Conclusions T h e major crystalline compound of lead in street dusts is PbS04, and this probably arises from water leaching of PbSO4.(NH&SO4 deposited from the atmosphere. Elemental lead appears to be important a t sites where vehicles are started from cold. Theslv compounds probably represent the best indication of crystalline compounds for use in assessing the hazards associated with ingestion of street dusts. I t is, however, concluded that crystalline compounds of lead can account a t most fclr only a few percent of total lead in the samples examined, and that alternative approaches to speciation of t h e lead are required.
demic Press: New E'i,rk. 1974. (5) chamberlain, A.C.; Heard, hl. J.: Little, P.; Newton. D.; \Yells, A. C.: Wiff'en, R. I). H.M.S.O.. London, 1978. L.K.A.E.A. Report, AERE-R 9198. ( 6 ) Harrison, R. M. J . Entsiron. Sci. Health, Ser. A 1976, 1 I , 417. ( 7 ) Olson, K. LV.; Skogerboe, R. K. EnL'iron. Sci. Techno/.1975, 9, 227. (8) Harrison, R. M.: Laxen. D. P. H. Water Air .Soil I'(~i/ut.1977,X, 487. (9) Moller. C.K.Acta Cheni. Scand. 1984,8, 81. (10) Rameau, J . T.L. B. Proc. I n t . .Sj,mp.Enciron. H c a i t h A.cpects Lead 1972, 189. (11) International Lead Zinc Research Organization Inc. "I.ead Chemicals"; New York. ( 1 2 ) Lott, P. F.; Foster. R. I,. ,Vat/. Bur. Stcind. ( C . S . )S p t Pubi. ~
A c k n o u ~ i e d g m e i ts ? T h e authors are grateful to Dr. I. F. Ferguson of the U.K.A.E.A., Springfields, for assistance in X R D data interpretation, and to Mrs. J . LL LValsh who performed some of the experimental w x k .
L i t e r a t u r e Cite($ (1) Duggan, hl. d.: Williams, S.Sci. Tot. Ent'iron. 1977, 7, 91. (2) Muskett, C. -J.;Roberts, L. H.; Page. B. J . Sci. Tot. Ent3iron. 1979, 1 1 , 73. ( 3 ) Harrison, R. !VI. .s'ci. Tot. Ent'iron. 1979, 1 1 , 89. (1)LValdron, H . A: Stiii'en, U."Sub-Clinical Lead Poisoning"; Aca-
(15) Biggins, P. D. E.: Harrison. R. M. EnL'iron. S c i . T ~ h n ( ~1979, l. 13, 558. (16) Hem, .I. D.; Durum, h',H. J . Am. Water Work.! Assoc. 1973,65, 562. (17) Zimdahl, R. L.; Skogerboe, K. K. Enciron. S c i . Tcchnol. 1977, 1 1 , 1202.
Recciced for r ~ c i e t i , J u n e18, 1979. Accepted Lkcemhrr 3, 1979. T h e prorision o / a Science Rehearch Council S t u d e n t s h i p ( t o P.D.E.H.) is grate f u / / y ac knoii,/edged.
A Mechanistic Kinetic Model for Chlorine Disinfection Charles N. Haals Department of Chemical and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, N.Y. 12181
A kinetic model for t h e inacti\.ation of virus by HOC1 has been derived assuming t h e existence of an intermediate disinfectant-organkm complex that governs the rate of microbial inactivation. T h e model predicts the existence of a lag phase prior to onset of logarithmic decay. T h e model has been tested against previously reported data on inactivation of poliovirus type I (Mahoney), and appears to satisfactorily describe these data. Other phl:nomenological observations appear to be consistent with this formulation. Traditionally, the kinetics of inactivation of microorganisms by chemical disinfectants have been modeled by Chick's law. In the case of chlorine, deviation from Chick's law due to possible clumping or multihit phenomena has been reported ( I , 2). Recently, work has been reported demonstrating t h a t inactivation kinetics of single viron preparations of poliovirus type I (Mahone:y) by chlorine a t low p H resemble such multihit or multitarget models (2).It is the purpose of this paper to present a simple model for such inactivation curves with "shoulders", and to demonstrate the observed fit of this model to data in t h e literature.
