Z =0.15 M

N=3OOrpm

/

I =015M

I

~

PO3=3.5 kPa

2

O

=

T =50 *c

~70,5

1.0

1.5

Z.O

0

V ,

0.5

~ ,

1.0

t x 10-3(s)

1.5

,

20

t x 10-~(s)

Fig. 4. Temperature influence on absorbed ozone concentration. Salt: sodium phosphate.

Fig. 6. Ozone partial pressure influence on absorbed ozone concentration. Salt: sodium phosphate.

transfer resistance, that is, on the mass transfer coefficients and the interfacial area. On the other hand, ozone partial pressure affects both liquid and gas phase driving forces. Figures 5, 6 and 7 show, as an example, the ozone absorption curves in water vs time, modifying the variables cited above. It is observed that the dissolved ozone concentration increases when these variables increase, as can be expected. F r o m Figs 5 and 7 it can also be seen that when the ozone concentration reaches its plateau level, different values have been obtained for every experiment conducted instead of a constant amount as would have been expected. Due to the impact of the simultaneous decomposition reaction occurring during the absorption process, this concentration does

not correspond to the equilibrium but to the steady state. It can be easily proved that both are related to the kinetic rate constant and to the volumetric mass transfer coefficient (Roth and Sullivan, 1981).

i pH =7 2 . 0 ~ T =20°C

Influence o f ionic strength In most cases, gas absorption decreases as ionic strength grows. In the ozone absorption it can be deduced from the experimental results that this effect is more significant when there are phosphates, chloride or carbonate ions; and in the presence of sulphate ions, the influence is practically insignificant. Figure 8 shows, as an example, the ozone absorption curves obtained when the process is carried out in the presence of chloride ions with different ionic strengths.

P03-- 2] kPa 1,5

N=IO0 rpm

I =0.15M

N = 800 rpm

Q = 7 O L h -1

1.5

(3 =60 L h-I

~ - - ~ = 5 ~"

O0 rpm 1.0

°o

1.0

o

o

rpm

Q =40

l h- I

~0

~

Q : 4 0 l~ -1

x

T =10 *C

0.5

I =015 M

~-~

0.5

o

=

0.5

1.o

1.5

Z.O

t xlO-3(s)

Fig. 5. Gas flow rate influence on absorbed ozone concentration. Salt: sodium phosphate,

o

i

o.5

~.o

I

I

1.5

2.0

t x 10-3(s)

Fig. 7. Speed agitation influence on absorbed ozone concentration. Salt: sodium phosphate.

Henry's law constant for ozone

1.oo

1243

i

pH-7

Q = 5 0 I.h-1

T =10 °C

N =300 rpm

I -0.15 M 0.75

L

8

x

41

i

~

0.50

t.

x

~Z 0.25

o~ OD

o

I 0.5

I 1.o

I 1.5

I 2.o

lo

t x lO-~ls )

20

30

[Oa]X105 ( m o t

Fig. 8. Ionic strength influence on absorbed ozone concentration. Salt: sodium chloride, pH = 5.94.

40

t-1 1

Fig. 9. Verification of equation (12). Ozone partial pressure influence. Salt: sodium phosphate.

eo3

Symbol

(kPa)

(M)

A O []

1.14 1.26 1.23

0.04 0.09 0.49

equation follows:

DISCUSSION

(3). T h i s e q u a t i o n c a n

r =

Ozone decomposition rate

be e x p r e s s e d as

d[O3] dt - - k [ O 3 ] "

(8)

by i n t e g r a t i o n a n d r e a r r a n g i n g :

A s w a s indicated p r e v i o u s l y , a n e x p r e s s i o n f o r o z o n e d e c o m p o s i t i o n rate is n e c e s s a r y f o r a p p l y i n g

[O3]=[O3]oexp(-kt)

m = 1

(9)

or [O3]l-m = [O3]1o-,,_ kt

Table 2. Ozone kinetic order deduced from best least squares fit of equations (9) and (10) Salt

2 2 1.5 1.5 2

Table 3. Experimental kinetic rate constants for ozone decomposition kinetics (I tool- t s- s) Salt type Sodium phosphate

pH = 2 pH = 7 pH = 8.5

Sodium phosphate and sodium carbonate

(10)

F r o m the literature (Sotelo et al., 1987) it c a n be n o t e d t h a t there are s o m e d i s a g r e e m e n t s w i t h respect to the o z o n e kinetic o r d e r m, w h i c h t a k e s the values o f l, 1.5 a n d 2. Hence, in this w o r k , least s q u a r e s a n a l y s i s o f e q u a t i o n s (9) a n d (10), f o r these values o f m, h a v e been p e r f o r m e d in all e x p e r i m e n t s . T h e best fits c o r r e s p o n d to the kinetic o r d e r s s h o w n in T a b l e 2.

