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The kinetics of ozone-phenol reaction in aqueous solutions
Water Res. Vol. 16, pp. 933 to 938. 1982 Printed in Great Britain. All rights reserved
0043-1354/82/060933-06S03.00/0 Copyright ~ 1982 Pergamon Press Ltd
THE KINETICS OF OZONE-PHENOL REACTION IN AQUEOUS SOLUTIONS MAKARAND G. Josm t and ROBERT L. SHAMBAUGH2 tSchool of Chemical Engineering, Cornell University, Ithaca, NY 14853 and 2E. I. duPont de Nemours & Co. Wilmington, DE, U.S.A.
(Received September 1981)
Abstract--The kinetics of the reaction of ozone and phenol in aqueous medium was studied. The reaction was first order with respect to both ozone and phenol. The rate constant was found to increase with increase in the pH of the reaction mixture. Four different catalysts were examined for their effect on the rate of reaction but none of them was found to have any appreciable effect. The presence of additional solutes like sodium chloride, sodium carbonate and sodium sulfate was found to affect the reaction significantly. The experiments indicated that hydroxyl radicals may not play a role in the attack of ozond on phenol and the reaction mechanism may be ionic rather than free radical.
INTRODUCTION Phenols are some of the most common aqueous pollutants. They are toxic to aquatic life and may pose a health hazard to humans. Phenols impart obnoxious taste and odor to water, particularly after chlorination. Furthermore, chlorination of water contaminated with phenols may lead to formation of much more toxic compounds (Labine, 1959; Sliter, 1974; ES&T, 1976). Coal and coal derived products will undoubtedly play a prominent role in providing future energy needs. As phenols are expected to be present in the effluents from gasification and iiquifaction complexes (Katzer e t a l . , 1976), the phenol pollution problem will be exacerbated. Effective methods to remove phenol are needed. Biological oxidation and adsorption on activated carbon can be used but uneconomically long residence times are required to reduce the phenol concentration to the discharge level allowed by emission regulations, especially for wastes with high phenolic content. Another logical way to remove phenols is by chemical oxidation. However, phenolic compounds are refractory to oxidation by air or oxygen at ambient conditions. Heating the waste stream in order to oxidize phenols is not feasible because of very high heating costs. Thus, a stronger oxidant applicable at ambient conditions is desirable. Ozone is a possible candidate because of its high oxidation strength, reasonable cost, ability to break down into harmless oxygen and likelihood of not forming more toxic compounds. Thus, ozonation appears to be an attractive method for treatment of industrial effluents (McCarthy & Smith, 1974; Sliter, 1974). Moreover, it is possible to increase ozone reaction rates and ozone utilization rates by using suitable solid catalysts. But despite the attractiveness of the process, reliable kinetic data on aqueous ozonation are not available and the information on solid catalyzed aqueous ozonation is very limited,
A waste stream rarely, if ever, contains just one pollutant. However, the experiments using actual wastes are not very amenable to kinetic analysis. Furthermore, the results cannot be easily extrapolated to other situations. Carefully designed experiments that allow the determination of kinetic parameters are much more useful. These experiments usually use syntbetic wastes with one or more model pollutants. Such experiments can indicate general results which can be used for optimal treatment of actual wastes. In present work phenol was chosen as the model poilutant and the kinetics of ozone-phenol reaction in aqueous solutions was studied. The possibility of using solid catalysts to enhance the reaction rates was also explored.
933
SURVEY OF PREVIOUS WORK Roth (1947) appears to be the first to have studied the ozonation of phenol in aqueous solution. Roth's work was followed by a number of other invcstigations (Cleary & Kinney, 1951; Niegowski, 1953; Hall & Neilist, 1959; Labine, 1959; Peppier & Fern, 1959) all of which were empirical in nature and did not attempt a detailed study of the parameters governing the reaction rates and efficiency. Eiscnhauer (1968) studied the oxidation of phenol in aqueous solution with a view to identify and evaluate the parameters which affect the reaction. He proposed an empirical rate equation to represent the degradation of aqueous phenol by ozone. His empirical rate constant was dependent on ozone gas flow rate and reactor geomerry. Eisenhauer detected catechol and o-hydroquinone in the reaction mixture and suggested that phenol was consecutively oxidized to muconic acid, maleic acid, oxalic acid and carbon dioxide. Bauch et al. (1970) found that the mole ratio of ozone consumed to phenol was the predominant factor in determining final products. Gould & Weber's (1976)
g34
\l',kxR~,xD G J,)SHI and
ROHERr[_ SHe;lUg, , H
investigation was very similar to Eisenhauer's. except that a phosphate buffer was used to control the pH of
~, o,,,,
~c~ '~"
'~c~'o~et,r
the reaction. Gould and Weber found that the empiri-
r4~ ' L
~
~
cal rate equation proposed by Eisenhauer fit their data and the empirical rate constant increased with increase in the pH of the reaction. Gould and Weber detected the intermediates catechol, hydroquinone, ~,lyoxal, glyoxylic acid and oxalic acid in the reaction mixture. Anderson {19771 found that the reaction rate between ozone and phenolate ions was at least 27 times faster than the rate between ozone and the toolecules of phenol. Neufeld & Spinola {1978) studied the ozonation of liquid waste sample from an experimental coal gasification plant using a packed column with countercurrent flow. The waste composed of simple phenol and polyduric phenols. As the liquid to gas ratio was decreased, there was substantial decrease in phenol with simultaneous increase in concentration of low boiling compounds. Li et al. (1979) eliminated the interference of mass transfer on reaction rate measurement by studying the kinetics of o z o n e - p h e nol reaction with a stopped flow method in h o m o geneous aqueous solutions. They determined that the rate of reaction in early reaction period was first order with respect to b o t h phenol and ozone concentrations. The rate constant was found to increase with both pH and temperature, Very few investigators have explored the possibility of using a catalyst to enhance the rate of oxidation of aqueous phenol by ozone. Furthermore, no attempts