Environ. Sci. Technol. 2010, 44, 7431–7436
Reduction Rate Constants for Nitroaromatic Compounds Estimated from Adiabatic Electron Affinities KATHY L. PHILLIPS,† PEI C. CHIU,‡ AND S T A N L E Y I . S A N D L E R * ,† Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, 150 Academy Street, Newark, Delaware 19716, Department of Civil and Environmental Engineering, University of Delaware, DuPont Hall, Newark, Delaware 19716
Received January 14, 2010. Revised manuscript received August 16, 2010. Accepted August 20, 2010.
Nitroaromatic compounds (NACs) are ubiquitous environmental contaminants and predicting their environmental fate is important. Linear free energy relationships (LFERs) have been reported relating one-electron reduction potentials (EoH) of NACs in water to their reduction rate constants (k) measured under various conditions. In a recent effort to calculate EoH, we found that EoH values of NACs are also linearly correlated with their adiabatic electron affinities (EA). This suggests that the reactivity of NACssand hence their half-livesscan be predicted based on their EA values. We report here a new set of LFERs relating EA and k for NACs. Reduction of substituted nitrobenzenes mediated by quinones, natural organic matter, Fe(II) complexes, and the (CH3)2COH radical was examined using EA values calculated from quantum mechanics. For monosubstituted nitrobenzenes without ortho substituents, strong linear correlations were found between EA and log k, leading to accurate estimates of k. Deviations between measured and estimated k values for most orthosubstituted and/or polysubstituted compounds were somewhat higher, but were accurate to within approximately an order of magnitude using the same LFER for all compounds. We report estimates of 169 reduction rate constants for 23 compounds in nine reducing systems for which no measured values are available.
Introduction Nitroaromatic compounds (NACs) are widespread environmental contaminants due to their use as pesticides, explosives, and in a variety of other applications (1). The toxicity of many NACs and/or their environmental transformation products (2-4) has prompted considerable interest in the fate of NACs in the environment. In particular, an understanding of their reductionsthe key transformation reactionsis critical for evaluating the risks associated with NAC contamination and developing remediation strategies. An important property affecting the environmental fate of NACs appears to be the standard one-electron reduction potential in water (EoH). Several studies (5-11) have demonstrated that a linear relationship exists between EoH and the logarithm of the reduction rate constant (k) for the * Corresponding author phone: (302) 831-2945; fax: (302) 8316858; e-mail:
[email protected]. † Department of Chemical Engineering. ‡ Department of Civil and Environmental Engineering. 10.1021/es100142v
2010 American Chemical Society
Published on Web 09/07/2010
reduction of NACs under various conditions. This correlation has previously been explained as follows (7, 12). For a series of chemically similar reactions, there may exist a linear relationship between the free energy of reaction and the free energy of activation: this is the Bell-Evans-Polanyi principle (13, 14). If the first electron transfer (NAC(aq) + e-(g) f NAC · -(aq)) is the rate-determining step (RDS) in the reduction of NACs, it would then follow that o log k ) aEH /(2.303RT/F) + b
(1)
where a and b are constants, R is the gas constant, T is the absolute temperature, and F ) 1 eV/V is the Faraday constant. (A detailed derivation of eq 1 is included in the Supporting Information (SI).) We assume a constant temperature of 25 °C in this work, such that 2.303 RT/F ) 0.059 V. Since eq 1 relies on the assumed linear relationship between two free energies, it is a linear free energy relationship (LFER). The values of a and b can be obtained from a linear regression of log k against EoH/(0.059 V), and depend on the reaction system, for example, the reductant, other species present, concentrations of those species, and the pH, but should be constant for a series of NACs. The value of a has been interpreted as an indication of the importance of the first electron transfer to the activation energy for the overall reaction. Using Marcus theory (15), Schwarzenbach et al. (7, 12) originally postulated that a ≈ 1.0 for cases in which the actual first electron transfer is the