Environ. Sci. Technol. 2000, 34, 1687-1693
Modeling Abiotic Processes of Aniline in Water-Saturated Soils J O S EÄ R . F AÄ B R E G A - D U Q U E A N D CHAD T. JAFVERT* School of Civil Engineering, Purdue University, West Lafayette, Indiana 47907
exchange dominates, than at high pH, where sorption of the neutral species to hydrophobic domains mostly occurs (8). In a previous paper (1), we introduced a two-site (TS) model to quantitatively describe these reversible processes. The TS model was employed to evaluate 24-h sorption isotherms of aniline and R-naphthylamine for three soils as a function of pH and ionic strength. The equilibrium processes considered in the TS model are illustrated in eq 1,
HUI LI AND LINDA S. LEE Department of Agronomy, Purdue University, West Lafayette, Indiana 47907
The long-term interactions of aromatic amines with soils are important in defining the fate and transport of these compounds in the environment. Abiotic loss of aniline from the aqueous phase to the soil phase occurs with an initial rapid loss due to reversible mass transfer processes, followed by a slow loss due to irreversible reactions. A kinetic model describing these processes in water-saturated soils was developed and evaluated. The model assumes that instantaneous equilibrium occurs for the following reversible processes: (i) acid dissociation of the protonated organic base (BH+ ) in the aqueous phase; (ii) ion exchange between inorganic divalent cations (D2+ ) Ca2+ + Mg2+) on the soil and the protonated organic base; and (iii) partitioning of the nonionic species of aniline (Baq ) to soil organic carbon. The model assumes that irreversible loss of aniline occurs through reaction of Baq with irreversible sites (Cir) on the soil. A kinetic rate constant, kir, and the total concentration of irreversible sites, CT, were employed as adjustable model parameters. The model was evaluated with measured mass distributions of aniline between water (with 5 mM added CaCl2) and five soils ranging in pH (4.4-7.3), at contact times ranging from 2 to 1600 h. Some experiments were performed at different soil mass to water volume ratios. A good fit was obtained with a single value of kir for all soils, pH values, and soil-water ratios. To accurately predict soilwater distributions at contact times < 24 h, mass transfer of the neutral species to the soil was modeled as a kinetic process, again, assuming that ion exchange processes are instantaneous.
Introduction Quantifying the long-term interactions between aromatic amines and soils is important to predict the environmental fate and transport of these compounds. Speciation and sorption of aromatic amines in the environment are highly pH dependent processes (1, 2). Among reversible mass transfer processes, ion exchange is dominant at low pH, where the protonated form of the aromatic amine is the dominant species (3). Sorption due to hydrophobic interactions is the predominant reversible process at high pH values where the neutral amine species dominates (4-7). For aniline, distribution to the soil is generally greater at low pH where ion * Corresponding author phone: (765) 494-2196; fax: (765) 4961107; e-mail:
[email protected]. 10.1021/es990622o CCC: $19.00 Published on Web 03/18/2000
2000 American Chemical Society
where Baq and BH+ are the nonionic and cationic aqueous species, Bs is the concentration of B associated with the soil organic matter, D2+ aq is the sum of aqueous calcium and magnesium ion concentrations, and BHS and D0.5S are cation exchange sites (S -) that are occupied by organic and inorganic cations, respectively. The thermodynamic constants are as follows: Ka, the acid dissociation constant of the conjugate acid; Ks, the partition coefficient of B to soil; and KG, the cation exchange selectivity coefficient. In our previous paper we set the value of Ks equal to focKoc, where foc is the fraction of organic carbon in the soil and Koc is the organic carbon normalized partition coefficient. Other processes, such as sorption of the neutral species to clays, may occur; however, most of the variability in mass distributions between water and soil phases were accounted for by considering the effects of changes in pH, foc, CEC, and divalent ion concentration on those three processes shown in eq 1. At longer equilibration periods, the formation of covalent bonds between specific chemical structures of soil organic matter (e.g., quinones and phenolic functional groups) and aromatic amines has been proposed as being partially responsible for irreversible loss (2, 9, 10). The time scale of kinetic processes responsible for irreversible loss is long (>100 h) relative to the time scale of those reversible reactions illustrated in eq 1 (e24 h). Based on the work of Hsu and Bartha (11-13) and employing quinones as model reactive constituents of soil, Parris (2) proposed two mechanisms for the reaction of aromatic amines with humates: (a) a rapid and reversible formation of imine linkages and (b) a slow and irreversible process that is initiated by 1,4-nucleophilic addition of the amino group to the quinone ring. In the latter case, addition is followed by rapid tautomerization and oxidation to form aminoquinones. Further reaction of the amino group may lead to formation of a variety of nitrogen heterocycles (2). Spectroscopic studies suggest that both mechanisms occur (14, 15). A conceptual way to model the overall irreversible process is to consider an initial adsorption step (or diffusion) to reactive sites followed by reaction kf
