Distribution of Proton Dissociation Constants for Model Humic and

Apr 17, 2009 - Modeling Ion Binding to Humic Substances: Elastic Polyelectrolyte Network Model. Silvia Orsetti , Estela M. Andrade and Fernando V. Mol...
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Environ. Sci. Technol. 2009, 43, 3626–3631

Distribution of Proton Dissociation Constants for Model Humic and Fulvic Acid Molecules YASEMIN B. ATALAY,† RICHARD F. CARBONARO,‡ AND D O M I N I C M . D I T O R O * ,† Department of Civil & Environmental Engineering, University of Delaware, Newark, Delaware 19716, and Department of Civil & Environmental Engineering, Manhattan College, Riverdale, New York 10471

Received October 29, 2008. Revised manuscript received March 16, 2009. Accepted March 17, 2009.

The intrinsic proton binding constants of 10 model humic acid and six model fulvic acid molecules are calculated using SPARC Performs Automated Reasoning in Chemistry (SPARC). The accuracy of the SPARC calculations is examined using estimated microscopic binding constants of various small organic acids. An equimolar mixture of the appropriate hypothetical molecules is used as a representation of soil and aqueous humic acid and fulvic acid. The probability distributions of the mixture microscopic proton binding constants and the intrinsic proton binding constants in the metal speciation models WHAM V and WHAM VI (Windermere humic aqueous models) are compared. The idea is to assess the predictive value of the molecular mixture models as representations of heterogeneous natural organic matter. For aqueous humic and fulvic acids, the results are comparable to the WHAM distribution. For soil humic acid, the WHAM probability distribution is less acidic for the carboxylic sites but similar to that of the phenolic sites. Computations made using the WHAM molecular distributions and WHAM VI are comparable to titration data for Suwannee River fulvic acid. These results suggest that mixture molecular models can be used to investigate and predict the binding of metal cations to humic and fulvic acids.

Introduction The acid-base chemistry of humic and fulvic acids is an important component of metal speciation models in natural systems (1). The acidic functional groups of humic and fulvic acids (mainly carboxylic and phenolic) determine their binding characteristics for protons and other major cations. Therefore, to understand the metal complexation behavior of dissolved natural organic matter (NOM), the proton binding properties are required. NOM is a heterogeneous collection of molecules, and its representation in speciation models uses distributions of binding sites to characterize its properties (2). Two modern models (WHAM V and WHAM VI) use a discrete (3, 4) and a continuous (non-ideal competitive adsorption (NICA)Donnan 5-8) representation. Various hypothetical molecular structures have also been proposed for humic and fulvic acid on the basis of data from * Corresponding author phone: (302) 831-4092; fax: (302) 8313640; e-mail: [email protected]. † University of Delaware. ‡ Manhattan College. 3626

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NMR and spectroscopic techniques. If these molecules are representative of humic and fulvic acid properties, they would be useful for many purposes. The purpose of this article is to compare the proton binding constants of these molecules to the binding constants employed in the speciation models. The proton binding constants for the molecular representations are calculated using SPARC Performs Automated Reasoning in Chemistry (SPARC), which uses only the molecular structure to estimate pK values. It has been thoroughly tested and is readily available (9). Since both WHAM and NICA-Donnan are equally successful in reproducing the results of acid-base titrations (10), we will use the simpler discrete WHAM representation for comparison. A series of molecular structures have been suggested for both humic and fulvic acid, each with different structural arrangements of acidic and other functional groups. Since there is no a priori way of choosing which molecule is best, and since NOM is a heterogeneous mixture of molecules, we represent humic and fulvic acids as an equimolar mixture of the molecules that have been suggested as representative. Soil humic, aquatic humic, and aquatic fulvic acid molecules are grouped separately. These equimolar mixtures are our molecular models. We compare the probability distribution of the binding constants in these mixtures of molecules to the WHAM probability distribution for humic and fulvic acid. Since WHAM is calibrated to extensive sets of proton binding data, its proton binding constants are a good representation of the acid-base chemistry of “average” humic and fulvic acids. As a final comparison, an experimental potentiometric titration of Suwannee River fulvic acid is compared to calculations using the fulvic acid proton binding constants from WHAM and from the equimolar mixture of fulvic acid molecules. Also included is the WHAM VI prediction that represents the electrostatic and ionic strength effects as well.

