catalytic effect of dissolved humic acids on the chemical degradation of phenylurea herbicides

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Pest Management Science Pest Manag Sci 64:768–774 (2008) Catalytic effect of dissolved humic acids on the chemical degradation of phenylurea herbicides Stefano Salvestrini, Sante Capasso and Pasquale Iovino Department of Environmental Sciences, Second University of Naples, via Vivaldi 43, 81100 Caserta, Italy Abstract BACKGROUND: Although biodegradation seems to be the main cause of herbicide degradation, abiotic degradation can also be important for chemicals such as phenylureas, which are subject to catalysed soil reactions. The aim of this work is to investigate the effect of dissolved humic acids (HAs), normally present in natural waters, on the hydrolysis of phenylurea herbicides, and it presents a kinetic model that takes into account the role of adsorption. RESULTS: The linearity of the adsorption isotherms indicates that phenylurea–humic acid interaction can be considered in terms of a repartition-like equilibrium of phenylurea between water and HAs. Kinetic experiments show that the degradation rates of phenylureas increase with HA concentration. CONCLUSION: The kinetic equation adopted adequately describes the experimental data trend, allowing the evaluation of the catalytic effect of HAs on the chemical degradation of phenylureas. Carboxyl groups of HAs seem to play a leading role in the catalysis. The kinetic equation derived in this work could be helpful in predicting the persistence of phenylureas and of related compounds in natural water. 2008 Society of Chemical Industry Keywords: phenylureas; abiotic degradation; humic acids; adsorption; kinetic equation 1 INTRODUCTION Phenylureas are chemical compounds utilised in agriculture as herbicides to preserve crops from the nutritional competition of weeds. In spite of their proved effectiveness, their abuse has led to serious damage to the environment. Once their task is accom- plished, these molecules are considered undesirable compounds in the environment owing to their harm- ful effects on the health of living organisms, including humans. Although biodegradation seems to be the main cause of herbicide degradation, 1–6 abiotic degradation can also be important for chemicals such as phenylureas, which are subject to catalysed soil reactions. 7,8 Among the various abiotic processes affecting the fate of agrochemicals in the soil, adsorp- tion–desorption is important since this controls the movement, persistence and degradation of agrochemicals. 9–11 Therefore, it is clear that, in order to determine the risks of a phenylurea (or its per- sistence, mobility, etc.), adsorption–desorption and abiotic degradation cannot be neglected. A previ- ous study 12 of abiotic degradation of phenylureas in soil/water systems showed that the reaction rate of this process was correlated with the soil organic matter content, although it was not clarified which fraction of this was responsible for the reaction. Among the various fractions of soil organic matter, humic substances are the most abundant, and are closely connected to soil fertility. 13 Humic substances are natural polymers of aromatic blocks, characterised by a broad molecular mass distribution, high chemical heterogeneity and acidic character. Humic substances include humic acids (HAs), which are components soluble in water at neutral and basic pH. HAs can be found in natural water, and in many cases their amount is particularly high and not acceptable for drinking water. Interaction with the core of HA molecules may also increase the concentration of hydrophobic pollutants in surface water above their solubility in pure water. 14 A previous study of phenylurea degradation in a homogeneous water phase in the presence of bifunctional buffers 15 has shown that, depending on pH and buffers, the reaction starts along parallel routes, each leading to the same intermediate zwitte- rion. Bifunctional acid–base buffers, HCO 3 /CO 3 2, H 2 PO 4 /HPO 4 2and CH 3 COOH/CH 3 COO , are particularly efficient catalysts, and at high buffer concentrations, as well as at pH <3 or >12, the breakdown of the zwitterion is rate determining. Correspondence to: Stefano Salvestrini, Department of Environmental Sciences, Second University of Naples, via Vivaldi 43, 81100 Caserta, Italy E-mail: [email protected] (Received 28 June 2007; revised version received 16 November 2007; accepted 17 November 2007) Published online 5 March 2008; DOI: 10.1002/ps.1556 2008 Society of Chemical Industry. Pest Manag Sci 1526–498X/2008/$30.00

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Pest Management Science Pest Manag Sci 64:768–774 (2008)

Catalytic effect of dissolved humic acidson the chemical degradation ofphenylurea herbicidesStefano Salvestrini,∗ Sante Capasso and Pasquale IovinoDepartment of Environmental Sciences, Second University of Naples, via Vivaldi 43, 81100 Caserta, Italy

Abstract

BACKGROUND: Although biodegradation seems to be the main cause of herbicide degradation, abioticdegradation can also be important for chemicals such as phenylureas, which are subject to catalysed soil reactions.The aim of this work is to investigate the effect of dissolved humic acids (HAs), normally present in natural waters,on the hydrolysis of phenylurea herbicides, and it presents a kinetic model that takes into account the role ofadsorption.