RDS, whereas a < 1 or no correlation between k and EoH indicates that some other step in the reduction is rate-determining. Until recently, it was widely assumed that the first electron transfer was often the RDS in the reduction of NACs (16). However, recent measurements of nitrogen isotope fractionation during the reduction of NACs have led Hartenbach et al. (17, 18) to hypothesize that the RDS could be either the first NsO bond cleavage step, or the protonation or reduction of the NAC radical anion. They reported that the overall NAC reduction rate also depends on the equilibrium constants for each electron and proton transfer that precedes the RDS, since these reactions determine the population of molecules up to the RDS (17). On this basis, the populations of reduced NAC intermediates may be determined by EoH, and the slope a in eq 1 may be reinterpreted as representing the relative sensitivities of k and EoH to the combined effects of the NAC substituents on the pre-RDS reactions (11). Regardless of the underlying mechanism, excellent correlations have been obtained between EoH and log k for several reducing systems (5-11). LFERs therefore provide a useful, established tool for predicting EoH or k (5, 7, 8). The values of both properties are important for environmental fate estimates of NACs, and accurate predictions are needed in cases where experimental data are not available or have large uncertainties. Also, a priori determination of EoH and k would be helpful as a screening tool when designing new chemicals. However, to use the LFERs as a predictive tool, a value of either EoH or k must be available for the compound of interest. In a recent study aimed at calculating EoH (19), we found that there exists a linear correlation between EoH and adiabatic electron affinities (EA). In our previous work (19), we have used that relationship to accurately predict values of EoH for substituted nitrobenzenes, without relying on computationally challenging solvation calculations for charged species. We now focus on another important implication of our finding: it suggests that a new set of LFERs exists between EA and log k, and that the reactivity of NACs may be readily predicted based on EA. Importantly, EA values can be VOL. 44, NO. 19, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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accurately predicted using quantum mechanics (QM) (19) when measured EA values are not available in the literature. The objectives of this work are three-fold. First, we will assess the validity of using a linear relationship between log k and QM-calculated EA values to estimate rate constants for the reduction of substituted nitrobenzenes. All homogeneous reduction systems for which sufficient data are available will be investigated; that is, reduction mediated by quinones, natural organic matter (NOM), Fe(II) complexes, and the (CH3)2COH radical. Second, we will report LFERs, along with their estimation accuracy, in cases where valid relationships can be established. Third, we will use these LFERs to make estimates of the rate constants for compounds for which data are not available.
Materials and Methods Rate Constants. Measured rate constants were obtained from the literature for the reduction of substituted nitrobenzenes in a variety of homogeneous reaction systems. Where available, measured EoH values were also obtained from the literature. Values are listed in SI Table S1. Based on the availability of data, the following 23 NACs were selected for use in this work: nitrobenzene (NB); 2-, 3-, and 4-methylnitrobenzene (n-CH3, where n ) 2, 3, or 4 respectively); 2-, 3-, and 4-chloronitrobenzene (n-Cl); 2-, 3-, and 4-aminonitrobenzene (n-NH2); 2-, 3-, and 4-acetylnitrobenzene (nCOCH3); 1,2-, 1,3-, and 1,4-dinitrobenzene (1,n-DNB); 2,4and 2,6-dinitrotoluene (2,4-DNT and 2,6-DNT); 2,4,6-trinitrotoluene (TNT); 2-amino-4,6-dinitrotoluene (2-ADNT); 4-amino-2,6-dinitrotoluene (4-ADNT); 2,4-diamino-6-nitrotoluene (2,4-DANT); and 2,6-diamino-4-nitrotoluene (2,6DANT). EA. EA is the negative of the change of enthalpy at 0 K (H0K) for the gas-phase one-electron reduction reaction (NAC(g) + e-(g) f NAC · -(g)); that is EA ≡ -∆gH0K ) -H0K(NAC·-(g)) + H0K(NAC(g))
(2)