were made by these few investigators to obtain conventional kinetic parameters. Eisenhauer (1971) investigated the catalytic action of ferrous sulfate a n d ferrous a m m o n i u m sulfate on ozonation of aqueous phenol. Eisenhauer observed that b o t h the ferrous salts inhibited the reaction. Chen et al. (1970) examined various catalysts to enhance the rate of ozonation of aqueous phenol. Activated Raney-Nickel was found to be the best catalyst out of ten different candidates considered. A few patents (Koezuka et al., 1977; Sata et al., 1977; Basila & Booersma, 1979) have appeared which claim efficient catalysts for the oxidation of aqueous phenol by ozone, In the work described herein, rate constants were determined for the reaction of ozone and phenol in water. Careful account was made of the mass transfer of ozone from gas phase to aqueous phase, and the effect of pH and various soluble salts on the rate constant for phenol ozonation was studied. Rate constants were determined for the solid catalyzed reaction of ozone and phenol in water for four different catalysts,
EXPERIMENTAL SECTION Apparatus Ozone was generated using a Welsbach Model T-816 ozonator. The reactor was a 2 I. resin kettle fitted with an air-tight polypropylene top. Four openings in the top housed a coarse sintered glass sparger for ozone, a ther-
, ~o~yprom,,,,,,J..-i ,op ------- ~ r~rmome,er .glsomp,,ng - / ~ ~or, S~pr z-,,,,, Resin ket'tte SmtePed
',', ,,
',{
U
UI
q _~
j+---
~,os, ------.r-----,~,g,r k.. ,_
)
.J '-~aog,,,,¢ ,,,rr,¢
Fig. 1 The ozonanon reactor mometer, an outlet tube for unreacted ozone and a manometer connecnon. A side opening in the kettle was sealed by a septum through which samples were withdrawn periodically with a hypodermic syringe. The contents of the reactor were stirred by a teflon coated magnetic bar (0.75 cm o.d. x 3.75 cm length) which was rotated by exterhal magnetic field at 250 rev rain- '. See Fig. 1 for a drawing of the reactor. The ozone concentrations in both inlet and outlet gas were monitored using a Dasibi Model 1003-HC ultraviolet spectrophotometer. See Fig. 2 for a schematic diagram of the equipment. Materials All the chemicals used were reagent grade compounds. The supported copper oxide catalyst was Harshaw Cu-0803, T 1/8, 10% CuO on ;,'-alumina. The supported manganese oxide catalyst was Mn-0201. T 1/8, 19% MnO: on ;.,-alumina. The pellets [0.0032 m (l/Sin.) o.d. × 0.0032m (l/8in.l length] of both these catalysts were crushed manually and the portions passing through a 325 mesh sieve were used. The unsupported cuprous oxide was reagent grade chemical, while 1% palladium on alumina was procured from Alfa products, Beverly, Mass. Both these catalysts were fine powders ( - 3 2 5 m~h) and were used as received. The water used was distilled twice. first in metal and then in a Coming Megapure ® all glass still. Analytical method The samples were analyzed for phenol using a gas chromatograph (Hewlett-Packard Model 5710-AI. The column used was a 1.83 x 0.0032 m {6ft x l/Sin, o.d.) stainless-steel column packed with Tenax-GC ® (2,6-diphenyl-p-phenylene oxide polymer} coated with polymetaphenyt ether (5% by weight}. The column temperature was 190°C while the injection port and the detector were both kept at 250'C. A flame ionization detector was used. The carrier gas was nitrogen and the sample size for injection was 1 ,ttl. Procedure The experimental runs were made using potassium dihydrogen phosphate (pH 6--8) or sodium tetraborate (pH = 9.0) as a buffer with 0.01 tool 1- t concentration. In a typical run, 100Oral of reaction mixture, equilibrated to desired temperature and pH, was charged into the reactor. Temperature variation during all experiments was monitored and found to be negligible (4-_0.5:C}. An ozone-oxy-
The kinetics of ozone-phenol reaction in aqueous solutions
935
TO vent
To vent
Reference
gas line
Ivalve Oo-_Lo_._.J
D~
J
.....
L.
gas
Jcy,inder
The
U
valve
, - , -~
I
~
I
I
o.v.
Spact rophotometer
reactor L ~ J Fig. 2. The schematic diagram of the apparatus.
gen mixture of premeasured composition (determined by u.v. spectrophotometer) was introduced into the reactor through a sparger at a metered rate. Representative samples were withdrawn through the sample port at preselected times using a hypodermic syringe. The ozone concentration in the reactor offgas was continuously monitored with the ultraviolet spectrophotometer.
RESULTS AND DISCUSSION
where D^ -- diffusivity of dissolving reactant (ozone), cm2s - t k2 = second order rate constant, cm 3 tool- t cm 2 s [-B]o = maximum (initial) concentration of reactant in liquid phase (phenol), tool cm -3 kL = mass transfer coefficient, cm s-~. For the reaction of ozone with aqueous phenol,
The kinetic parameters were determined by the method outlined in Appendix. A simple second order
DA = 1.743 x 10-s cm 2 s - t from Wilke Chang (1955) correlation kz = l0 s cm 3 m o l - t s- z, typical value
rate expression rVhOtI = -- k z [ P h O H ] [ 0 5 ]
&
[B]o = 1.0632 x 10- 6 tool c m - 3, typical value
was found to describe the reaction adequately, Initially a few experiments were carried out to check for mass transfer limitations. In these experi-
and
ments only the flow rate of ozone-oxygen mixture fed to the reactor was varied keeping everything else same. The results (Table 1) indicated that the mass transfer resistance was not likely to be a limiting factor. The absence of mass transfer limitations was further confirmed by checking the criterion for no reaction in the film developed by Danckwerts (1970). For an irreversible second order reaction the criterion
(1976). Setting these values in the inequality yielded a value of 0.009 for iefthand side. This conclusively proved that the reaction was not mass transfer limited. The effects of the following three variables on the reaction kinetics were studied:
can be reduced to
kL = 0.0142 cm s- t from Shambaugh & Melnyk
(a) The pH of the reaction mixture. (b) The solid catalysts. (c) The presence of certain solutes in the reaction mixture. (a) The effect ofpH. Niegowski (1953), Hall & Nellist (1959) observed that all else being equal, the rate
D^kz[B]o <1 k~
Table 1. The effect of total gas flow rate Experiment No.
Total gas flow rate 1 (STP) rain- t
s tool Phenol mol- t of 03
k2 cm 3 tool- a s" '
17 9 18
0.717 1.433 2.150
0.235 0.226 0.245
0.175 x 106 0.180 x 106 0.183 x 106
The other conditions held constant in these experiments were: temp. = 20"C; pH = 8.0; ozone concentration in the inlet gas = 3~ by weight; initial concentration of phenol -- 1.0632/~M ml- t.
936
5,IAK~RA>:D
O.