Deriuation of t h p Model I t is assumed that a homogeneous suspension of microorganisms is exposed to disinfectant a t zero time. T h e bulk solution concentration of disinfectant remains practically constant throughout the course of the experiment. It is further assumed that inactivation occurs as a two-step processdisinfectant molecules (C) are bound a t some receptor sites (S)in a reversible manner; the amount of bound disinfectant then determines the rate of microorganism inactivation. I t is assumed t h a t there is a uniform number of binding sites per organism, 3, and t h a t both viable and killed microorganisms bind disinfectant in a uniform and constant manner. T h e process may be depicted as a chemical reaction in the following 0013-936X/80/0914-0339$01.00/0
@
1980 American Chemical Society
manner: C
+S
kl
h?
C S +inactive
microbe
k-i
If the disinfectant concentration is regarded as practically constant, and if it assumed t h a t the inactivation step is first order in viable microorganism concentration ( N ) ,then it can be shown t h a t the following integrated rate law applies ( 3 ) :
This model has two salient features important to the current analysis. First, it predicts an apparent lag which is concentration dependent. Second, it predicts that the rate of inactivation, defined as the slope of the linear portion of the curve, can be given as a Monod-type function:
rd = k & d / ( C
+ Kn)
(2)
Discussion Before demonstrating agreement of m'odel predictions with previously published results, it is necessary to review evidence for the plausibility of a disinfectant-organism bound complex. Early workers attempted to explain the mode of action of chlorine upon microorganisms as being based upon the greater uptake of the undissociated hypochlorous acid vis-&vis hypochlorite anion ( 4 ) . Chang ( 3 )observed a yellowing of the interior of cysts of E n t a m o e b a histolj'tica upon exposure to chlorine, which was correlated qualitatively with inactivation, and which was attributed to the intracellular localization of chlorine. Using "%I, Friberg (6, 7) observed the association of free and combined chlorine with cells of Escherichia coli and Staphj,lococcus a u r e u s . More recently, Haas ( 8 )attributed the mode of action of chlorine on E. coli, C a n d i d a p a r ~ p d o s k and , Mycobactprium f o r t u i t u m to cell-associated Volume 14, Number 3, March 1980
339
chlorine, which was formed during the time course of exposure to chlorine: and could be modeled by either the Langmuir or Freundlich isotherms. Dennis (9) noted that the rate of incorporation of :%l from labeled solutions of hypochlorous acid or hypochlorite by bacteriophage f 2 was directly correlated to the rate of viral inactivation. It, therefore. seems plausible that a disinfectant-organism coniplex may be an intermediary in the inactivation process. A test of the utility of this model is possible using recent data of Floyd et al. ( I 0 ) . These workers used poliovirus type I ( Mahoney) in a well-controlled experiment, in which chlorine demand free preparations of predominantly single particles were exposed to various concentrations of hypochlorous acid a t p H 6 and various temperatures. T h e data of these workers indicate the existence of a lag, on the order of seconds, before the onset of logarithmic decay. T h e data of Floyd et al. (IO) were analyzed in the following manner: The rate of viral inactivation at each temperature (2, 10, 20, and 30 “C)for several disinfectant concentrations as shown in Figure ,5 of their paper was used to determine K D and h2/3 from a Lineweaver-Burk transformation of Equation 2. T h e observed lag times reported in Figures 1-4 of Floyd et al. ( I O ) were used in conjunction with estimates of K D to estimate h l . The geometric mean of h l values for various concentrations a t a single temperature was then taken as an estimate of the true value of h 1 a t that temperature. Survival data from Figures 1-4 of Floyd et al. ( I O ) were then used, in conjunction with estimates of K D and h i , and in Equation 1 to obtain a best fit value of h28. Values of the parameters in Equation 1 obtained from analysis of the results of Floyd et al. (10)are shown in Table I. T h e values in Table I were used in Equation 1 to calculate predicted survivals for each concentration-contact time combination. Correlations between the logarithms of survivals a t each of the four temperatures were very good, ranging from 0.969 to 0.981. These are each significant a t the 0.001 level for n - 4 degrees of freedom ( n = 12-16). Slopes of regression lines were not significantly different from 1.0, and y intercepts were not significantly different from zero. I t is, therefore, concluded that the