RESULTS: The linearity of the adsorption isotherms indicates that phenylurea–humic acid interaction can beconsidered in terms of a repartition-like equilibrium of phenylurea between water and HAs. Kinetic experimentsshow that the degradation rates of phenylureas increase with HA concentration.

CONCLUSION: The kinetic equation adopted adequately describes the experimental data trend, allowing theevaluation of the catalytic effect of HAs on the chemical degradation of phenylureas. Carboxyl groups of HAs seemto play a leading role in the catalysis. The kinetic equation derived in this work could be helpful in predicting thepersistence of phenylureas and of related compounds in natural water. 2008 Society of Chemical Industry

Keywords: phenylureas; abiotic degradation; humic acids; adsorption; kinetic equation

1 INTRODUCTIONPhenylureas are chemical compounds utilised inagriculture as herbicides to preserve crops from thenutritional competition of weeds. In spite of theirproved effectiveness, their abuse has led to seriousdamage to the environment. Once their task is accom-plished, these molecules are considered undesirablecompounds in the environment owing to their harm-ful effects on the health of living organisms, includinghumans.

Although biodegradation seems to be the maincause of herbicide degradation,1–6 abiotic degradationcan also be important for chemicals such asphenylureas, which are subject to catalysed soilreactions.7,8

Among the various abiotic processes affectingthe fate of agrochemicals in the soil, adsorp-tion–desorption is important since this controlsthe movement, persistence and degradation ofagrochemicals.9–11 Therefore, it is clear that, in orderto determine the risks of a phenylurea (or its per-sistence, mobility, etc.), adsorption–desorption andabiotic degradation cannot be neglected. A previ-ous study12 of abiotic degradation of phenylureas insoil/water systems showed that the reaction rate of thisprocess was correlated with the soil organic matter

content, although it was not clarified which fraction ofthis was responsible for the reaction.

Among the various fractions of soil organic matter,humic substances are the most abundant, and areclosely connected to soil fertility.13 Humic substancesare natural polymers of aromatic blocks, characterisedby a broad molecular mass distribution, high chemicalheterogeneity and acidic character. Humic substancesinclude humic acids (HAs), which are componentssoluble in water at neutral and basic pH. HAs can befound in natural water, and in many cases their amountis particularly high and not acceptable for drinkingwater. Interaction with the core of HA moleculesmay also increase the concentration of hydrophobicpollutants in surface water above their solubility inpure water.14

A previous study of phenylurea degradation ina homogeneous water phase in the presence ofbifunctional buffers15 has shown that, depending onpH and buffers, the reaction starts along parallelroutes, each leading to the same intermediate zwitte-rion. Bifunctional acid–base buffers, HCO3

−/CO32−,

H2PO4−/HPO4

2− and CH3COOH/CH3COO−, areparticularly efficient catalysts, and at high bufferconcentrations, as well as at pH <3 or >12, thebreakdown of the zwitterion is rate determining.

∗ Correspondence to: Stefano Salvestrini, Department of Environmental Sciences, Second University of Naples, via Vivaldi 43, 81100 Caserta, ItalyE-mail: [email protected](Received 28 June 2007; revised version received 16 November 2007; accepted 17 November 2007)Published online 5 March 2008; DOI: 10.1002/ps.1556

2008 Society of Chemical Industry. Pest Manag Sci 1526–498X/2008/$30.00

Degradation of phenylureas by humic acids

Since HAs are characterised by the presenceof acidic functional groups such as carboxyls andphenols, they could promote the degradation ofphenylureas by a similar mechanism.

On this basis, the goal of this work was to investigatethe effect of dissolved HAs on the hydrolysis ofphenylureas. In order to evaluate the reaction rate ofphenylureas in the presence of dissolved humic acids, akinetic model proposed for a heterogeneous soil/watersystem12 was adapted to a homogeneous humicacid/water system. The possible role of adsorptionprocesses was also considered.

2 MATERIALS AND METHODS2.1 ChemicalsCommercial samples of humic acids were pur-chased from Fluka (Switzerland). Diuron [3-(3,4-dichlorophenyl)-1,1-dimethylurea], isoproturon [3-(4-isopropylphenyl]-1,1-dimethylurea], fenuron (3-phenyl-1,1-dimethylurea), 3,4-dichloroaniline, 3-iso-propylaniline and aniline were supplied by Dr Ehren-storfer (GmbH, Germany). Dialysis tubes were fromSpectrum (California, USA). All the other chemicalswere from Sigma-Aldrich (Missouri, USA).