]q)SH~ and ROBFRT L SHX~B~L(~H
Table 2. The effect of pH on the reaction kinencs Experiment No.
pH
s mol phenol mot- ~ ozone
13 14 9 15
6.0 7.0 8.0 9.0
0.240 0,240 0.226 0.420
kz cm 3 tool- ~ s 0.09 x l0 ~' 0.i40 x 106 0,180 × I0 "° 0.246 >: 10 +~'
The other conditions for these experiments were: temp. = 20~C: initial phenol concentration -- 1.0632 ,uM ml- ~; ozone concentration in feed gas = 3°~ by weight; total gas flow rate to the reactor = 1.433 1 (STP) rain- t. of oxidation of aqueous phenol by ozone increased with pH of the reaction mixture. Eisenhauer (1971) found that, based on experiments using unbuffered solutions whose initial pH was adjusted, the rate of phenol removal increased about threefold between pH = 3.0 and 10.0. Eisenhauer attributed this increase to the increased concentration of phenolate ions at higher pH values. These ions are more susceptible to attack by ozone. Gould (1971) discarded this hypothesis based on his observations that most of the increase in the rate occurred between pH = 4.0 and 7.5 and that the rate was essentially constant above pH = 8.0. Gould argued that. since the p K , of phenol was about 10,0, the increase in the rate was complete long before phenolate ions attained a significant level relative to phenol and thus, the higher susceptibility of phenolate ion was not the reason for the increase in the rate. To probe this phenomenon further four experiments were conducted over a pH range 6.0-9.0. The results are summarized in Table 2. We see from Table 2 that the rate of ozonation of aqueous phenol increa,~s with p H value above pH = 8.0--contrary to the observations of Gould (1971). Anderson (1977) has reported that the rate of reaction of ozone with phenolat¢ ion was 27 times that of ozone with the phenol molecule. Hence, it appears that phenolate ions are formed as intermediates and ozone preferentially
As shown in Table 3. none of the catalysts had any significant effect on the rate. Sadana & Katzer (t974) found that Harshaw Cu-0803 and Harshaw Mn-0201 enhanced the rate of oxidation of aqueous phenol by oxygen. The catalysts' inactivity in the present study suggests that the mechanism of ozonation is quite different from that of simple oxidation by oxygen. Find. ing a suitable catalyst for a reaction is still more an art than science. (c) The effect of solutes in the reaction mixture. In real life situations waste effluents always have dissolved inorganic material. These solutes sometimes radically affect the reaction kinetics. To determine such effects on the ozonation of aqueous phenol, four experiments were conducted; results are summarized in Table 4. The presence of additional solutes affects the stoichiometry as well as the rate constant. Though no mathematical generalizations could be made, there experiments illustrate that the effect of solutes should be taken into account in the design of ozone comaetots for waste treatment.
reacts with these tons, (b) The effect of solid different catalysts were the rate of ozonation of (1) Harshaw Cu-0803 (2) Harshaw Mn-0201
The literature contains two opposing theories regarding the mechanism of reaction of ozone a n d phenol in water. According to the first theory which was proposed by Bailey (1958), the reaction is ionic in nature. Eisenhauer (1971) confirmed this view based on his experiments, Razumovskii et aL (1972) pro-
catalysts. The following four examined for their effect on aqueous phenol: ( - 3 2 5 mesh), (-325mesh).
(3) Cuprous oxide. (4) 15/o Palladium on alumina.
MECHANISTIC CONSIDERATIONS
Table 3. The effect of catalysts on the reaction kinetics s
Experiment No 5 6 7 8 9
Catalyst Cu20 1% Pd on Alumina Harshaw Cu-0803 Harshaw Mn-0210 None
k2
tool phenol tool- t O~ cm 3 tool- ~s0.230 0.240 0.240 0.243 0.226
0.1B0 0.190 0.170 0.230 0.180
x
x x x x
106 106 106 106 106
The other conditions which were held constant for these experiments were: temp. = 20°C; pH ffi 8.0; initial phe-ol concentration = 1.0632/aM ml- t ; o z o n e concentration in feed gas = 3% by weight; total gas flow rate to the r e a c t o r = 1,433 1 (STP) rain- t.
The kinetics of ozone--phenol reaction in aqueous solutions
937
Table 4. The effect of additional solutes in the reaction mixture Experiment No. 9 10 11 12 20
Additional solute added and concentration None NaCI (1 g 1- t) NaCI (0.5 M I- t) NazCO~ (0.05 M 1- t) NazSO.t (0.05 M I- t)
s k2 mot phenol tool- t O3 cm 3 tool- t s- t 0.226 0.277 0.291 0.335 0.249
0.180 0.180 0.180 0.371 0.283
x x x x x
106 l& l& 106 10~
The other conditions which were held constant in these experiments were: temp. = 20°C; pH = 8.0; initial phenol concentration = 1.0632 pM m l - l ; ozone concentration in the inlet gas -- 3% by weight; total gas flow rate to the reactor = 1.4331 (STP) min-t.
posed a free radical mechanism for ozone-phenol reaction. Based on their own experiments Hoign~ & Bader (1976) supported this theory. Interestingly, Li et al. (1979) have proposed a free radical mechanism with an electrophilic reaction for the formation of initial catechyl radical. In the present work, no separate experiments were carried out to elucidate the mechanism of ozone--phenol reaction in water. However, the following observation can be made. The OH" radicals are known to oxidize carbonate ions and, consequently, the concentration of OH" radicals is reduced whenever carbonate ions are present. Thus, if the ozone-phenol reaction proceeds through the formation of OH" radicals, the rate constant for this reaction should decrease whenever carbonate ions are present. In the present work the presence of sodium carbonate in the reaction mixture increased the rate of the reaction. Thus it appears that the reaction of ozone with aqueous phenol does not proceed through the formation of OH" radicals. CONCLUSIONS The reaction of ozone with phenol in aqueous solution can be adequately represented by a second order rate equation and does not involve OH" radicals. The catalysts which are effective in the oxidation of aqueous phenol by molecular oxygen are not effective in enhancing the rate of ozonation of aqueous phenol. Hence, the mechanism of ozonation is quite different from that of oxidation with simple oxygen. Acknowledgements---The authors wish to thank Professor Chi Tien, Chairman, Chemical Engineering Department, Syracuse University, Syracuse, New York, for many fruitful discussions. REFERENCES Anderson G. L. (1977) Ozonation of high levels of phenol in water. AIChE Syrup. Set. No. 166 73, 265-269. Bailey P. S. (1958) The reactions of ozone with organic compounds. Chem. Rev. 511, 925-1010. Basila M. R. & Booersma F. R. (1979) German Often, 2, 666, 879. Bauch H., Burchard H. & Arsovic H. (1970) Ozone as oxidant for phenol degradation in aqueous solution. Gesundheitsingenieur 91,258-262.