proposed model is capable of describing the qualitative and quantitative aspects of inactivation of poliovirus type I (Mahoney) by hypochlorous acid to a significant degree of precision. The apparent thermal effects upon the parameters in Table I are consistent with the model. For example, the apparent enthalpy of reaction for K D is f 2 3 kcal/mol, indicating that the binding reaction (Le., the reverse of the dissociation reaction) is moderately exothermic. In addition, the activation energy for binding ( h J is 17.8 kcal/mol. These two values are consistent with the hypothesis of a chemical complex as a n intermediate to inactivation. T h e activation energy for the quantity hpp is relatively low (5.85 kcal/mol), and possibly diffusional in nature. CVhile no studies appear to have been conducted on the dynamics of W : C1during inactivation of poliovirus type I, future work using this technique should be capable of directly testing the validity of these observations. In addition to the reasonable fit to previously reported data on HOC1 inactivation of poliovirus by Floyd et al. ( I O ) . the model appears capable of explaining certain other phenomenological observations of disinfection kinetics. Engelbrecht et al. ( I I ) observed a plateau of the inactivation rate of poliovirus type I with increasing chlorine concentration. Bi i a n o et al. (12) reported a plateau of the inactivation rate in the case of poliovirus contacted with C102. Previous data by Floyd et al. (13)indicate that both t h e plateau effect and the presence of a shoulder may be real phenomena in the inactivation of poliovirus by various bromine species. 340
Environmental Science & Technology
Table 1. Kinetic Coefficients for HOC1 Inactivation O C
ki, LIpM-3
k2& L /e
2 10 20 30
0.00279 0.00973 0.0238 0.0389
1.335 0.721 1.490
temp,
?,
na5
KD, P M I L
51.8 12.3 9.7 2.9
Earlier workers (14-16) have attempted to describe the shoulder, or apparent lag phase, by a semiempirical model of the following type:
In several cases, in which a shoulder is found, m has been reported to be on the order of 1.3-2.2 ( I 5 , 16). If the product h l t t C Kl,) is sufficiently small, the exponential term in Equation 1 may be replaced by the first three terms of a series expansion. If this approximation is made, the following is obtained:
+
(4)
Therefore, the common practice of rationalizing aberrant survival curves by plotting log survival vs. t 2 ( 1 6 ) appears consistent with the derived model. Conclusion Analysis of previously reported data for the inactivation of poliovirus type I (Mahoney) by chlorine at p H 6 according to a mechanistic model derived in this paper has yielded good correspondence between theory and observed results. Thermal properties of the model parameters are consistent with the hypothesis that a chlorine-microorganism complex is a n important intermediate in the inactivation process. The derived model also appears to satisfactorily explain certain other phenomena of disinfection kinetics.
L i t e r a t u r e Cited (1) Wei, J. H., Chang, S. L., in “Disinfection: Water and Wastewater”, .Johnson. J . D., Ed., Ann Arbor Science, Ann Arbor, Mich., 1975, Chapter 2. ( 2 ) Young, D. C., Sharp, D. G., Appi. Enairon. iMicrobiol., 33, 168 11977). ( 3 ) Bailey, J . E., Ollis, D. F., “Biochemical Engineering Fundamentals”, McGraw-Hill, New York, 1977, pp 103-4. (4) Fair, G. M., Morris, J. C., Chang, S.L., Weil, J.,Burden, R. P., J . A m . Water Works Assoc., 40,1051 (1948). (5) Chang, S. L.. J . A m . Water Work ( 6 ) Friberg, L., Acta Pathol. Microbiol. Scand., 38, 135 (1956). ( 7 ) Friberg, L., Acta Pathol. Microbiol. Scand., 40,67 (1957). (81 Haas. C. N.. Ph.D. Thesis. University of Illinois a t UrbanaChampaign, 1978. (9) Dennis, W., Sc.D. Thesis, Johns Hopkins University, 1977. (10) Floyd, R., Sharp, D. G., Johnson, J.D., Enciron. Sci. Technol., 13,438 (1979). 111) Eneelbrecht. R. S.. Weber. M.J.. Schmidt, C. A., Salter, B. L., “Virus Sensitivity of Chlorine Disinfection of h’ater Supplies”, Report No. EPA-600/2-78-123, US.Environmental Protection Agency, Cincinnati, Ohio, August 1978. (12) Brigano, F. A. O., Scarpino, P., Cronier, S.,Zink, M. L., Hoff, J. C., paper presented at the 78th Annual Meeting of the American Society for Microbiology, 1978. (13) Floyd, R., Sharp, D. G., .Johnson, J . D., Enuiron. Sci. Techno!., 12, 1031 (1978). (14) Horn, L. W., “Proceedings of the National Specialty Conference on Disinfection”, American Society of Civil Engineers, New York, 1970, p 515. 1151 Severin. B. F.. M.S. Thesis. Universitv of Illinois a t UrbanaChampaign, 1975. (16) Fair, G. M., Geyer, J. C., Okun, D. A., ”LVater and Waste Engineering”, h‘iley, New York, 1968. Receiued for reuieu M a y 4 , 1979. Accepted December 12, 1979.