(The 0 K enthalpy of the free electron is zero (20).) The enthalpies of the NAC neutral and radical anion species can each be calculated from gas-phase QM. In a previous study (19), we evaluated several QM methods for calculating the EA for substituted nitrobenzenes, including density functional theory approaches and composite Gaussian-n methods (21, 22). EA predictions using the B98 density functional (23, 24) and the MG3S (25) basis set (EAB98) were found to accurately reproduce the measured EA values after scaling the predictions by a factor of 0.802 to account for a systematic error. This method of calculating EA (i.e., EA ) 0.802 × EAB98) offers the advantage of computational efficiency with no loss of accuracy compared to higher level QM methods (19). As the calculated EA values are in excellent agreement with the measured values (19), either set of EA values may be used for developing LFERs. In this work, we have used the calculated EA values for all compounds (listed in SI Table S1), since some measured values are not available. EA-Log k LFERs. LFERs relating EA and log k (eq 3) were fitted to the measured k values for a given reduction system and the calculated EA values using least-squares linear regression. log k ) REA + β
(3)
This process was repeated for subsets of the data differing in the number and position of substituents. In cases where a strong linear correlation between log k and EA was found, parameters for the corresponding LFERs have been reported and estimates of the rate constants have been made for all applicable compounds. 7432
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Terminology. In the discussion that follows, we use “LFER” to refer to any relationship of the form of eq 1 or 3. The subscript “expt” is used to denote measured values, and “calc” indicates the values calculated using QM. Units of k are M-1s-1, unless otherwise indicated; EA is in eV; EoH is in V; a, b, and β are dimensionless; and R has units of eV-1. The accuracy of LFERs in estimating k values is assessed using the mean and the maximum absolute deviation (AD) between the estimated log k value and log kexpt. For convenience, we will henceforth refer to these quantities as the MAD and the maximum AD in log k, respectively. Nitrobenzene is used as the reference (“unsubstituted”) compound, and substituent designations ortho (o), meta (m), and para (p), refer to the position of any substituent relative to the reference nitro group. We use the notation o-NB, m-NB, and p-NB to refer to o-, m-, and p-substituted nitrobenzenes respectively. Mono-NB is used to indicate compounds with only one substituent in addition to the single nitro group of the nitrobenzene, and poly-NB refers to compounds with more than one substituent in addition to the single nitro group. All compounds and their classifications are listed in SI Table S2.
Results and Discussion EAcalc-Versus EoH,expt-Based LFERs. LFERs based on EoH and log k for the reduction of NACs involving quinones, NOM, and Fe(II) complexes (5-11) are listed in SI Table S3. Before proceeding to examine each of these reduction systems and others, we first demonstrate that there is no significant loss in accuracy in replacing the usual form of the LFER relating EoH,expt to log k (eq 1) with a relationship between EAcalc and log k (eq 3). The compounds most commonly used to develop LFERs are NB and those mono-, non-o-NBs for which both EoH,expt and kexpt values are available (listed in SI Table S2). Since the largest available data set is for the juglone/H2S reduction system, we will use these rate constants. LFERs of the form of eqs 1 and 3 were determined using the EoH,expt and EAcalc values, respectively, for the same nine compounds. The resulting r2 values are 0.978 (eq 1, a ) 1.23 ( 0.07, b ) 9.06 ( 0.49) and 0.988 (eq 3, R ) 4.89 ( 0.20, β ) -5.61 ( 0.26), and MADs in log k are 0.15 and 0.13, respectively. These results confirm that there is little difference in accuracy between the two approaches. A visual comparison is provided in Figure 1. Establishing LFERs Based on EAcalc. We now proceed to evaluate the validity of a linear relationship between EAcalc and log k for the different compounds in each of the reduction systems. For most of the systems, it has been established that accurate LFERs can be determined for NB and the set of mono-, non-o-NBs (5-11). Therefore, we will begin by developing LFERs relating EAcalc and log kexpt using the data for these compounds only. Next, we will examine how well these LFERssalong with alternative LFERs fitted to different subsets of the datasdescribe the relationship between EAcalc and log kexpt for the remaining compounds. As LFERs reported in the literature were obtained using data for few or no o-NBs, and no poly-NBs, the utility of LFERs as a predictive tool for these compounds is yet to be established. 