Chen J. W., Chang J. V. & Smith G. V. (1970) Chem. Engng Prog. Syrup. Ser. No. 109 67, 18-26. Cleary E. J. & Kinney J. F. (1951) Findings from a cooperative study of phenol waste treatment. Proc. 6th Purdue Ind. Waste Conf. 76, 158-170. Danckwerts P. V. (1970) Gas-Liquid Reactions, 156 pp. McGraw-Hill, New York. Eisenhauer H. R. (1968) The ozonization of phenolic waste. J. War. Pollut. Control Fed. 40, 1887-1899. Eisenhauer H. R. (1971) Increased rate and efficiency of phenolic waste ozonation. J. War. Pollut. Control Fed. 43, 200-208. ES&T (1976) Impacts of water chlorination. Envir. Sci. Technol. 1O, 20-21. Gould J. P. (1971) Ph.D. Thesis Department of Water Resource Science, University of Michigan, Ann Arbor, Michigan. Gould J. P. & Weber Jr W. J. (1976) Oxidation of phenols by ozone. J. War. Pollut. Control Fed. 48, 47-60. Hall D. A. & Nellist G. R. (1959) Treatment of phenolic effluents. J. appl. Chem. 9, 565--576. Hoign~ J. & Bader H. (1976) The role of hydroxyl radical reaction in ozonation process in aqueous solutions. Water Res. 10, 377--386. Katzer J. R., Ficks H. H. & Sadana A. (1976) An evaluation of aqueous phase catalytic oxidation. J. War. Pollut. Control Fed. 48, 920-933. Koezuka J., Koyama M., Sakurai K. & Sata Y. (1977) Japan Kokai 7708, 649. Labine R. A. (1959) Phenol free waste water. Chem. Engng 66, 114--117. Li K. Y., Kuo C. H. & Weeks Jr J. L. (1979) A kinetic study of ozone-phenol reactions in aqueous solution. AIChE Jl 25, 583-591. McCarthy J. J. & Smith C. H. (1974) A review of ozone and its application to domestic waste water treatment. J. Am. War. Wks Ass. 66, 718--725. Neufeld R. D. & Spinola A. A. (1978) Ozonation of coal gasification plant wastewater. Envir. Sci. Technol. 12, 470--472. Niegowski S. J. (1953) Destruction of phenols by oxidation with ozone. Ind. Engng Chem. 45, 632-634. Peppier M. L. & Fern G. R. H. (1959) A laboratory study of ozone treatment of refinery phenolic wastes. Oil Can. 11, 84-86, 88, 90. Razumovskii S. D., Giobenko G. M, Nikiforov G. A., Gurvich Ya. A., Karelin N. A. & Zaikov G. Ye. (1972) Kinetics of interaction of phenols with ozone in aqueous solutions. Nefiekhimiya 12, 65-68. Roth W. (1947) Ozonation of phenol in water solutions. M.S. Thesis, New York University, New York, NY. Sadana A. & Katzer J. R. (1974) Catalytic oxidation of phenol in aqueous solution over copper oxide. Ind. Engng Chem. Fundam. 13, 127-134. Sata Y., Koyama M., Koezuka J. & Sakurai K. (1977) Japan Kokai 7708, 650.
93~
M~,KARI~.>~DLJ JOSHI and ROBk~i L SH~,t,IB-~Et;'H let
12
E E 8
.
-4,8
:::L
z"
_o
o
6
°\o
~ 4
4~ ¢D
o
TIME,s
Fig. 3. The typical fit obtained. The circles represent the data of experiment 9. T h e continuous curves depict the values calculated with s = 0.226 tool P h O H m o l - ~ O3 kz = 1.8 x 10 ~ cm 3 m o l - t s" 1 and k t --- 0.00334s -~
Shambaugh R. L. & Melnyk P. B. (1976) The influence of spontaneous decomposition and mass transfer upon soluble ozone concentration. Proc. o f International Ozone Institute's Forum on Ozone Disinfection Chicago. Sliter J. T. (1974) Ozone: an alternative to chlorine. J. War. Pollut. Control Fed. 46, 4-6.
where
Spendley W., Hext G. R. & Himsworth F. R. (1962) Sequential application of simplex design in optimization and evolutionary operation. Technometrics 4, 441-461. Wilke C. R. & C h a n g P. (1955) AIChE Jl I, 264.
The second term in the equation (2) represents the spontaneous and simultaneous decomposition o f ozone which is a s s u m e d to take place independent of its reaction with phenol. The value of f(t) can be easily found by a mass balance on gaseous phase. At any t~me t
APPENDIX The reaction between ozone and phenol can be represented by the general reaction
Inflowof ozone mot s - z
O~ + s P h O H --, products s = stoichiometric coefficient, moles of P h O H m o l - ~ of O3. If one assumes that the disappearance of phenol can be adequately represented by a second order rate equation, then dB = -sk2AB (1) dt where B = phenol concentration in wateL m o t c m -3 kz = second order rate constant, cm 3 tool -~ s -~ A = ozone concentration in water, m o l c m - 3 , The change in ozone concentration in the reaction mixture is given by dA = _ kzAB _ kt A + f(t) dt
k t = first order rate constant for the spontaneous decomposition of ozone, s" f(t) = rate of transfer of ozone from gas b u l l i e s per umt volume of reaction mixture, m o l c m - 3 s - ~.
(2)
_
outflowof ozone mol s - '
,...volumeof = I t t ) reaction mixture mol (cm 3 s)- ~ - cm 3
The value of f(t) at any time t can be calculated by monitoting the ozone concentration in reactor off-gas during the experiment. Thus, with the value of k t known from literature or separate experiments, and the value of f(t) known from reactor off-gas data, it is possible to calculate the phenol concentration vs time c u r v e - - i f values of s a n d k2 can be determined. "Best" values of s and k2 can be found by assuming starting values for s and k2 and then carrying out a two dimensional search aimed at minimizing the difference between observed and calculated phenol concentration vs time curve. T h e sequential search method of Spendley et al. (1962) was used to carry out multivariable search. The equations (1) and (2) were sealed before integration to avoid numerical errors. A typical fit obtained is shown in Fig. 3. The values of s and k2 could be determined with an accuracy of two significant digits with the method. The reproducibility of k z was checked by conducting experiments at identical conditions and was found to be in the same range.