Materials and Methods Molecular Structures Used for Analysis. A selection of the hypothetical molecular structures used in this analysis is presented in Figure 1. The model Leonardite humic acid molecule was derived from 13C NMR analysis (11). The model Chelsea soil humic acid molecules were obtained using a combination of experimental and computational analysis by Diallo et al. (12). Data from FT-IR spectroscopy, 1-D/2-D 1 H and 13C solution NMR spectroscopy, and mass spectrometry were employed. The analysis used the computerassisted structure elucidation program SIGNATURE to generate 3-D structures (12). Similarly, the Altamaha River humic acid (AR-HA) molecules were constructed using the results from NMR techniques (13). A suggestion for a molecular structure by Aiken et al. (14) is also included. All but one of the model fulvic acid molecules are representative of Suwannee River fulvic acid (SRFA) as proposed by Leenheer et al. (15, 16). The distributions of carbon, hydrogen, and oxygen were obtained using 13C NMR and 1H NMR techniques. Nitrogen, sulfur, and phosphorus atoms were not considered since these are minor components of SRFA (17). Models were also based on hypothetical processes that transform plant tannins and lignins into fulvic acid. For instance, the aromatic functional group in SR-FA-1 was related to tannin and lignin precursors (16). One additional structure proposed by Aiken et al. (14) is also included. The structures of the molecules included in this analysis are presented either in Figure 1 or in the Supporting Information. SPARC. The proton binding constants of the humic and fulvic acid molecules are calculated using the online program 10.1021/es803057r CCC: $40.75

 2009 American Chemical Society

Published on Web 04/17/2009

FIGURE 1. Structures of model humic acid and fulvic acid molecules. (A) Leonardite humic acid (11), (B) fulvic acid from Aiken et al. (14), (C) (CS-HA9) from Chelsea soil humic acid (12), (D) humic acid from Aiken et al. (14), and (E) Suwannee River fulvic acid model (15). SPARC. The pK for the deprotonation of a single site from the fully protonated molecule is calculated. Every site that can be deprotonated is considered separately. These pK values are compared to the WHAM intrinsic constants, which are similarly defined (4). Both the SPARC results and the WHAM intrinsic equilibrium constants apply to the ionization of a single site of the fully protonated molecule. Therefore, they represent the same chemical reaction and are directly comparable. The SPARC computational procedure is as follows: The simplified molecular input line entry specification (SMILE) string, which defines the structure of the molecule as an ASCII string, is specified (Supporting Information) and the proton to be ionized is selected. The computation that SPARC performs to determine the pKa is described by Hilal et al. (18) as follows: The molecular structures are broken into a reaction center (C), which can ionize and whose pK is either known or can be estimated, and the perturber (P), which is appended to the reaction center and assumed not to change during the reaction. The pK of the reaction center is modified by the effects of the perturber pKa ) (pKa)c + δelepKa + δrespKa + δsolpKa +...

(1)

where (pKa)c is the pK of the reaction center and δrespKa, δelepKa, and δsolpKa describe the differential resonance, electrostatic, and solvation effects of P on the initial and final states of C, respectively. A more complete description of the methods is available (18). As reported in ref 19, a comparison of observed and computed pKa for 3685 organic compounds using this method yielded a root mean square deviation ) 0.37.

Results and Discussion SPARC Validation. SPARC is used to estimate the pKa values of single sites, which are called microscopic constants Ks1

and are not experimentally determined except for molecules that have only one ionizable site (monodentate ligands). Experimental titrations are used to determine the macroscopic binding constants that apply to sites that are ionizing successively. The second ionization constant found from titrations applies to the ligand with a -1 charge, which is not the same as the ionization constant for the same site for the ligand with a zero charge. Therefore, to examine its reliability to predict microscopic constants, SPARC was tested for a series of monodentate ligands for which the microscopic (Ks1) and macroscopic constants (Ka1) are equal. For symmetric bidentate, tridentate, and tetradentate ligands with a measured macroscopic constant Ka1, the microscopic constant is Ks1 ) Ka1/n for an n-dentate symmetric ligand (20, 21). A comparison of predicted and observed pKs1 values using the NIST Critical Database for Ka1 (22) is presented for 47 monoacids in Figure 2a and Table 1 (root mean square error, RMSE ) 0.24) and for 12 symmetric polydentate ligands in Figure 2b and Table 2 (RMSE ) 0.26). The outlier in Figure 2b is maleic acid whose carboxylic groups are cis to each other. SPARC can not differentiate between cis and trans isomers. Therefore, fumaric acid whose carboxylic groups are trans to each other appears to be the isomer that SPARC is using and is included in the calculation of RMSE.