1. Mono-, Non-o-NBs. Table 1 lists LFERs developed for each of the reduction systems using all available data for NB and the mono-, non-o-NBs. The data are also plotted in Figure 1 for the juglone/H2S reduction system, and in SI Figures S1 to S13 for the other systems. In most cases, very strong correlations (r2 g 0.97) were found, indicating that these LFERs will provide highly accurate estimates of the rate constants for this category of compounds. The general absence of outliers suggests that NB and/or any subset of the mono-, non-o-NBs can be used to develop an accurate LFER. For example, if the (arbitrarily selected) compounds NB, 3-Cl and 4-Cl are used instead of the full set of
FIGURE 1. Comparison of data and LFERs for the reduction of substituted nitrobenzenes in the juglone/H2S reaction system (25 °C, pH 6.79), using (panel A) E oH,expt and (panel B) EAcalc. Solid diamonds: data for mono-, non-o-NBs (used to determine the LFER indicated by the line); open circles: data for mono-, o-NBs; open triangles: data for poly-NBs. LFER in panel A: eq 1 with a ) 1.23, b ) 9.06. LFER in panel B: LFER 1 (Table 1). Error bars indicate 95% confidence intervals in measured rate constants and standard deviations in the measured EoH values, where reported. Some compounds shown in panel B are not included in panel A, since measured EoH values are not available in those cases. As LFER 1 was fitted using data including these additional compounds, the equation differs slightly from the LFER discussed in the text when comparing EAcalc-based LFERs with EoH,expt-based LFERs, but the difference is insignificant for the purposes of visual comparison. compounds, the LFER for the juglone/H2S system has R ) 4.77 ( 0.94 and β ) -5.60 ( 1.03. This result is almost identical to LFER 1 in Table 1. For the NOM/H2S reduction system, strong correlations between EAcalc and the carbon-normalized rate constants were only found within the pH range 7.2 to 8.6 (Figures S2 to S7). Therefore, no LFERs are reported for reduction at lower pH. We caution that NOM has variable composition that may affect the accuracy of the LFERs, as differences in the reduction characteristics of NOM samples may not be fully accounted for by carbon-normalization of the rate constants. For the AHQDS (anthrahydroquinone-2,6-disulfonate) reduction system (18), no LFER has previously been reported. Since kexpt values are only available for two mono-, non-oNBs, we cannot confirm the accuracy of LFER 4 in Table 1, and we recommend that more kexpt values should be used to validate this relationship. However, based on the result for other quinones, we expect that the LFER approach will also be accurate for this reduction system. For reduction by the (CH3)2COH radical, rate constants are available (26), but no LFER has previously been reported. Our results indicate that the LFER approach provides good accuracy for this reduction system also. 2. Mono-, o-NBs. For several reduction systems involving quinones or NOM (juglone/H2S, lawsone/H2S, and NOM/ H2S at selected pH values) it has been reported that the same LFERs can accurately describe all mono-NBs (SI Table S3) (7, 8). In contrast, Schwarzenbach et al. (7) reported that different LFERs for non-o-substituted and o-substituted compounds were needed for the Fe(II) porphyrin-cysteine reaction system (SI Table S3). However, each of those analyses involved only a single measured EoH value for a mono-, o-NB (2-CH3; estimated EoH values were also used in some studies). Therefore, the applicability of the LFERs to mono-, o-NBs needs further investigation. We first examine the juglone/H2S reduction system, since this is the largest available data set. The data are plotted in Figure 1B, along with the LFER determined using the mono-, non-o-NBs (LFER 1). All of the compounds follow an approximately linear relationship between EAcalc and log k. The poly-NBs and/or o-NBs, which were not used to