0043-1354/82/060933-06S03.00/0 Copyright ~ 1982 Pergamon Press Ltd
THE KINETICS OF OZONE-PHENOL REACTION IN AQUEOUS SOLUTIONS MAKARAND G. Josm t and ROBERT L. SHAMBAUGH2 tSchool of Chemical Engineering, Cornell University, Ithaca, NY 14853 and 2E. I. duPont de Nemours & Co. Wilmington, DE, U.S.A.
(Received September 1981)
Abstract--The kinetics of the reaction of ozone and phenol in aqueous medium was studied. The reaction was first order with respect to both ozone and phenol. The rate constant was found to increase with increase in the pH of the reaction mixture. Four different catalysts were examined for their effect on the rate of reaction but none of them was found to have any appreciable effect. The presence of additional solutes like sodium chloride, sodium carbonate and sodium sulfate was found to affect the reaction significantly. The experiments indicated that hydroxyl radicals may not play a role in the attack of ozond on phenol and the reaction mechanism may be ionic rather than free radical.
INTRODUCTION Phenols are some of the most common aqueous pollutants. They are toxic to aquatic life and may pose a health hazard to humans. Phenols impart obnoxious taste and odor to water, particularly after chlorination. Furthermore, chlorination of water contaminated with phenols may lead to formation of much more toxic compounds (Labine, 1959; Sliter, 1974; ES&T, 1976). Coal and coal derived products will undoubtedly play a prominent role in providing future energy needs. As phenols are expected to be present in the effluents from gasification and iiquifaction complexes (Katzer e t a l . , 1976), the phenol pollution problem will be exacerbated. Effective methods to remove phenol are needed. Biological oxidation and adsorption on activated carbon can be used but uneconomically long residence times are required to reduce the phenol concentration to the discharge level allowed by emission regulations, especially for wastes with high phenolic content. Another logical way to remove phenols is by chemical oxidation. However, phenolic compounds are refractory to oxidation by air or oxygen at ambient conditions. Heating the waste stream in order to oxidize phenols is not feasible because of very high heating costs. Thus, a stronger oxidant applicable at ambient conditions is desirable. Ozone is a possible candidate because of its high oxidation strength, reasonable cost, ability to break down into harmless oxygen and likelihood of not forming more toxic compounds. Thus, ozonation appears to be an attractive method for treatment of industrial effluents (McCarthy & Smith, 1974; Sliter, 1974). Moreover, it is possible to increase ozone reaction rates and ozone utilization rates by using suitable solid catalysts. But despite the attractiveness of the process, reliable kinetic data on aqueous ozonation are not available and the information on solid catalyzed aqueous ozonation is very limited,
A waste stream rarely, if ever, contains just one pollutant. However, the experiments using actual wastes are not very amenable to kinetic analysis. Furthermore, the results cannot be easily extrapolated to other situations. Carefully designed experiments that allow the determination of kinetic parameters are much more useful. These experiments usually use syntbetic wastes with one or more model pollutants. Such experiments can indicate general results which can be used for optimal treatment of actual wastes. In present work phenol was chosen as the model poilutant and the kinetics of ozone-phenol reaction in aqueous solutions was studied. The possibility of using solid catalysts to enhance the reaction rates was also explored.
933
SURVEY OF PREVIOUS WORK Roth (1947) appears to be the first to have studied the ozonation of phenol in aqueous solution. Roth's work was followed by a number of other invcstigations (Cleary & Kinney, 1951; Niegowski, 1953; Hall & Neilist, 1959; Labine, 1959; Peppier & Fern, 1959) all of which were empirical in nature and did not attempt a detailed study of the parameters governing the reaction rates and efficiency. Eiscnhauer (1968) studied the oxidation of phenol in aqueous solution with a view to identify and evaluate the parameters which affect the reaction. He proposed an empirical rate equation to represent the degradation of aqueous phenol by ozone. His empirical rate constant was dependent on ozone gas flow rate and reactor geomerry. Eisenhauer detected catechol and o-hydroquinone in the reaction mixture and suggested that phenol was consecutively oxidized to muconic acid, maleic acid, oxalic acid and carbon dioxide. Bauch et al. (1970) found that the mole ratio of ozone consumed to phenol was the predominant factor in determining final products. Gould & Weber's (1976)
g34
\l',kxR~,xD G J,)SHI and
ROHERr[_ SHe;lUg, , H
investigation was very similar to Eisenhauer's. except that a phosphate buffer was used to control the pH of
~, o,,,,
~c~ '~"
'~c~'o~et,r
the reaction. Gould and Weber found that the empiri-
r4~ ' L
~
~
cal rate equation proposed by Eisenhauer fit their data and the empirical rate constant increased with increase in the pH of the reaction. Gould and Weber detected the intermediates catechol, hydroquinone, ~,lyoxal, glyoxylic acid and oxalic acid in the reaction mixture. Anderson {19771 found that the reaction rate between ozone and phenolate ions was at least 27 times faster than the rate between ozone and the toolecules of phenol. Neufeld & Spinola {1978) studied the ozonation of liquid waste sample from an experimental coal gasification plant using a packed column with countercurrent flow. The waste composed of simple phenol and polyduric phenols. As the liquid to gas ratio was decreased, there was substantial decrease in phenol with simultaneous increase in concentration of low boiling compounds. Li et al. (1979) eliminated the interference of mass transfer on reaction rate measurement by studying the kinetics of o z o n e - p h e nol reaction with a stopped flow method in h o m o geneous aqueous solutions. They determined that the rate of reaction in early reaction period was first order with respect to b o t h phenol and ozone concentrations. The rate constant was found to increase with both pH and temperature, Very few investigators have explored the possibility of using a catalyst to enhance the rate of oxidation of aqueous phenol by ozone. Furthermore, no attempts were made by these few investigators to obtain conventional kinetic parameters. Eisenhauer (1971) investigated the catalytic action of ferrous sulfate a n d ferrous a m m o n i u m sulfate on ozonation of aqueous phenol. Eisenhauer observed that b o t h the ferrous salts inhibited the reaction. Chen et al. (1970) examined various catalysts to enhance the rate of ozonation of aqueous phenol. Activated Raney-Nickel was found to be the best catalyst out of ten different candidates considered. A few patents (Koezuka et al., 1977; Sata et al., 1977; Basila & Booersma, 1979) have appeared which claim efficient catalysts for the oxidation of aqueous phenol by ozone, In the work described herein, rate constants were determined for the reaction of ozone and phenol in water. Careful account was made of the mass transfer of ozone from gas phase to aqueous phase, and the effect of pH and various soluble salts on the rate constant for phenol ozonation was studied. Rate constants were determined for the solid catalyzed reaction of ozone and phenol in water for four different catalysts,
EXPERIMENTAL SECTION Apparatus Ozone was generated using a Welsbach Model T-816 ozonator. The reactor was a 2 I. resin kettle fitted with an air-tight polypropylene top. Four openings in the top housed a coarse sintered glass sparger for ozone, a ther-
, ~o~yprom,,,,,,J..-i ,op ------- ~ r~rmome,er .glsomp,,ng - / ~ ~or, S~pr z-,,,,, Resin ket'tte SmtePed
',', ,,
',{
U
UI
q _~
j+---
~,os, ------.r-----,~,g,r k.. ,_
)
.J '-~aog,,,,¢ ,,,rr,¢
Fig. 1 The ozonanon reactor mometer, an outlet tube for unreacted ozone and a manometer connecnon. A side opening in the kettle was sealed by a septum through which samples were withdrawn periodically with a hypodermic syringe. The contents of the reactor were stirred by a teflon coated magnetic bar (0.75 cm o.d. x 3.75 cm length) which was rotated by exterhal magnetic field at 250 rev rain- '. See Fig. 1 for a drawing of the reactor. The ozone concentrations in both inlet and outlet gas were monitored using a Dasibi Model 1003-HC ultraviolet spectrophotometer. See Fig. 2 for a schematic diagram of the equipment. Materials All the chemicals used were reagent grade compounds. The supported copper oxide catalyst was Harshaw Cu-0803, T 1/8, 10% CuO on ;,'-alumina. The supported manganese oxide catalyst was Mn-0201. T 1/8, 19% MnO: on ;.,-alumina. The pellets [0.0032 m (l/Sin.) o.d. × 0.0032m (l/8in.l length] of both these catalysts were crushed manually and the portions passing through a 325 mesh sieve were used. The unsupported cuprous oxide was reagent grade chemical, while 1% palladium on alumina was procured from Alfa products, Beverly, Mass. Both these catalysts were fine powders ( - 3 2 5 m~h) and were used as received. The water used was distilled twice. first in metal and then in a Coming Megapure ® all glass still. Analytical method The samples were analyzed for phenol using a gas chromatograph (Hewlett-Packard Model 5710-AI. The column used was a 1.83 x 0.0032 m {6ft x l/Sin, o.d.) stainless-steel column packed with Tenax-GC ® (2,6-diphenyl-p-phenylene oxide polymer} coated with polymetaphenyt ether (5% by weight}. The column temperature was 190°C while the injection port and the detector were both kept at 250'C. A flame ionization detector was used. The carrier gas was nitrogen and the sample size for injection was 1 ,ttl. Procedure The experimental runs were made using potassium dihydrogen phosphate (pH 6--8) or sodium tetraborate (pH = 9.0) as a buffer with 0.01 tool 1- t concentration. In a typical run, 100Oral of reaction mixture, equilibrated to desired temperature and pH, was charged into the reactor. Temperature variation during all experiments was monitored and found to be negligible (4-_0.5:C}. An ozone-oxy-
The kinetics of ozone-phenol reaction in aqueous solutions
935
TO vent
To vent
Reference
gas line
Ivalve Oo-_Lo_._.J
D~
J
.....
L.
gas
Jcy,inder
The
U
valve
, - , -~
I
~
I
I
o.v.
Spact rophotometer
reactor L ~ J Fig. 2. The schematic diagram of the apparatus.
gen mixture of premeasured composition (determined by u.v. spectrophotometer) was introduced into the reactor through a sparger at a metered rate. Representative samples were withdrawn through the sample port at preselected times using a hypodermic syringe. The ozone concentration in the reactor offgas was continuously monitored with the ultraviolet spectrophotometer.
RESULTS AND DISCUSSION
where D^ -- diffusivity of dissolving reactant (ozone), cm2s - t k2 = second order rate constant, cm 3 tool- t cm 2 s [-B]o = maximum (initial) concentration of reactant in liquid phase (phenol), tool cm -3 kL = mass transfer coefficient, cm s-~. For the reaction of ozone with aqueous phenol,
The kinetic parameters were determined by the method outlined in Appendix. A simple second order
DA = 1.743 x 10-s cm 2 s - t from Wilke Chang (1955) correlation kz = l0 s cm 3 m o l - t s- z, typical value
rate expression rVhOtI = -- k z [ P h O H ] [ 0 5 ]
&
[B]o = 1.0632 x 10- 6 tool c m - 3, typical value
was found to describe the reaction adequately, Initially a few experiments were carried out to check for mass transfer limitations. In these experi-
and
ments only the flow rate of ozone-oxygen mixture fed to the reactor was varied keeping everything else same. The results (Table 1) indicated that the mass transfer resistance was not likely to be a limiting factor. The absence of mass transfer limitations was further confirmed by checking the criterion for no reaction in the film developed by Danckwerts (1970). For an irreversible second order reaction the criterion
(1976). Setting these values in the inequality yielded a value of 0.009 for iefthand side. This conclusively proved that the reaction was not mass transfer limited. The effects of the following three variables on the reaction kinetics were studied:
can be reduced to
kL = 0.0142 cm s- t from Shambaugh & Melnyk
(a) The pH of the reaction mixture. (b) The solid catalysts. (c) The presence of certain solutes in the reaction mixture. (a) The effect ofpH. Niegowski (1953), Hall & Nellist (1959) observed that all else being equal, the rate
D^kz[B]o <1 k~
Table 1. The effect of total gas flow rate Experiment No.
Total gas flow rate 1 (STP) rain- t
s tool Phenol mol- t of 03
k2 cm 3 tool- a s" '
17 9 18
0.717 1.433 2.150
0.235 0.226 0.245
0.175 x 106 0.180 x 106 0.183 x 106
The other conditions held constant in these experiments were: temp. = 20"C; pH = 8.0; ozone concentration in the inlet gas = 3~ by weight; initial concentration of phenol -- 1.0632/~M ml- t.
936
5,IAK~RA>:D
O.