Comparison of Cumulative Probability Distribution Functions Comparison to Molecular Models. The method employed to compute the microscopic constants for a molecular structure is illustrated using a representative molecule, D8 from Chelsea soil humic acid (Figure 3a). D8 has seven carboxylic, one phenolic, and three alcohol groups with a total of 11 functional groups. The numbered functional groups are the ionizable groups of the acid. They are numbered from the most acidic to the most basic group. The VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Computed and Observed Microscopic Contantsa type of ligand bidentate

tridentate

FIGURE 2. Comparison of NIST and SPARC intrinsic binding constants for (A) monodentate ligands (RMSE ) 0.24) and (B) bidentate, tridentate, and tetradentate ligands (RMSE ) 0.26).

TABLE 1. pKa Values of Monodentate Ligands from NIST and SPARC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

acid

NIST pKa

SPARC pKa

formic acid acetic acid propanoic acid butanoic acid (butyric acid) pentanoic acid (valeric acid) isovaleric acid isohexanoic acid isooctanoic acid pivalic acid allylacetic acid phenylacetic acid 3-phenylpropanoic acid 4-phenylbutanoic acid chloroacetic acid dichloroacetic acid 3-chloropropanoic acid bromoacetic acid 2-bromobutanoic acid 2-bromopentanoic acid iodoacetic acid 3-iodopropanoic acid cyanoacetic acid benzoic acid 3-fluorobenzoic acid 4-fluorobenzoic acid 3-nitrobenzoic acid 4-nitrobenzoic acid phenol m-cresol p-cresol 3-fluorophenol 4-fluorophenol 3-chlorophenol 4-chlorophenol 3-bromophenol 4-bromophenol 3-iodophenol 4-iodophenol 3-nitrophenol 4-nitrophenol 3-cyanophenol 4-cyanophenol 3-hydroxybenzaldehyde 4-hydroxybenzaldehyde 3-acetylphenol 4-acetylphenol water

3.74 4.76 4.87 4.82 4.84 4.78 4.85 4.93 5.03 4.68 4.31 4.66 4.76 2.86 1.10 4.11 2.90 2.97 3.05 3.18 4.10 2.47 4.20 3.86 4.13 3.45 3.44 10.00 10.10 10.27 9.21 9.91 9.13 9.43 9.03 9.35 9.03 9.33 8.36 7.15 8.57 7.97 8.99 7.62 9.25 8.05 14.00

3.75 4.78 4.74 4.74 4.74 4.74 4.74 4.74 4.66 4.61 4.42 4.60 4.66 3.06 1.57 4.04 3.05 3.02 3.02 3.00 4.00 2.47 4.06 3.67 3.81 3.21 4.06 10.01 10.14 10.33 9.27 9.50 9.14 9.38 9.14 9.38 9.07 9.30 8.38 6.74 8.38 7.26 9.48 7.84 9.45 8.22 14.60

alcohol groups, which are numbered as 10 and 11 in Figure 3a, are not considered, because they have intrinsic pKs values greater than 10.3, which is the maximum range for phenolic 3628

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tetradentate

index

ligand

SPARC pKs1

NIST pKs1

1 2 3 4 4 5 6 7 1 2 3 1 2

malonic acid methylmalonic acid oxalic acid maleic acid fumaric acid succinic acid catechol phthalic acid trimesic acid trimellitic acid tricarballylic acid isocitric acid citric acid

2.97 2.94 1.30 3.40 3.40 4.20 9.20 3.26 3.32 2.88 3.92 3.48 3.57

3.15 3.31 1.55 2.23 3.32 4.51 9.75 3.25 3.60 2.96 4.16 3.66 3.73

a Computed SPARC microscopic constant NIST pKa. Computed NIST microscopic constant pKs1.