2.2 Humic acid purificationA quantity of 10 g of HA was suspended in 1 L of watercontaining 10 mL of concentrated hydrofluoric acidand 10 mL of concentrated hydrochloric acid. Aftervigorous stirring for 1 day, the mixture was filtered,the precipitate was washed with 1 M hydrochloric acidand water and it was finally suspended in 0.8 L ofwater. A suitable volume of 1 M aqueous potassiumhydroxide was added to the suspension to bring the pHto 9.0. After 1 day, the mixture was filtered and storedin a refrigerator for 1 week after bringing the pH to 1.5by adding concentrated hydrochloric acid. Afterwards,the purified HA was collected by centrifugation andwashed with water. HA was introduced in a dialysistube (molar mass cut-off = 3500 Da) and dialysedagainst distilled water until no significant change wasobserved in the conductance of the water externalto the dialysis bag (<100 µS cm−1 day−1). Finally, thepurified HA was collected by lyophilisation and ovendried at 40 ◦C. The elemental contents, determinedwith a CHN elemental analyser, were: C = 63%,H = 5% and N = 3%. The ash content, determinedby keeping the sample in an oven at 600 ◦C for 6 h,was <0.1%, against a value of 20% declared by theproducer for the non-purified HA sample.

2.3 Phenylurea measurementsHPLC analysis was performed on a Waters instrumentequipped with a 515 pump system, a 2486 dual λ

detector and a precolumn containing a C18 cartridge,connected to a reversed-phase column (3.9 × 150 mm,4.6 mm ID). Phenylureas were eluted by the followinglinear gradient: 10–80% acetonitrile in water in6 min, isocratic conditions for 5 min and return to

initial conditions in 2 min, flowrate 1 mL min−1,λ = 248 nm.

GC/MS analysis was performed on a Clarus500 GC/MS (Perkin Elmer). Sample solutions wereextracted with ethyl acetate and concentrated underreduced pressure. Gas chromatographic measure-ments were performed with a capillary column DB-5(30 m × 0.25 mm × 0.25 µm) with a helium flowrateof 1 mL min−1.

2.4 Adsorption isothermsThe phenylurea adsorption experiments on HAswere carried out utilising the well-known biochemicaltechnique of equilibrium dialysis.16

The experiments were conducted utilising a solidsample of HA purified as detailed in Section 2.2,mixed with an aqueous solution of KH2PO4 0.5 M andK2HPO4 0.5 M and kept under agitation for 24 h. Themixture was filtered and the HA concentration wasdetermined by spectrophotometry at 450 nm (PerkinElmer Lambda 40), according to the proceduredeveloped in a previous work.17 Aliquots of 10 mLwere introduced in dialysis tubes, cut-off 3500 Da.The tubes containing the HA solution were dialysedagainst an aqueous solution of KH2PO4 0.5 mM andK2HPO4 0.5 mM and subsequently dipped in 30 mL ofa phenylurea solution buffered with phosphate buffer.The phenylurea concentration outside the tubes wasperiodically monitored by HPLC analysis accordingto the experimental procedure in Section 2.3 untilequilibrium was achieved. Since the dialysis membranewas permeable to the phenylureas tested but not toHAs, the adsorption capacity of HAs was determinedfrom the difference in phenylurea concentration beforeand after equilibrium.

2.5 Kinetic experimentsA quantity of 5 mL of aqueous solutions of the selectedphenylureas containing sodium nitride (5 mg L−1) asa sterilising agent were mixed with different amountsof HA solution; after bringing the final sample volumeto 10 mL with bidistilled water, the HA concentrationranged between 0.01 and 5 g L−1. The samples werestored in the dark at 40 ◦C, and aliquots were removedand analysed by HPLC at set intervals (see Fig. 3).The temperature was set to a value slightly higherthan natural conditions in order to obtain a quickerresponse to HA catalysis.

