Environ. Sci. Technol. 1985, 79, 1206-1213
Conclusion Fill-in with expected values is by far the best estimator. Fill-in with constants can be seen to be, in general, orders of magnitude worse. Appendix Let p* and u* be the estimators for fill-in with expected values. Let f and F be the probability density function and the cumulative distribution function for the standard normal distribution. Then
By use of these formulas and the tables for the MLE, the algorithm d ~ c r i b e d&ove can be implemented. Literature Cited (1) Cohen, A. C. Ann. Math. Stat. 1950, 21, 557-569. (2) Gupta, A. Biometrika 1952, 39, 260-273. (3) Harter, H.; Moore, A. H. Biometrika 1966, 53, 205-213. (4) Sarhan, A.; Greenberg, B. G. Ann. Math. Stat. 1956,27, 427-451; Ann. Math. Stat. 1958,29, 79-105. ( 5 ) Saw, J. Biometrika 1959, 46, 150-159. Dixon, W. J. Ann. Math. Stat. 1960, 31, 385-391. Ipsen, J. Hum. Biol. 1949, 21, 1-16.
Gleit, A. Air Force Off. Sei. Res., [Tech.Rep.] AFOSR-TR (U.S.),in press. Gleit, A. Air Force Off. Sci. Res., [Tech.Rep.] AFOSR-TR (U.S.), in press.
L
f ( ( L- P * ) / U * ) - Np"2 p * ) ' * ~ ~ (-(p~* ) / a * )
1
Received for review July 12,1984. Revised manuscript received March 21,1985. Accepted July 22,1985. This work was sponsored by the Air Force Office of Scientific Research under Contract F49620-82- C-0079.
Decomposition of Ozone in Water in the Presence of Organic Solutes Acting as Promoters and Inhibitors of Radical Chain Reactionst Johannes Staehelld and Jurg Hoignd" Swiss Federal Institute for Water Resources and Water Pollution Control, EAWAG, 8600 Dubendorf, Switzerland
The decomposition of aqueous ozone is generally due to a chain reaction involving -OH radicals. Many organic solutes (impurities) can react with .OH to yield eo2-upon addition of O2 -0, transfers ita electron to a further ozone molecule in a rather selective reaction. The ozonide anion (-Os-) formed immediately decomposes into a further .OH radical. Compounds that convert .OH radicals into ozone-selective .OF, therefore, act ai promoters of the chain reaction. The efficiencies of different .OH to so2-converters (e.g., formic acid, primary and secondary alcohols (including sugars), glyoxylic acid, and humic acids) are tested in the presence of other .OH radical scavengers that do not primarily produce .02-(carbonate, aliphatic alkyl compounds, and tert-butyl alcohol). The derived reaction kinetics allows one to qualitatively interpret the variation of the lifetime of O3found in model solutions and even in natural waters and during drinking water treatment. Introduction The decomposition kinetics of aqueous ozone are of interest because of the wide application of ozone for water-treatment processes (see, e.g., ref 3) and because of their importance for the understanding of the chemistry of atmdspheric water droplets and of other environmental systems (4). 'This publication is dedicated to Prof. Dr. Werner Stumm on the occasion of his 60th birthday (date of submission). It recognizes Stumm's early contribution to this field (I, 2) and his stimulating interest. Thirty years elapsed since Stumm observed and reviewed, in his first EAWAG project, that organic solutes present in lake waters, and even compounds such as sugars, can accelerate the catalytic decomposition of aqueous ozone. We hope that this study now presents him a rationalized answer to his early suggestions. *Present address: Swiss Federal Research Station for Fruit Growing, Viticulture and Horticulture, CH-8820 Wiidenswil, Switzerland. 1206
Environ. Sci. Technol., Vol. 19, No. 12, 1985
Scheme 1. Reactions of Aqueous Ozone in "Pure Water"
1
02
In water, ozone may react directly with dissolved substances, or it may decompose to form secondary oxidants such as .OH radicals, which then themselves immediately react with solutes. These different pathways of reactions lead to different oxidation products, and they are controlled by different types of kinetics (5). Therefore, their relative importance must be known when the oxidation effects of ozone and the rate of ozone consumption are to be predicted or generalized. Early observations of the lifetime of aqueous ozone indicated that the decomposition of the ozone becomes accelerated by increasing the pH (for literature reviews see, e.g., ref 6 and 7). In addition, it became evident that, as suggested by Weiss (8,9), the decomposition of ozone at a given pH is often accelerated by a radical-type chain reaction which in nonpure solutions can be initiated, promoted, or inhibited by various solutes (2,lO-12). Because of the interaction of multiple pathways, the empirical
0013-936X/85/0919-1206$01.50/0
0 1985 American Chemical Society
Scheme 11. Reactions of Aqueous Ozone in the Presence of Solutes M which React with 0, or which Interact with .OH Radicals by Scavenging and/or Converting .OHinto HO,.