kp
Baq + Cir y\ z BC 98 Bir k
(2)
r
where Baq is the aqueous phase species, Bir is chemical that is irreversible lost to the soil through chemical reaction, Cir are available irreversible sites (e.g., quinone functional groups), and BC is the physically sorbed complex that eventually leads to the chemisorbed or released product, Bir. The rates of BC formation and decay and Bir formation may be expressed as VOL. 34, NO. 9, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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d[BC] ) kf[Baq][Cir] - (kr + kp)[BC] dt d[Bir] ) kp[BC] dt
(3)
[B]T ) [B]T,n-ir + (4)
where kf and kr are the forward and backward rate constants for physical sorption, and kp is the overall rate constant for chemical reaction. Bir and Cir have units of mol/kg, and all aqueous species have units of mol/L. As in the development of the Michaelis-Menten equation, if the absolute rate of change of the concentration of the intermediate complex is small compared to that of reactants and products, a steadystate approximation on the complex (d[BC]/dt ≈ 0) may be assumed, leading to
d[B]ir kpkf[B]aq[C]ir ) kir[B]aq[C]ir ) dt kr + kp
Model Development Kinetic Model. We may consider the three mass action processes in eq 1 to be at equilibrium at all time where
[B]aq[H+]aq [BH+]aq
Kd ) focKoc )
KG )
[B]S [B]aq
[BHS][D2+]0.5 aq [BH+]aq[D0.5S]
(6)
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(9)
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 34, NO. 9, 2000
(10)
m ([B]S + [BHS]) (11) v
Combining eqs 6-8 with 11 leads to
[B]aq ) where P is defined as
P)1+
[B]T,n-ir P
(
(12)
)
KG[H+]CEC [H+] m + Kocfoc + Ka v K [D2+]0.5 a
(13)
and is constant and unique for each set of experimental conditions. The empirical rate law for irreversible reaction as expressed in eq 5 also defines the change in [C]ir and [B]T,n-ir
d[B]ir d[B]T,n-ir v d[C]ir ))) kir[B]aq[C]ir (14) dt dt m dt Introducing eqs 9, 10, and 12 into eq 14 yields the following
d[B]ir d[B]T,n-ir v )) dt dt m m [B]T - [B]ir v kir ([C]T - [B]ir) ) k′r[B]T,n-ir[C]ir (15) P where k′r is equal to kir/P. Equation 15 has the following analytical solution
[B]ir )
[C]T{1 - eQ(t)} 1-
and where all aqueous and solid-phase species concentrations have units of mol/L and mol/kg, respectively. An analytical solution to these and the associated material balance equations exists if some reasonable simplifying assumptions are made. First, because Ca2+ is the dominant cation in our experiments, we assume that a nearly constant concentration of divalent inorganic cations exists in the aqueous ([D2+]aq) and solid ([D0.5S]) phases at all times. This assumption is valid within an average error of 1.5% over all experiments, with a calculated maximum error of 12% for one experiment. Quantitatively, this assumption leads to equating [D0.5S] equal to the cation exchange capacity of the soil (CEC) and [D2+]aq equal to the concentration of CaCl2 added in the experiments (5 mM). Defining [C]T (mol/kg) as the total initial concentration of reactive sites and assuming that every product, Bir, is the result of a 1:1 reaction between [B]aq and [C]ir
[C]T ) [C]ir + [B]ir
[B]T,n-ir ) [B]aq + [BH+]aq +
(7)
(8)
m [B]ir v
where [B]T (mol/L) is the total concentration of organic base normalized to the aqueous phase volume, m/v (kg/L) is the soil mass to aqueous phase volume ratio, and [B]T,n-ir (mol/ L) is the total concentration of organic base in the system that has not undergone irreversible reaction and is defined by
(5)
where kir (M-1 h-1) is a second-order irreversible reaction rate constant. Although soil heterogeneity dictates that the constant kir for any compound is not singular, this equation seems to be a reasonable starting place to model irreversible loss under conditions where the more rapid processes described in eq 1 also occur. In this work, we develop a simple kinetic model that accounts for the processes described by eqs 1 and 2 and apply this model to experimental data on several soils in which the concentrations of aniline reversibly sorbed to soil, irreversibly bound, and in the aqueous phase are measured. In our approach, acid dissociation and cation exchange are treated as equilibrium processes, whereas sorption of the neutral species, the slowest of the rapid processes, is treated first as an equilibrium process and second as a kinetic process for comparison purposes.