determine LFER 1, are generally less accurately described by the LFER. Comparing LFER 1 with a new LFER fitted using all of the data (R ) 4.60 ( 0.35, β ) -5.50 ( 0.42, r2 ) 0.91), we find that in both cases the MAD in log k for all 19 compounds in the data set is 0.40, and the largest errors are mostly for the poly- and/or o-NBs. This indicates that the accuracy that can be obtained using a single “general” LFER is limited by variations in the relationship between EAcalc and log k for different compounds. Considering the data only for the mono-, o-NBs, a separate LFER can be determined (R ) 5.15 ( 1.22, β ) -6.75 ( 1.24) that is slightly more accurate for these compounds. However, the correlation is weaker (r2 ) 0.90) than for the mono-, non-o-NBs, and the scatter in the data set demonstrates that the mono-, o-NBs do not all closely follow a single linear EAcalc-log kexpt relationship. For example, a quite different LFER would be obtained if the data point for 2-COCH3 was not used. Therefore, a LFER cannot consistently provide the same level of accuracy in estimating rate constants for mono-, o-NBs as for mono-, non-o-NBs. It is notable that the maximum AD in log k (1.13) when using LFER 1 is for 2-CH3. This result is inconsistent with previous findings (7, 8) that 2-CH3 can be accurately described by the same EoH,expt-based LFER as the mono-, non-o-NBs. The inconsistency reflects the difference between the EoH,calc value (-0.519 V; calculated from the linear correlation with EAcalc described in ref 19) and the EoH,expt value (-0.590 V) for 2-CH3, which is larger than for any of the other compounds. This leads to a difference of about an order of magnitude between the estimated values of k using LFERs based on EoH,expt and EAcalc, respectively. The question arises as to whether important information about how an o-substituent affects the solvation of the nitro group is lost by using LFERs based on EAcalcsa gas phase propertysrather than EoH,expt. However, as we have discussed elsewhere (19), a calculation method that included solvation effects led to a value similar to EoH,calc (-0.512 V), and we observed a strong linear relationship between EAcalc and EoH,expt for a range of NACs, with only relatively small and nonsystematic differences in that relationship for some of the o-NBs versus other NACs. Therefore, while there are clear differences for 2-CH3 in the accuracy of LFERs based on EoH,expt versus those based on EAcalc, we do not expect that the same is true for all mono-, o-NBs. A more detailed analysis cannot be performed at this time due to the lack of EoH,expt values for most mono-, o-NBs. In Table 1, we report the accuracy of each LFER for the mono-, non-o-NBs and mono-, o-NBs in each of the reduction systems. This information is also displayed graphically in Figure 1B and SI Figures S1-S13. In all reduction systems, the LFERs developed using mono-, non-o-NBs are generally less accurate for mono-, o-NBs, and the latter do not follow a strong linear relationship. Nonetheless, the LFERs in Table 1 can provide estimates of the rate constants for the mono-, o-NBs that are sufficiently accurate to be useful in environmental fate modeling. For example, estimation errors for rate constants in the juglone/H2S reduction system are all within approximately an order of magnitude of the experimental value, which is a good level of accuracy considering that the overall variation in k values is almost 7 orders of magnitude. For the reduction systems involving quinones, NOM or the (CH3)2COH radical, the LFERs overestimate the rate constants for all mono-, o-NBs, indicating that the osubstituted mono-NBs are reduced more slowly than would be expected on the basis of their EAcalc values when compared with their m- and p-isomers. (In some cases, the reduction rate of 2-Cl is well-described by the LFER.) This is true for compounds with both electron-donating (CH3, NH2) and electron-withdrawing (Cl, COCH3) substituents, as well as substituents that are capable of hydrogen bonding (NH2) VOL. 44, NO. 19, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Summary of LFERs of the Form Log k = r EA + β for the Homogeneous Reduction of Substituted Nitrobenzenes in Various Reducing Systemsa reduction system juglone/H2S, pH 6.79, 25 °C (5, 7) lawsone/H2S, pH 6.98, 25 °C (7) NOM/H2S, pH 7.2, 25 °C (8) NOM/H2S, pH 7.5, 25 °C (8) NOM/H2S, pH 7.9, 25 °C (8) NOM/H2S, pH 8.6, 25 °C (8) AHQDS, pH 5, 25 °C (18) Fe(II) porphyrin-cysteine, pH 7.01, 25 °C (7) Fe(II)-tiron complex, pH 5.75 to 5.79, 25 °C (10) Fe(II)-thioglycolate complex, pH 6.50, 25 °C (11) Fe(II)-cysteine complex, pH 7.50, 25 °C (11) (CH3)2COH radical, pH 7, 25 °C (26)
LFER
mono-, non-o-NBs
mono-, o-NBs
poly-NBs
no.