3 RESULTS AND DISCUSSION3.1 Phenylurea adsorption on HAsFigure 1 shows the adsorption isotherms on dissolvedhumic acids of three selected phenylureas (diuron,isoproturon and fenuron) obtained by dialysis experi-ments at 40 ◦C and pH 7.0, as given by

qe = (C0 − Ce)Vw/mHA

Pest Manag Sci 64:768–774 (2008) 769DOI: 10.1002/ps

S Salvestrini, S Capasso, P Iovino

0

1000

2000

3000

4000

5000

6000

7000

0 5 10 15 20 25 30

q e (

mg

kg-1

)

Ce (mg L-1)

Figure 1. Adsorption isotherms of diuron (ž), isoproturon (�) andfenuron (♦) on dissolved HAs (40 ◦C, pH 7.0).

where qe is the adsorbate amount per HA mass unit,C0 is the initial phenylurea water concentration, Ce isthe equilibrium concentration, Vw is the water volumeand mHA is the HA mass. The lines in the figure derivefrom the least-squares fit of qe and Ce to the linearequation qe = KCe, where the slope of the line, K ,represents the equilibrium adsorption coefficient.18

Table 1 reports the calculated K values and thestatistical parameter R2, whose values, being near to1, indicate that the experimental data are in goodagreement with a linear trend. This result suggests thatphenylurea–humic acid interaction can be described interms of a repartition-like equilibrium of phenylureasbetween water and HAs.

Table 1. Dissolved HA–water partition coefficient K of diuron,

isoproturon and fenuron

Compound K (L kg−1) R2

Diuron 227 (±30) 0.98912Isoproturon 186 (±8) 0.99563Fenuron 85 (±4) 0.99158

As expected for neutral molecules in the presence ofan organic sorbent, the slope of the curves increaseswith the hydrophobicity of the phenylurea.9,19

3.2 Chemical degradationExperiments in sterile soil/water mixtures12 haveshown that the chemical degradation of phenylureasirreversibly gives aniline derivatives as the onlyproducts containing the phenyl ring. Likewise, inthe presence of dissolved HAs, the authors haveobserved, during the kinetic runs, the formation of 3,4-dichloroaniline, 3-isopropylaniline and aniline fromdiuron, isoproturon and fenuron respectively (Fig. 2).

The presence of these compounds was confirmedby HPLC co-injection of the pure compounds andby GC-MS analysis. Their water concentration is notstoichiometrically related to the rate of phenylureadissipation, as aniline and its derivatives bindirreversibly to HAs.20–23 No biotic metabolites suchas N-demethylated phenylureas24,25 were detected,which suggests that phenylurea reactivity can beascribed solely to abiotic factors.

The results presented in Section 3.1 indicate thatHAs adsorb phenylureas. This implies that, accordingto the adsorption equilibrium, phenylureas in solution

Figure 2. Typical chromatograms for phenylurea degradation in the presence of HAs (after 220 days at 40 ◦C).

770 Pest Manag Sci 64:768–774 (2008)DOI: 10.1002/ps

Degradation of phenylureas by humic acids

in the presence of HAs are in both their free and linkedform.

In accordance with the reaction mechanism pro-posed by Salvestrini et al.,15 which asserts that pheny-lurea degradation proceeds through the formation ofa zwitterionic intermediate, spontaneous degradationof phenylureas in the HA–water system is likely tobe mainly restricted to the free molecules in solution.The adsorbed phenylurea does not react because thelow dielectric constant of HAs is expected to inhibitthe formation of the zwitterion.

Kinetic experiments conducted by HPLC to mon-itor phenylurea degradation must take into accountthat, during analysis, the weak phenylurea–humic acidadducts, interacting with the mobile and the station-ary phase of the chromatographic column, may breakup. The measured concentration at the outlet of thechromatographic column derives from the sum of thephenylurea adsorbed and its free fraction in solution.Consequently, the time dependence of the measuredphenylurea concentration is not strictly related to thedegradation reaction rate.

Moreover, the adsorption/desorption process alsotakes place during the chemical reaction. As thereaction proceeds, a part of the adsorbed herbicideis released in order to maintain the adsorptionequilibrium controlled by the equilibrium adsorptioncoefficient, and this fact accentuates the apparentslower reactivity in solution.

Assuming that the reaction takes place only whenthe reactant is not adsorbed, as in the scheme

Phenylurea (HAs)K→← Phenylurea (water)

↓k

Degradation products

and that phenylurea hydrolysis is a first-order reactionand phenylurea adsorption on HAs is described by alinear isotherm (qe = KCe), it is possible to estimatethe reaction rate constant k by the following equation(derived in the Appendix):

Cmeas = C0 e− kt

1+K[HA] (1)

where Cmeas is the phenylurea concentration measuredat the outlet of the chromatographic column, K is theequilibrium adsorption constant, [HA] is the dissolvedHA concentration, C0 is the initial phenylureaconcentration in the solution before interacting withHAs and t is the time after partition equilibrium hasbeen reached.