02 kinetic laws describing the rate of ozone depletion deduced by different authors disagree even with respect to the kinetic orders of the reactions (1,2, 6, 7). We therefore started a research program to separate the kinetics of the successive individual reaction steps and to investigate their interdependency. In a preliminary study we analyzed the decomposition of ozone in pure water and in aqueous solutions in which radical-type chain reactions were inhibited by -OH radical scavengers such as bicarbonate (13). Bewere the assumed intermediates, we cause .OH and .02then studied the reactions of these species with ozone by producing them independently using pulse radiolyses (14, 15). The interpretation of the results for “pure water” are summarized in Scheme I. When comparing our earlier experimental observations (10, 11, 16-18) with results published by radiation chemists (19-24), we then noticed that those organic solutes which are known to convert .OH radicals into so2-always accelerate the decomposition of ozone unless an ample amount of other radical scavengers is present. The aim of the present publication is therefore to formulate an appropriate reaction model describing the decomposition of aqueous ozone in the presence of promoters and inhibitors and to test its applicability for interpreting the kinetic behavior of ozone in natural waters and wastewaters. Reaction Model Scheme I1 represents the reactions that we assume describe the decomposition kinetics of aqueous ozone in the presence of solutes which interact with the radical chain reactions. I t is based on the following assumptions: Initiation Step. The reaction between OH- ions and ozone (step 1) leads to the formation of one superoxide anion (-0,) and one hydroperoxylradical (HO,.) which are
in an acid-base equilibrium (pK, = 4.8). For this initiation we determined a rate constant for free radical formation of 2 X 70 M-l s-l whereby the factor 2 is due to the fact that two radicals are produced per reaction (13, 25). A comparable rate constant was found by Forni et al. (26) when measurements were made in the high pH range. In addition, solutes M may react with ozone and thereby either consume the ozone by a direct reaction (d) or produce an ozonide ion radical by an electron transfer (d’). Propagation Step. Upon protonation .O, decomposes into .OH radicals (steps 3 and 4) (14). These now react with solutes M. Typical rate constants for reactions of .OH with organic solutes are in the range 108-1010 M-l s-l (29). .OH even reacts with HCO, and CO2- with a rate constant of 2 X lo’ M-l s-l and 4 X lo8 M-’ s-l, respectively. Some functional groups present in organic molecules M are known to react with -OH to form an organic radical which adds O2and then eliminates H02./.0,- in a base-catalyzed reaction (see Figure 1, examples A and B; for literature review, see ref 23). The rate constant with which the .02formed reacts with additional ozone is very high when compared with that of its (slow) reactions with other solutes possibly present in ozonated water (for rate constants, see ref 29). Therefore, the conversions of the less ozonemay selective .OH radical into the highly selective .02promote the chain reaction. Termination Step. Many other organic and inorganic substrates react with .OH radicals to form such secondary radicals which do not predominantly produce H02./.02(see Figure 1,examples C-F). These scavengersgenerally terminate the chain reaction (10). Even .00CH2C00- and .COB-radicals formed when acetic acid or carbonate are used as .OH scavengers do not interact with further ozone (27, 28). Environ. Sci. Technol., Vol. 19, No. 12, 1985
1207
A_ Formic acid I
OH
-02-
02 fast
B. Methanol
Reactions with Solutes. The kinetics of all reactions considered in Scheme I1 are first order with respect to the concentration of M and the oxidant (16-18, 29). The overall rate can therefore be expressed as a sum of the rates with which different types i of solutes M react. The following notations will be used: rate of direct reaction, d, of ozone with solutes (the sum comprises all solute species Mi) rd
= C(kd,&[Mi1[031)
(1)
rate of initiation of chain reaction by M and OH?I
+
E. Bicarbonate and carbonate ion
OH-
+t HP042-
poi
4t
HPOI/
0 05
*/' P = glucose pH.70
/A
o.ooo
5
10
15
20
25
30 mM
0.00
[PI
Figure 5. Rate constant for depletion of ozone vs. promoter concentration (P = methanol and glucose) in the presence of an .OH radical scavenger (S = 0.13 mM tert-butyl alcohol): 6 mM phosphate buffer.