FIGURE 3. Example of the microscopic proton binding constants of a Chelsea soil humic acid molecule. (A) Molecule D8, numbered according to the order of deprotonation. (B) Comparison of the cumulative distribution function (CDF) of the microscopic proton binding constants of D8 and the WHAM intrinsic proton binding constants. groups in WHAM for humic acids. In Figure 3b, the cumulative probability distribution function (CDF) of the

TABLE 3. Computed Microscopic Constants Using SPARCa SPARC computed microscopic pKa molecule CS-HA-9 CS-HA-8 CS-HA-6 CS-HA-5 CS-HA-4 AR-HA-1 AR-HA-2 AR-HA-3 Leonardite-HA Stevenson-HA Buffle SR-FA-a SR-FA-b SR-FA-c SRFA-1 SRFA-2

2.11 1.74 1.73 1.68 1.26 2.89 2.99 3.75 2.61 3.04 2.33 2.21 1.98 3.18 3.16 2.87

2.16 1.89 1.84 1.93 1.6 3.59 3.6 3.94 3.01 3.39 2.88 3.38 1.98 4.05 3.61 3.22

2.28 2 1.9 2.21 1.74 4.16 3.94 8.35 3.46 3.6 3 4.61 2.99 4.05 3.7 3.26

3.03 2.77 2.43 3.36 2.02 6.91 5.03 8.35 5.72 3.82 3.01 6.83 4.38 4.24 3.85 3.57

3.26 3.94 3.43 3.4 2.27 6.91 8.45 12.6

3.79 4.16 3.97 3.67 3.37 7.13 9.31 13.61

4.03 4.23 3.99 4.07 3.76 7.13

7.89 8.08 8.22 7.77 3.9 11.13

10.33 10.26 10 12.79 8.28 11.57

12.48 12.34 11.43 13.78 10.25 12.17

6.29 3.91 7.19 6.62 6.39 3.96 4.13

7.34 4.39 13.34 9.17 8.22 4.59 4.57

7.63 5.29

7.73 6.22

7.88 13.17

13.48 13.54 8.25 5.64

8.26 6.79

9.63 6.8

13.9 12.56

13.66

10.25

11.32

8.02

9.33

10.96

12.22 12.18

12.27

13.09

a

CS-HA-9 refers to Chelsea soil humic acid #9. AR-HA-1 refers to Altamaha River humic acid #1. SR-FA-a refers to Suwannee River fulvic acid a.

FIGURE 4. Comparison of the cumulative distribution function and quantile-quantile plots of microscopic pKs values to WHAM intrinsic proton binding constants for Altamaha River humic acid molecules (A,D), Chelsea soil humic acid molecules (B,E), and Suwannee River fulvic acid molecules (C,F). proton binding constants in D8 F(pKs) is compared to the CDF of proton binding constants in WHAM. The differences indicate that the WHAM carboxylic sites are more basic than the D8 molecule until approximately the 80th percentile. In addition, the number of WHAM phenolic sites is larger than the number of the phenolic groups of the molecule. This comparison is for illustrative purposes only. The next section presents the comparisons for the mixture models. Comparison to All Molecules - Molecular Mixture Models for NOM. We computed the microscopic constants for each of the molecules representing Chelsea Soil humic acid (five molecules), Altamaha River humic acid (3 + 2 others), and Suwannee River fulvic acid (5 + 1 other) (Table 3). Each model molecule represents a possible structure that is consistent with the experimental data used to construct it. Actual NOM is a mixture of molecules. The WHAM model

also represents a typical mixture of molecules. Since we have no way of preferring one molecule over another and in the absence of any further information, it is assumed that actual soil and aqueous humic and aqueous fulvic acids are equimolar mixtures of the individual model molecules. We suggest these mixtures as molecular models for soil HA, aqueous HA, and aquatic FA, respectively. The molecular mixture model CDFs are compared with the WHAM intrinsic proton binding constant CDF in Figure 4. The soil carboxylic groups of the mixture model molecules are more acidic than the WHAM sites. However, the phenolic groups have a similar distribution (Figure 4A). The deviation in carboxylic sites of the molecules is apparent in the quantile-quantile plot, which compares equal quantiles from the WHAM and molecular mixture model CDFs (Figure 4D). It is known that soil humic acid is more acidic than aqueous VOL. 43, NO. 10, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. Comparison of acid-base titrations of Suwannee River fulvic acid. Observed data, model computations using the WHAM constants, the molecule constants, and a WHAM VI computation using the complete solution chemistry.