Order m

Sodium phosphate Sodium phosphate and sodium carbonate Sodium sulphate Sodium chloride Sodium chloride and sodium phosphate

m ~ 1.

k = 4.157 x l07 exlR-4900/T)ll'2~/[S] r 2=0.997 SD=0.146 k = 7.120 x 10I° exp( - 6858/T)I1'°3°/[S] r 2 = 0.988 SD = 0.348 k = 4.77 x l012exp(-8211/T)I°'794/[S]

pH = 7

k = 3.713 × I016exp( - 10754/T)I°'9~/[S] r 2=0.997 SDffi0.146

Sodium sulphate

pH = 6 T=20"C

k = 1.0114 I1"22/[Sl r 2=0.999 S D f 7 . 7 5 x l0 -2

Sodium chloride

pH = 6 T=20cC

k = 7.47 × l0 -2 II°l/[S l r2=0.999 SDffi2.66x10 -2

Sodium chloride and sodium phosphate

pH = 7 T = 20°C

k = 0.315 I°'59/[S] r 2= 0.999 SD ffi 2.61 x 10-2

r 2 = Multiple correlation coefficient. SD = Standard deviation.

1244

J.L. SOTELOet al. pH=7 T = 2 0 aC

Pm

-\

4~,~

I

PO~2kPa

pH=7

P%= 1 k ~ a

N = 1 0 0 rpm

T =10"C

Q=40

t h -1

I =015M

=0.15 M 12 i

v

r-0 x

7 0 L h -1

E

£

8

x

g r---1

,o, 1

t_...a "O

"o

0

,oo,~,~

I

I

8

16

24

-~---V.~

4

[03] x lOS ( mot L-1)

8

, 12

[03]x 105( mot t-1)

Fig. 10. Verification of equation (12). Gas flow rate influence. Salt: sodium phosphate.

Fig. 11. Verification of equation (12). Speed agitation influence. Salt: sodium phosphate.

On the other hand, the kinetic rate constant k is a function of pH and hydroxyl radical scavenger concentration (Sotelo et al., 1987). Concretely, Staehelin and Hoign6 (1985) proposed a proportionality between the ozone decomposition kinetic rate constant and the inverse of hydroxyl radical scavenger concentration. Besides, due to the high salt concentrations used in this work, the ionic strength can also possibly affect the kinetics (Stumm and Morgan, 1970). Therefore, for a given pH, the following empirical equation for the kintic rate constant has been assumed here:

[S] represent the ionic strength, temperature and hydroxyl radical scavenger concentration. The values of k corresponding to the best least square fits of experimental results were expressed as a function of L T and [S] according to equation (11) by means of multiple regression analysis, and are indicated in Table 3.

k = ko 1° exp( - b / T)/[S]

(11)

where ko, a and b are constants, and L T and

Determination o f ozone solubility

In ozone absorption in water, gas phase resistance to mass transfer can be considered negligible because ozone is a sparingly soluble gas in water (Li and Kuo, 1980). In the liquid phase, the presence of dissolved free ozone in water allows us to assume that the process

Table 4. Determination o f H a t t a number* Salt type

TCC)

Sodium phosphate Sodium phosphate and sodium carbonate Sodium sulphate Sodium chloride Sodium chloride and sodium phosphate *[O~]=5x10 5moll f U n i t s i n l ~ ~mol ~ ++Units in m o l l i.

[S]~

m

k~-

Ha

5

pH 2

0.5

11:

0.37

2

1.032

1.99 × 10 2

10 20 20

7 6 7

0.1 0.09 0.04

7.2 x 10 -~ 5 x 10 : 1 × 10 :

2 1,5 1.5

1.906 1.072 0.289

2.93 × 10 3.33 × 10 -" 1.73 × 10 -~

20

7

0.5

5 × 10 ~

2

41,8

1.60 × 10 '

~. I)s i

Table 5. Experimental Henry's law constants (kPa mol fr ' ) Agitation speed* (rpm) 100 500 800 Average value:

H x 10 •

G a s flow rater (lh t)

5.84 5.39 5,14 5.46

40 60 70 Average value:

Hx

10 ~

6.20 5.67 5.72 5.86

Ozone partial pressure++ (kPa)

H x 10 5

0.5 2 3.5 Average value:

5.22 5.64 5.41 5.41

Other experimental conditions. Salt: sodium phosphate. I = 0.15 M. *T=IO'~C; Po3=lkPa; Q = 4 0 1 h '; p H = 7 . t T = 20"C; N = 100 rpm; Po3 = 2 kPa; p H = 7. ++T=IO'C; N = 3 0 0 r p m ; Q = 5 0 1 h ] ; p H = 7 .