]q)SH~ and ROBFRT L SHX~B~L(~H
Table 2. The effect of pH on the reaction kinencs Experiment No.
pH
s mol phenol mot- ~ ozone
13 14 9 15
6.0 7.0 8.0 9.0
0.240 0,240 0.226 0.420
kz cm 3 tool- ~ s 0.09 x l0 ~' 0.i40 x 106 0,180 × I0 "° 0.246 >: 10 +~'
The other conditions for these experiments were: temp. = 20~C: initial phenol concentration -- 1.0632 ,uM ml- ~; ozone concentration in feed gas = 3°~ by weight; total gas flow rate to the reactor = 1.433 1 (STP) rain- t. of oxidation of aqueous phenol by ozone increased with pH of the reaction mixture. Eisenhauer (1971) found that, based on experiments using unbuffered solutions whose initial pH was adjusted, the rate of phenol removal increased about threefold between pH = 3.0 and 10.0. Eisenhauer attributed this increase to the increased concentration of phenolate ions at higher pH values. These ions are more susceptible to attack by ozone. Gould (1971) discarded this hypothesis based on his observations that most of the increase in the rate occurred between pH = 4.0 and 7.5 and that the rate was essentially constant above pH = 8.0. Gould argued that. since the p K , of phenol was about 10,0, the increase in the rate was complete long before phenolate ions attained a significant level relative to phenol and thus, the higher susceptibility of phenolate ion was not the reason for the increase in the rate. To probe this phenomenon further four experiments were conducted over a pH range 6.0-9.0. The results are summarized in Table 2. We see from Table 2 that the rate of ozonation of aqueous phenol increa,~s with p H value above pH = 8.0--contrary to the observations of Gould (1971). Anderson (1977) has reported that the rate of reaction of ozone with phenolat¢ ion was 27 times that of ozone with the phenol molecule. Hence, it appears that phenolate ions are formed as intermediates and ozone preferentially
As shown in Table 3. none of the catalysts had any significant effect on the rate. Sadana & Katzer (t974) found that Harshaw Cu-0803 and Harshaw Mn-0201 enhanced the rate of oxidation of aqueous phenol by oxygen. The catalysts' inactivity in the present study suggests that the mechanism of ozonation is quite different from that of simple oxidation by oxygen. Find. ing a suitable catalyst for a reaction is still more an art than science. (c) The effect of solutes in the reaction mixture. In real life situations waste effluents always have dissolved inorganic material. These solutes sometimes radically affect the reaction kinetics. To determine such effects on the ozonation of aqueous phenol, four experiments were conducted; results are summarized in Table 4. The presence of additional solutes affects the stoichiometry as well as the rate constant. Though no mathematical generalizations could be made, there experiments illustrate that the effect of solutes should be taken into account in the design of ozone comaetots for waste treatment.
reacts with these tons, (b) The effect of solid different catalysts were the rate of ozonation of (1) Harshaw Cu-0803 (2) Harshaw Mn-0201
The literature contains two opposing theories regarding the mechanism of reaction of ozone a n d phenol in water. According to the first theory which was proposed by Bailey (1958), the reaction is ionic in nature. Eisenhauer (1971) confirmed this view based on his experiments, Razumovskii et aL (1972) pro-
catalysts. The following four examined for their effect on aqueous phenol: ( - 3 2 5 mesh), (-325mesh).
(3) Cuprous oxide. (4) 15/o Palladium on alumina.
MECHANISTIC CONSIDERATIONS
Table 3. The effect of catalysts on the reaction kinetics s
Experiment No 5 6 7 8 9
Catalyst Cu20 1% Pd on Alumina Harshaw Cu-0803 Harshaw Mn-0210 None
k2
tool phenol tool- t O~ cm 3 tool- ~s0.230 0.240 0.240 0.243 0.226
0.1B0 0.190 0.170 0.230 0.180
x
x x x x
106 106 106 106 106
The other conditions which were held constant for these experiments were: temp. = 20°C; pH ffi 8.0; initial phe-ol concentration = 1.0632/aM ml- t ; o z o n e concentration in feed gas = 3% by weight; total gas flow rate to the r e a c t o r = 1,433 1 (STP) rain- t.
The kinetics of ozone--phenol reaction in aqueous solutions
937
Table 4. The effect of additional solutes in the reaction mixture Experiment No. 9 10 11 12 20
Additional solute added and concentration None NaCI (1 g 1- t) NaCI (0.5 M I- t) NazCO~ (0.05 M 1- t) NazSO.t (0.05 M I- t)
s k2 mot phenol tool- t O3 cm 3 tool- t s- t 0.226 0.277 0.291 0.335 0.249
0.180 0.180 0.180 0.371 0.283
x x x x x
106 l& l& 106 10~
The other conditions which were held constant in these experiments were: temp. = 20°C; pH = 8.0; initial phenol concentration = 1.0632 pM m l - l ; ozone concentration in the inlet gas -- 3% by weight; total gas flow rate to the reactor = 1.4331 (STP) min-t.
posed a free radical mechanism for ozone-phenol reaction. Based on their own experiments Hoign~ & Bader (1976) supported this theory. Interestingly, Li et al. (1979) have proposed a free radical mechanism with an electrophilic reaction for the formation of initial catechyl radical. In the present work, no separate experiments were carried out to elucidate the mechanism of ozone--phenol reaction in water. However, the following observation can be made. The OH" radicals are known to oxidize carbonate ions and, consequently, the concentration of OH" radicals is reduced whenever carbonate ions are present. Thus, if the ozone-phenol reaction proceeds through the formation of OH" radicals, the rate constant for this reaction should decrease whenever carbonate ions are present. In the present work the presence of sodium carbonate in the reaction mixture increased the rate of the reaction. Thus it appears that the reaction of ozone with aqueous phenol does not proceed through the formation of OH" radicals. CONCLUSIONS The reaction of ozone with phenol in aqueous solution can be adequately represented by a second order rate equation and does not involve OH" radicals. The catalysts which are effective in the oxidation of aqueous phenol by molecular oxygen are not effective in enhancing the rate of ozonation of aqueous phenol. Hence, the mechanism of ozonation is quite different from that of oxidation with simple oxygen. Acknowledgements---The authors wish to thank Professor Chi Tien, Chairman, Chemical Engineering Department, Syracuse University, Syracuse, New York, for many fruitful discussions. REFERENCES Anderson G. L. (1977) Ozonation of high levels of phenol in water. AIChE Syrup. Set. No. 166 73, 265-269. Bailey P. S. (1958) The reactions of ozone with organic compounds. Chem. Rev. 511, 925-1010. Basila M. R. & Booersma F. R. (1979) German Often, 2, 666, 879. Bauch H., Burchard H. & Arsovic H. (1970) Ozone as oxidant for phenol degradation in aqueous solution. Gesundheitsingenieur 91,258-262.