TABLE 4. Parameters Used To Compute Titrations WHAM VI intrinsic constants site density for COOH groups, meq/g of FA site density for OH groups, meq/g of FA total site density meq/g of FA average molecular weight NOM concentration, mg/L total number of sites, n total ligand concentration (mM) pH range ionic strength, M

SRFA molecules

4.8

4.6

2.4 7.2 1500 300 8 2.16 2-11 0.1

2.3 6.9 5500 300 38 2.07 2-11 N/A

humic acid (23). However, the WHAM calibration used soil as well as aqueous humic acid data. This result suggests that a separate set of parameters for soils might be appropriate for WHAM. For Altamaha River humic acid (Figure 4B), the molecular mixture model binding constant CDF is nearly identical with the WHAM CDF (Figure 4BE). For Suwannee River fulvic acid, the molecular mixture model distribution carboxylic groups are slightly more acidic than WHAM and the phenolic sites are slightly less basic. However, the deviations are less than one log unit (Figure 4C,F). Titration Comparisons. The usual method of determining the distribution of proton site parameters is from experimental acid-base titrations. The titration data (pH vs base added) for SRFA reported by Boyer and Singer (24) and the variation in surface charge extracted from the data using the usual charge density equation (24) are shown in Figure 5A,B. Also included are the predictions calculated from the WHAM model intrinsic constants (labeled WHAM constants in Figure 5B) and from an equimolar mixture of the hypothetical Suwannee River fulvic acid molecules (labeled molecule constants in Figure 5B) proposed by Leenheer et al. (15, 16). These computations use the microscopic molecular constants and intrinsic WHAM pKa values with no electrostatic corrections. The effects of electrostatic and ionic strength are examined with a WHAM VI model computation (labeled WHAM VI in Figure 5B). This computation includes electrostatic corrections and the appropriate solution chemistry. The parameters are listed in Table 4. The effect of including the solution chemistry and electrostatic corrections using WHAM VI is seen to be small when compared to the WHAM constant computation. The WHAM intrinsic constant model requires slightly more base to reach the same pH than the Leenheer molecule 3630

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mixture because the WHAM proton binding constants are slightly more acidic than the molecular mixture (Figure 4C). Although the SRFA is more acidic than either model (Figure 5A), the differences are small. However, unlike the WHAM model, the molecular mixture model is not calibrated to any titration data. The molecular mixture could be adjusted so that agreement is achieved. It is well-known that different sets of pKa values can fit titration data equally well. Therefore, different relative weightings of the molecules in the mixture would likely produce equivalently good fits. But it is interesting that a simple equimolar mixture is a reasonable representation. The molecular mixture models for humic and fulvic acids proposed in this article have acid-base chemistry that is comparable (within one log unit) of the WHAM representation of average aqueous humic and fulvic acids. It might be expected that the mixture of molecular models would have a greater diversity of sites than the WHAM representation of “average” humic and fulvic acids. However, this does not appear to be the case. The results suggest that these molecular mixture models could be used to investigate additional properties of humic and fulvic acids. In particular, they could be used to estimate the metal binding constants using Irving-Rossotti slopes, a linear free energy relationship between metal and proton binding constants to oxygen functionality (25), or other methods (26). For structures with nitrogen- and sulfurcontaining functional groups, analogous estimation methods could be applied as well. Also, as quantum chemical methods improve (e.g., ref 27), the molecules could be used to compute metal binding constants directly or at least as a basis for understanding the chemical basis for NOM-metal binding (e.g., as in an analogous recent application by Helz and Tossell (28)). The results also suggest that further investigations and proposals for molecular structures could be added to the molecular mixtures for a more realistic representation of the full range of NOM. In principle, there is no limit to the complexityofthemolecularmixturethatcanbeaccommodated.

Acknowledgments This research was funded by the National Institute of Environmental Health Sciences through a Superfund Basic Research Program Grant (5R01ES015444) and the Center for the Study of Metals in the Environment at the University of Delaware. We thank Undine Kipka and Kevin J. Rader for their support. The anonymous reviewers provided useful and extensive comments that greatly improved the manuscript, and we thank them for their efforts.

Supporting Information Available SMILE strings and structures of the hypothetical molecules and additional tables. This material is available free of charge via the Internet at http://pubs.acs.org.

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