Ka )
The mass balance equation on the organic base is
m[C]T Q(t) e v [B]T
(16)
or, in terms of [B]T,n-ir
[B]T,n-ir )
[B]T - (m/v)[C]T 1-
m[C]T Q(t) e v [B]T
(17)
where
Q(t) ) kir
(m/v)[C]T - [B]T t P
(18)
Addition of Kinetic Terms for Sorption of B. Because sorption of the nonionic species occurs over a period of hours, an alternate approach is to treat this process as a kinetic process ks,f
[B]s y\ z [B]aq k s,r
(19)
where ks,f and ks,r (h-1) are the forward and reverse rate constants for sorption of the neutral species. Again, normal-
TABLE 1. Aniline Properties
TABLE 2. Soil Properties
characteristics
values
characteristics
values
soil
MWa (g/mol) Swb (mg/L) log Kowc
93.1 34000 0.90
p Ka Koc (L/kg) KG (M-0.5)
4.63 1.48d 5.75,d 2.80e
Bloomfield Chalmers Drummers Okoboji Toronto
a MW ) molecular weight. b S c w ) solubility in water. log Kow: octanol-water partition coefficient. d Calculated previously by Fabrega et al. (1). e Value employed to model Toronto soil.
izing sorption to the fraction of organic carbon in the soil, the relationship between ks,f and ks,r is
Kocfoc )
ks,f v ks,rm
pHa CEC (cmol/kg) foc (%) a
6.40 4.40 0.36
6.50 13.0 1.17
7.20 26.5 2.91
7.40 36.2 4.98
4.40 11.2 1.34
Measured in a 1 g/mL distilled water slurry.
acetonitrile:acetate buffer (pH ) 4.7) at a flow rate of 1.5 mL/min. The total concentration of aniline in the soil, qT, was calculated by difference
(20)
qT )
v ([B]T - [C]aq) m
(24)
The differential equation on Bs is
d[B]S ks,f v v ) ks,f [B]aq [B] dt m Kocfocm S
(21)
and a new expression for [B]aq is found
[B]aq )
[B]T,n-ir -
m [B]S v
P1
(22)
where P1 is defined as
P1 ) 1 +
+ [H+] mKG[H ]CEC + Ka v K [D2+]0.5 a
(23)
and is constant and unique for each set of experimental conditions. Equations 15 and 21 are simultaneous ordinary differential equations that were solved with the explicit Euler method. Initial conditions were as follows: [B]s,o ) 0, [B]ir,o ) 0, [C]ir,o ) [C]T, [B]T,n-ir,o ) [B]T, and [B]aq,o ) [B]T /P1, where the subscript “o” identifies the value at time ) 0. Mass transfer rate constants describing the sorption of nonionic organic compounds to soils, are inversely proportional to compound partition coefficients (16, 17). Aniline has a relatively low partition coefficient, with Koc ) 30 mL/g, and the value of ks,f should correspond to a short “characteristic half-life” (t1/2 ) 0.693/ks,f) on the order of hours.