The ratio Cmeas/(1 + K[HA]) represents the freephenylurea concentration at the equilibrium in thewater phase.

Figure 3 illustrates the time dependence of themeasured diuron concentration in the water phase.The curve, obtained by the least-squares fit of Cmeas

and t to equation (1), is in good agreement with

0

5

10

15

0 50 100 150 200 250 300 350

Cm

eas

(mgL

-1)

time (days)

Figure 3. Time dependence of the free diuron concentration in thewater phase (40 ◦C, [HA] = 500 mg L−1).

Kinetic model for HA/water systems

First order reaction

Maximum limit value expectedin

homogeneous phase

0

0.002

0.004

0.006

0.008

0 2000 4000 6000 8000 1 104

k (d

ays-1

)

[HA] (mg L-1)

Figure 4. Kinetic rate constant of diuron in the HA/water system,estimated by equation (1) and by a simple first-order kinetic equation.

the experimental data. The kinetic equation alsogives satisfactory results for all the other samples,thus permitting the determination of the kinetic rateconstant of the reaction.

Figure 4 shows the dependence of the kineticrate constants determined by equation (1) on theconcentration of HAs added to the reacting mix-ture. The increment of the kinetic rate constantwith [HA] is a clear indication that HAs catalysephenylurea degradation. Therefore, the presence ofHAs has a dual effect on phenylureas, determiningboth their adsorption and promoting their degrada-tion.

If the breakdown of HA–phenylurea adducts isignored during the chromatographic analysis, athigh [HA] the kinetic rate constant (determinedaccording to a simple first-order reaction) seems tostabilise around the value of 0.0022 day−1. On theother hand, utilising equation (1), the kinetic rateconstant at high [HA] tends to have a definitelyhigher value that is very close to the maximumvalue expected in homogeneous systems in the sameconditions of temperature and pH. This indicatesthat the degradation reaction in the presence ofdissolved humic acids takes place by a mechanismanalogous to that determined in water solutionin the presence of buffers with low molecularweight.15

Pest Manag Sci 64:768–774 (2008) 771DOI: 10.1002/ps

S Salvestrini, S Capasso, P Iovino

The curves in Fig. 4 were obtained by least-squaresfits of the observed rate constant k and catalystconcentration data to the equation

k = k0 + kM[HA]a + [HA]

where k0 is the rate constant at zero HA concentration,kM/a is the slope at zero HA concentration andkM + k0 is the limiting value of the rate constantreached at high HA concentration.

Bifunctional buffers such as phosphate, carbonateand acetate were reported to be more efficientcatalysts than monofunctional buffers, probably owingto their capacity to promote a proton switch in thephenylurea molecule.15 Similarly, it is possible thatacidic functional groups of HAs, such as carboxylicgroups, are responsible for the HA catalytic effect onphenylurea degradation.

In order to validate this hypothesis, the catalyticHA activity was normalised for the carboxylic groupcontent (using the literature value of 3.1 mol kg−1

HAs)26 and compared with acetic acid, which hadbeen demonstrated to be a very efficient catalyst forphenylurea hydrolysis.15 The results, shown in Fig. 5,indicate that, within the experimental errors, HAsand acetic acid have a comparable catalytic activity,suggesting that carboxyl groups play a leading role inHA catalysis.

In order to verify that the results obtained fordiuron could be applied to other phenylureas,degradation experiments were conducted on the othertwo compounds, fenuron and isoproturon. Kineticexperiments showed that the kinetic rate constantof the abiotic degradation of these two compoundsincreased with [HA] according to a hyperbolictrend (Fig. 6), thus strengthening the hypothesis thatphenylurea hydrolysis proceeds through a multistepreaction27 with the appearance of an intermediatewhose formation is catalysed by HAs.

4 CONCLUSIONSMathematical models are effective tools for supportingan environmentally friendly use of pesticides. Here, a

0

0.002

0.004

0.006

0.008

0.01

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

k (d

ays-1

)

Catalyst concentration (mol L-1)

Figure 5. HA (°) and acetic acid (ž) concentration dependence ofthe kinetic rate constant for diuron (the HA concentration isnormalised for the content of carboxylic groups).