0 1.0 2.0 mM lglyoxylic acid]
Figure 7. Rate constant for depletion of ozone vs. concentration of glyoxylic acld. k'values are corrected for direct reaction of glyoxylic acld with ozone. '
> 0.1 5-1
S-'
0.008 k\Ol
0.004
Flgure 8. Mean kinetlc chain length n for decomposltion of ozone, calculated from measurements of k',,, by using eq 14. Assumption: OH- is the only chain initiator to be accounted for.
The upper limit for the kinetic chain length n can be estimated from experimental k,' (=k'bt) values using eq 14. Because of uncertainties considering the rate of additional initiation reactions, these n values must, however, be regarded as apparent. Figure 6 shows that they vary with pH. As expected, they decrease when the alkyl chains become longer and therefore become a better scavenger for .OH radicals. In the presence of 1 mM ethanol an increase in the phosphate concentration from 0.5 to 50 mM resulted in the elevation of the rate constant kiot for the ozone deto 15 X s-l. This enhancement pletion from 3 X may be due to the fact that the product of the reaction of an -OH radical with phosphate is a phosphate radical that selectively abstracts an H atom standing a to the alcoholic (-OH) group (see Figure 1, scheme F, and literature mentioned above). In this case, phosphate acts as a secondary chain carrier. Glyoxylic Acid as Initiator and Promoter. The direct reaction of ozone with this substrate, determined at high scavenger concentrations (17), is significant but still relatively slow. Figure 7 shows that the acceleration of the decomposition of ozone increased approximately with the square of the concentration of the glyoxylic acid. This is formally expected from eq l l b for the case where the square term kIIM] X k,[M] cannot be neglected. Benzene as a Promoter. The decomposition of ozone in an aqueous solution of benzene is highly reduced by adding .OH radical scavengers (8, 10, 11). It, however, increases with pH with an unusually high slope. On the basis of available literature, the possibility remains that aromatic hydrocarbons convert -OH into other reactive intermediates such as H20z. H202also would act as a secondary chain carrier (13). Humic Acid as a Promoter. In Figure 8, the results from systems containing preozonized humic acids are described. Preozonation was performed to eliminate the sites that exhibit a spontaneous ozone consumption. (In practice, this would correspond to the initial ozone consumption phase observed in a water-treatment plant.) In
0.002
0.OK
Figure 8. Rate constant for depletion of ozone in the presence of preozonated humlc acid (2 mg/L) vs. dilution of tert-butyl alcohol (=l/[S] (pH 8).
ktotl I
Lakewater Greifensee
(DOC-4mgil : j H C O j ] = l m M pH = 7 . 5 )
0.06
0.02
-
Groundwater Oubendorf
( O O C - l . Z m g / l : (HC03-1' 6 m M , pH: 7 . 5 )
OO
0.2
0.4 mM
I9lYCOIl
Figure 9. Rate constant for depletion of ozone in natural waters vs. additional concentrations of glycol acting as promoter.
this system also, addition of an efficient .OH radical scavenger inhibits the decomposition of ozone significantly. This effect decreases proportionally to the dilution of this scavenger. It depends strongly on pH (see also entries in Figure 2). Constituents of Natural Waters as Promoters and Inhibitors. On the other hand, we have shown before (11) that tert-butyl alcohol spiked to natural waters or additional bicarbonate both act as efficient inhibitors for the decomposition of ozone. In addition, decarbonation (with later pH adjustment) before ozonation resulted in a faster ozone depletion (11). These effects were interpreted by assuming radical chain reactions which occur in not fully inhibited waters and which become further inhibited by Envlron. Sci. Technoi., Vol. 19, No. 12, 1985 1211
Table 11. Typical Initiators, Promoters, and Inhibitors for Decomposition of Ozone by Radical-Type Chain Reaction, Encountered in Natural Waters and Wastewaters initiator
promoter
inhibitorC
OHHZOdH02-
aryl-(R)
formate humics (TOC) etc.
formate (humics) 03
etc.
alkyl-(R) HCOMg-OH) or silicon (>Si-OH) are possible adsorption sites for protons, other cations, or anions. It is assumed that ions adsorb to both >Mg-OH and >Si-OH sites as inner-sphere complexes. One valid thermodynamic description of surface adsorption is the constant-capacitance model, which provides a simple, mathematical statement of the relation between proton adsorption and surface charge. Although choice of surface species and values of parameters are model dependent, the constant-capacitance model can provide a self-consistent
0 1985 American Chemical Society
Environ. Sci. Technol., Vol. 19, No. 12, 1985 1213