Henry's law constant for ozone

1245

Table 6. General equations for Henry's law constant (kPa mol fr- ~) Salt type Sodium phosphateS"

0~T~<20°C

2~
Sodium phosphate and sodium carbonate:[: Sodium sulphatet

T=20°C

Sodium chloride:~

r 2 = 0.94 T=20°C

Sodium chloride and sodium phosphate:~

r 2 = 0.979 T=2ff'C r 2 = 0.976

(13) (14)

2~
*r 2 = Multiple correlation coefficient; SD = standard deviation. t Buffered solutions. ~Unbuffered solutions, pH initial value.

is in the slow reaction regime. This is confirmed by the d e t e r m i n a t i o n of the H a t t a n u m b e r : Table 4 shows, as examples, some o f the values for this p a r a m e t e r after applying e q u a t i o n (1). The kinetic order a n d the ozone decomposition kinetic rate c o n s t a n t were o b t a i n e d from Tables 2 a n d 3. The individual mass transfer kL has been deduced experimentally by a chemical m e t h o d (Alper a n d Deckwer, 1980); the value o b t a i n e d for all experiments was 8.26 x 1 0 - S m s-~; a n d the ozone diffusivity has been o b t a i n e d from the literature ( M a t r o z o v et al., 1976). This c o n f i r m a t i o n indicates t h a t e q u a t i o n s (2) a n d (3) can be used for the study of ozone a b s o r p t i o n in water. T h e equality o f b o t h equations, after substituting e q u a t i o n (8), yields a n ozone balance: d[O3] k[O3] m + ~ =

kLa ([O~'] -- [03])

(12)

where the a c c u m u l a t i o n rate has been evaluated from the a b s o r p t i o n curves vs time by m e a n s o f p o l y n o m i c regressions (multiple correlation coefficients were always higher t h a n 0.97). According to e q u a t i o n (12), by plotting the left side against the dissolved ozone c o n c e n t r a t i o n , straight lines must be obtained. The values o f kLa a n d [O~] can be deduced from their c o r r e s p o n d i n g slopes a n d intercepts. If the ozone partial pressure is modified, parallel straight lines m u s t be obtained, as can be seen in Fig. 9. However, if gas flow rate a n d agitation speed are varied, b o t h slope a n d intercept m u s t be different because of the changes in the volumetric mass transfer coefficient (Figs 10 a n d 11). F r o m the ozone partial pressure a n d its corres p o n d i n g equilibrium concentration, H e n r y ' s law c o n s t a n t s have been calculated for every experiment

I" = 0 . 4 5 M

~

154

I0

~-

~B

10

"15

pH 300

T (KI

310

Fig. 12. Comparison of results. Salt: sodium phosphate, x : This work. Data from Li's work (1977); T = 298 K; pH = 2-7. Deviations, %: I), 16.6; O, 20.0; C), 12.8; O, 10.4.

1246

J.L. SOTELOet al.

[equation (5)]. Table 5 indicates the values of these constants corresponding to the experiments carried out at different agitation speeds, gas flow rates and ozone partial pressures for constant temperature, pH and ionic strengths. As expected the results obtained are practically constant and only deviate ___10% from the average values. The Henry's law constants were fitted as a function of temperature, p H and ionic strength for all salts by multiple regression analysis leading to the general equations depicted in Table 6. The values of Henry's law constant calculated from equations (13)-(17) always deviate less than + 15% from their corresponding experimental values. Numerical integration of equation (12) by fourth order R u n g e - K u t t a method (Mickley et al., 1975), allowed us to obtain the theoretical ozone concentrations at different experimental conditions and absorption times. It was observed that deviations between these values and the corresponding experimental ozone concentrations were always less than +13%. Comparison with other authors

The results from this work have been compared to those obtained from the works listed in Table 1. The following aspects were noted: (1) Most of the works cited before (Kawamura, 1932; Rawson, 1953; Stumm, 1958; Mailfert, 1970; Nebel, 1981; Caprio et al., 1982) were carried out in unbuffered water; so, during the process, the pH probably varied. In addition, the ionic strength used was not indicated. Therefore, these results are not reliable and cannot be compared to ours. (2) With respect to other works carried out in buffered water (Li, 1977), Fig. 12 shows a tridimensional plot of Henry's law constant against pH and temperature with 0.45 M of ionic strength as a parameter, corresponding to this research [derived from equation (9)] and those of Li (1977). It can be observed that deviations are always less than 20%. The observed disagreements can be due to the ozone decomposition: in this work an ozone decomposition rate experimentally deduced has been used, while in Li's work (1977) the absorption process did not take into account this action. Acknowledgement--This research was supported by the Spanish "Comisi6n Interministerial de Ciencia y Technologia" (Grant No. PA 85/332). REFERENCES

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