Chen J. W., Chang J. V. & Smith G. V. (1970) Chem. Engng Prog. Syrup. Ser. No. 109 67, 18-26. Cleary E. J. & Kinney J. F. (1951) Findings from a cooperative study of phenol waste treatment. Proc. 6th Purdue Ind. Waste Conf. 76, 158-170. Danckwerts P. V. (1970) Gas-Liquid Reactions, 156 pp. McGraw-Hill, New York. Eisenhauer H. R. (1968) The ozonization of phenolic waste. J. War. Pollut. Control Fed. 40, 1887-1899. Eisenhauer H. R. (1971) Increased rate and efficiency of phenolic waste ozonation. J. War. Pollut. Control Fed. 43, 200-208. ES&T (1976) Impacts of water chlorination. Envir. Sci. Technol. 1O, 20-21. Gould J. P. (1971) Ph.D. Thesis Department of Water Resource Science, University of Michigan, Ann Arbor, Michigan. Gould J. P. & Weber Jr W. J. (1976) Oxidation of phenols by ozone. J. War. Pollut. Control Fed. 48, 47-60. Hall D. A. & Nellist G. R. (1959) Treatment of phenolic effluents. J. appl. Chem. 9, 565--576. Hoign~ J. & Bader H. (1976) The role of hydroxyl radical reaction in ozonation process in aqueous solutions. Water Res. 10, 377--386. Katzer J. R., Ficks H. H. & Sadana A. (1976) An evaluation of aqueous phase catalytic oxidation. J. War. Pollut. Control Fed. 48, 920-933. Koezuka J., Koyama M., Sakurai K. & Sata Y. (1977) Japan Kokai 7708, 649. Labine R. A. (1959) Phenol free waste water. Chem. Engng 66, 114--117. Li K. Y., Kuo C. H. & Weeks Jr J. L. (1979) A kinetic study of ozone-phenol reactions in aqueous solution. AIChE Jl 25, 583-591. McCarthy J. J. & Smith C. H. (1974) A review of ozone and its application to domestic waste water treatment. J. Am. War. Wks Ass. 66, 718--725. Neufeld R. D. & Spinola A. A. (1978) Ozonation of coal gasification plant wastewater. Envir. Sci. Technol. 12, 470--472. Niegowski S. J. (1953) Destruction of phenols by oxidation with ozone. Ind. Engng Chem. 45, 632-634. Peppier M. L. & Fern G. R. H. (1959) A laboratory study of ozone treatment of refinery phenolic wastes. Oil Can. 11, 84-86, 88, 90. Razumovskii S. D., Giobenko G. M, Nikiforov G. A., Gurvich Ya. A., Karelin N. A. & Zaikov G. Ye. (1972) Kinetics of interaction of phenols with ozone in aqueous solutions. Nefiekhimiya 12, 65-68. Roth W. (1947) Ozonation of phenol in water solutions. M.S. Thesis, New York University, New York, NY. Sadana A. & Katzer J. R. (1974) Catalytic oxidation of phenol in aqueous solution over copper oxide. Ind. Engng Chem. Fundam. 13, 127-134. Sata Y., Koyama M., Koezuka J. & Sakurai K. (1977) Japan Kokai 7708, 650.
93~
M~,KARI~.>~DLJ JOSHI and ROBk~i L SH~,t,IB-~Et;'H let
12
E E 8
.
-4,8
:::L
z"
_o
o
6
°\o
~ 4
4~ ¢D
o
TIME,s
Fig. 3. The typical fit obtained. The circles represent the data of experiment 9. T h e continuous curves depict the values calculated with s = 0.226 tool P h O H m o l - ~ O3 kz = 1.8 x 10 ~ cm 3 m o l - t s" 1 and k t --- 0.00334s -~
Shambaugh R. L. & Melnyk P. B. (1976) The influence of spontaneous decomposition and mass transfer upon soluble ozone concentration. Proc. o f International Ozone Institute's Forum on Ozone Disinfection Chicago. Sliter J. T. (1974) Ozone: an alternative to chlorine. J. War. Pollut. Control Fed. 46, 4-6.
where
Spendley W., Hext G. R. & Himsworth F. R. (1962) Sequential application of simplex design in optimization and evolutionary operation. Technometrics 4, 441-461. Wilke C. R. & C h a n g P. (1955) AIChE Jl I, 264.
The second term in the equation (2) represents the spontaneous and simultaneous decomposition o f ozone which is a s s u m e d to take place independent of its reaction with phenol. The value of f(t) can be easily found by a mass balance on gaseous phase. At any t~me t
APPENDIX The reaction between ozone and phenol can be represented by the general reaction
Inflowof ozone mot s - z
O~ + s P h O H --, products s = stoichiometric coefficient, moles of P h O H m o l - ~ of O3. If one assumes that the disappearance of phenol can be adequately represented by a second order rate equation, then dB = -sk2AB (1) dt where B = phenol concentration in wateL m o t c m -3 kz = second order rate constant, cm 3 tool -~ s -~ A = ozone concentration in water, m o l c m - 3 , The change in ozone concentration in the reaction mixture is given by dA = _ kzAB _ kt A + f(t) dt
k t = first order rate constant for the spontaneous decomposition of ozone, s" f(t) = rate of transfer of ozone from gas b u l l i e s per umt volume of reaction mixture, m o l c m - 3 s - ~.
(2)
_
outflowof ozone mol s - '
,...volumeof = I t t ) reaction mixture mol (cm 3 s)- ~ - cm 3
The value of f(t) at any time t can be calculated by monitoting the ozone concentration in reactor off-gas during the experiment. Thus, with the value of k t known from literature or separate experiments, and the value of f(t) known from reactor off-gas data, it is possible to calculate the phenol concentration vs time c u r v e - - i f values of s a n d k2 can be determined. "Best" values of s and k2 can be found by assuming starting values for s and k2 and then carrying out a two dimensional search aimed at minimizing the difference between observed and calculated phenol concentration vs time curve. T h e sequential search method of Spendley et al. (1962) was used to carry out multivariable search. The equations (1) and (2) were sealed before integration to avoid numerical errors. A typical fit obtained is shown in Fig. 3. The values of s and k2 could be determined with an accuracy of two significant digits with the method. The reproducibility of k z was checked by conducting experiments at identical conditions and was found to be in the same range.