Experimental Methods and Parameter Estimation Experimental Methods. Soil-water mass distributions of aniline over time were measured with four Indiana soils and one Iowa (Okoboji) soil at the natural pH values of the soil slurries. Tables 1 and 2 provide some physical and chemical properties of aniline and the soils, respectively. These soils varied in CEC, foc, and solution pH. Prior to experiments, 500 g of each soil were sterilized with 60Co radiation at the rate of 3.0 krad/min for 16 h. For each soil, a series of weighed soil samples were hydrated with 5 mM CaCl2 in 8, 15, or 35 mL glass centrifuge tubes outfitted with Teflon-lined screw caps. The same initial concentration of aniline ([B]T ) was added to all tubes containing the same soil, with the initial concentration of aniline among the different soils varying from 1.01 to 1.16 mM. Tubes were rotated end-over-end, with individual tubes sacrificed at intervals over a 2-month period for chemical analysis. The pH values of sacrificed tubes were measured prior to centrifugation at 1750 g for 30 min. Aniline concentrations in the supernatants were measured with a Shimadzu HPLC equipped with a Supelcosil ABZ+ reversed-phase column and UV detector, monitoring absorbance at 254 nm. The mobile phase was (40:60) (v:v)
where [C]aq is the total concentration of organic amine in the aqueous phase ([BH+] + [B]aq). The centrifuged soil samples remaining in tubes were extracted with 3:1 (v:v) acetonitrile:0.3 M ammonium acetate solution by shaking for several hours, followed by refluxing for 1 h. Samples were again centrifuged at 1750g for 10 min, and supernatants were collected for analysis. The mass of aniline extracted was assumed to equal the amount associated with both reversible mass transfer processes. The mass on irreversibly bound sites was calculated as the difference between the total mass added and the sum of aqueous- and soil-recovered masses. In all cases peak areas were compared to those of standards. A more complete description of experimental methods is reported elsewhere (9). For the Toronto soil, experiments at two additional m/v ratios were run for a period of 7 days. Parameter Estimation. In a previous paper (1) we varied concentrations of Ca2+, aniline, and H+ systematically to measure distribution to these same soils at 24 h and from this information determined global (across all the soils) values for KG and Koc for aniline. These values are reported in Table 1 and were used in the current model without modification with one exception: We found better predictions for the initial rapid loss to the soil in the current study if one-half the original value of KG for the Toronto Soil was employed (see Table 1). The reason for adjusting KG rather than Koc is that Toronto is a low pH soil, and ion exchange is the dominant process controlling reversible loss to the soil. The kinetic constant, kir, and the initial concentration of reactive sites, [C]T, were calculated for some of the experimental data. Values for kir were obtained with an initial guess on [C]T by linear regression analysis of eq 17 after combining with eq 18 and rearranging
{(
ln
)(
[B]T,n-ir + [C]T(m/v) - [B]T [B]T,n-ir
)}
[B]T ) [C]T(m/v) [C]T(m/v) - [B]T kir t (25) P
The value of [C]T was adjusted until the global minimum was found for the following objective function j)n
SSRB )
∑([B]
T,n-ir,m
- [B]T,n-ir,p)2
(26)
j)1
where subscripts m and p denote measured and predicted values, respectively, SSRB is the sum of squared residuals between experimental and model predictions of [B]T,n-ir , and n is the number of datum points. Values of kir and [C]T VOL. 34, NO. 9, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. (A) Aniline in the water phase normalize to the total concentration of aniline added to the system ([C]aq/[B]T) and (B) total concentration of aniline in the soil phase (qT) with time. Solid lines are model predictions. The experimental conditions and model parameters are provided in Tables 2 and 3.
TABLE 3. Experimental Conditions and Calculated Constants soil
pHa
Bloomfield Chalmers Drummers Okoboji Toronto
6.40 6.68 7.20 7.04 4.53
a
m /v [B]T [C]Tb (kg/L) m (kg) (mmol/L) (mmol/kg) 0.9 0.7 1.0 0.4 0.2
0.0045 0.007 0.004 0.004 0.002
Average of all sample tubes.
b
1.01 1.03 1.12 1.03 1.16
0.414 0.355 0.962 1.98
kir (R 2) (M-1 h-1)
8.64 (0.91) 13.8 (0.98)
Calculated with kir,av )11.2 M-1 h-1.
were calculated with the data at t < 500 h where the rate of change in irreversible loss was the greatest.
Results and Discussion Reversible and Irreversible Loss. Data and model results are summarized in Figures 1-5 and in Tables 3 and 4. Experimental conditions and the calculated values of [C]T and kir are reported in Table 3. Figures 1 and 2 report experimental concentrations of aniline in the aqueous and solid phases with time. The solid lines on these figures are calculated by the model and will be discussed along with Figure 3 in the next section. Figure 1A normalizes the loss of aniline to soil by plotting the ratio [C]aq/[B]T versus time. This figure indicates that the concentration of aniline in the aqueous phase asymptotically approaches a value greater 1690
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TABLE 4. Experimental Conditions for m/v Experiments m/v (kg/L)
pH
[B]T (mmol/L)
m (kg)
P
with kir ) 26.1 M-1 h-1/ kir′ (M-1 h-1)
0.65 0.20 0.10
4.37 4.40 4.57
1.07 1.16 1.07
0.0065 0.002 0.001
8.51 4.34 2.72
3.07 6.01 9.60
than zero for each experiment. Figure 1B reports the measured total loss of aniline (qT) to the soil and clearly indicates that two processes occur with different characteristic times. Rapid loss of aniline from the aqueous phase to the soil occurs over a short period of time ( Drummers > Chalmers) as expected. Sorption of the Nonionic Species as a Kinetic Process. Although the sparse data at short times (