[HA] (mg L-1)

0

0.001

0.002

0.003

0.004

0.005

0.006

0 500 1000 1500 2000 2500 3000 3500

k (d

ays-1

)

Figure 6. Kinetic rate constant of fenuron (ž) and isoproturon (°) inthe HA/water system.

kinetic model is proposed for estimating phenylureabehaviour in the presence of dissolved HA. This workdemonstrates that humic acids have a catalytic effecton the abiotic dedradation of phenylureas, and thatadsorption–desorption processes deeply influence thedegradation rate. The kinetic model developed inthis study fairly describes the experimental data andpermits the evaluation of the kinetic rate constant. Theresults suggest that catalysis of phenylurea hydrolysisby humic acids follows a mechanism similar tothat proposed for bifunctional buffers. The onlyaromatic products of phenylurea degradation areaniline derivatives which irreversibly bind to HAs.The reaction rate increases with the carboxyl groupcontent of humic acids, strengthening the convictionthat carboxyl groups are really responsible for thecatalysis. It is worth noting that the kinetic equationderived in this work could be helpful in predicting thepersistence of phenylureas and similar chemicals innatural water. Humic substances in natural waterscan reach concentrations of 50 mg L−1,21 whichcorresponds, according to the present model, to akinetic rate constant for diuron of about 0.0015 day−1.

From the above considerations it is expected thatthe presence of dissolved HAs could contribute toincreasing the degradation rate of phenylureas up to 4times that in pure water (0.0004 day−1) under similarconditions of temperature and pH.12

APPENDIXThe kinetic model proposed for degradation ofphenylureas in soil/water systems12 can be adaptedfor the study of dissolved HA/water systems byconsidering that in the latter case the adsorptionprocess, which occurs simultaneously to hydrolysis,is described by a linear isotherm.

Assuming that hydrolysis occurs only when pheny-lurea is not bound to HAs, and is a first-order reactionwith respect to phenylurea concentration in solution,the reaction rate ν can be expressed by the equation

ν = CwVwk (2)

772 Pest Manag Sci 64:768–774 (2008)DOI: 10.1002/ps

Degradation of phenylureas by humic acids

where ν is defined as −dn/dt, n is the number ofmoles of phenylurea in solution, Cw is the molarconcentration of the reactant in solution, Vw is thevolume of the aqueous solution and k is the first-orderrate constant.

Moreover

ntot = CwVw + CHAVHA (3)

where ntot is the total amount of moles of phenylureain the system (water + HAs), and CHA and VHA arethe concentration in the HA phase and the HA volumerespectively.

If it is assumed that the HA/water partition rate ofphenylureas is markedly higher than their hydrolysis(pre-equilibrium hypothesis), and that the equationqe = KCe describes the adsorption process [whereK is the equilibrium adsorption constant, qe is theconcentration (w/w) at equilibrium of the adsorbatemolecule in the HA phase and Ce is the concentration(w/v) at equilibrium in the water phase], then

ntot = CeVw + mHAKCe (4)

where mHA is the HA mass (in the pre-equilibriumhypothesis Ce = Cw).

Relating this to the time:

dntot/dt = VwdCe/dt + KmHA dCe/dt (5)

As it has been assumed that hydrolysis takes placeonly in the water phase, the variation in total molesdntot is obtained by equation (2):

dntot = −(CeVwk)dt (6)

Combining equations (4) and (5) yields

−(CeVwk) = VwdCe/dt + KmHAdCe/dt (7)

which, rearranged and integrated, gives

Ce = Ce,0 e− kt

1+K[HA] (8)

where [HA] is the dissolved HA concentration inwater ([HA] = mHA/Vw) and Ce,0 is the phenylureaconcentration in water phase at t ∼= 0 after the partitionequilibrium has been reached. Its values can be derivedby the adsorption equation, qe = KCe, knowing theinitial phenylurea concentration C0 in the water beforeits contact with HAs:

Ce,0 = C0

1 + K[HA](9)

It is important to remember that Ce cannot beexperimentally determined. In fact, the phenylureaconcentration measured, Cmeas, on account of the

HA–phenylurea complex dissociation during the chro-matographic run, is the total phenylurea concentra-tion:

Cmeas = Ctot = Ce + CHA (10)

As the adsorption equation can be written as

Ctot − Ce

mHAVw = KFCe (11)

Ce can be expressed as

Ce = Ctot

1 + K[HA](12)

Combining equations (8), (9) and (12) finally yields

Cmeas = C0 e− kt

1+K[HA]

which permits the determination of the kinetic rateconstant for the hydrolysis of phenylureas in thepresence of dissolved HAs.

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774 Pest Manag Sci 64:768–774 (2008)DOI: 10.1002/ps