r ( SE
β ( SE
r2
MAD
max. AD
MAD
max. AD
MAD
max. AD
1 2 3A 3B 3C 3D 4 5
4.87 ( 0.18 4.03 ( 0.26 4.91 ( 0.32 5.09 ( 0.33 5.40 ( 0.44 5.31 ( 0.41 4.43 2.44 ( 0.16
-5.60 ( 0.22 -3.36 ( 0.29 -8.86 ( 0.35 -8.90 ( 0.38 -9.06 ( 0.50 -8.81 ( 0.46 -2.04 -2.26 ( 0.18
0.99 0.98 0.98 0.98 0.97 0.97 N/A 0.98
0.12 0.10 0.12 0.19 0.35 0.49 N/A 0.07
0.30 0.17 0.21 0.35 0.57 0.71 N/A 0.11
0.87 1.10 0.59 0.75 0.91 1.06 0.60 0.54
1.13 1.54 0.90 1.02 1.22 1.35 1.00 0.64
0.57 N/A N/A N/A N/A N/A N/A N/A
0.85 N/A N/A N/A N/A N/A N/A N/A
6
4.48 ( 0.43
-9.23 ( 0.47
0.96
0.14
0.36
N/A
N/A
N/A
N/A
7
3.68 ( 0.16
-8.26 ( 0.18
0.99
0.06
0.10
N/A
N/A
N/A
N/A
8
2.63 ( 0.17
-6.57 ( 0.19
0.98
0.06
0.12
N/A
N/A
N/A
N/A
9
0.84 ( 0.15
8.38 ( 0.15
0.94
0.06
0.09
0.26
0.42
N/A
N/A
a Notes: Full details of the reduction systems are provided in the references listed. All LFERs developed using EAcalc and kexpt values for NB and all mono-, non-o-NBs in the data set. For LFERs 3A-3D, the rate constants are carbon-normalized and have units (mg C/L)-1 h-1. SE is the standard error. N/A indicates insufficient data were available to determine that result. The parameters for LFER 1 and the LFER discussed in the section “EAcalc-Versus EoH-Based LFERs” differ slightly, since the data set used to fit the latter LFER was restricted to mono-, non-o-NBs for which EoH,expt values are available.
and those that are not. This suggests that the effect is steric rather than electronic. This observation is consistent with the hypothesis of Schwarzenbach et al. (7) that the ortho substituent sterically hinders the resonance of the nitro group with the aromatic ring, causing destabilization of the radical anion (NAC · -), as a result of which the concentration of the reaction intermediate would be decreased, lowering the reaction rate. In contrast, the compounds with electron-withdrawing substituents are reduced more quickly than is estimated by the LFER in the Fe(II) porphyrin-cysteine system. Schwarzenbach et al. (7) also reported faster reduction rates for o-NBs in this system than predicted by the LFER describing m- and p-NBs. They suggested that the rate of reduction for the mand p-NBs is slowed by the reorganization of the solvent molecules to accommodate formation of the precursor complex between the nitro group and the Fe(II) center, whereas, for the o-NBs, the effect of the ortho substituent on the solvation of the nitro group may lower the reorganization energy, facilitating faster reaction (7). These examples demonstrate that the effect of ortho substituents on the relative reaction rate of mono-NBs depends on the reduction system. 3. Poly-NBs. The juglone/H2S reduction system is the only one for which data for poly-NBs are available. (Since there are few data, we have not attempted to treat the poly-, o-NBs separately from the poly-, non-o-NBs.) A new LFER determined using only these data (R ) 3.63 ( 0.41, β ) -4.20 ( 0.54) has an r2 value of 0.96, indicating a good linear correlation between EAcalc and log kexpt. Compared with LFER 1, this new LFER has a smaller R value, indicating that the rate constants for these poly-NBs are less sensitive than the mono-, non-o-NBs to changes in EAcalc caused by changes in substitution. While the rate constant data are sparse and the underlying mechanism is unclear, it is consistent with expectation that the effect of an individual substituent on the molecular properties will generally be different in a polyNB than in a mono-NB, due to interactions between multiple substituents and the nitro group. Another difference between the poly-NBs and mono-NBs is that many of the poly-NBs contain multiple, distinguishable nitro groups, each of which may act as the reaction center. Regioselectivitysthat is, 7434
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preferential reduction of one of the nitro groupssis known to occur (27), and may change depending on the reducing conditions (28). 4. Recommendations. Based on the above analyses, we conclude the following. LFERs that are established using EAcalc and log kexpt data for NB and/or any mono-, non-o-NBs (Table 1) provide high accuracy in estimating rate constants for this category of compounds in most homogeneous reduction systems examined. The LFER coefficients are essentially invariant to which of these compounds are used to establish the LFER. The same LFERs are quite good, though usually less accurate, when applied to poly-NBs and/or o-NBs. Using data for all three categories of compounds to establish a LFER provides little improvement in accuracy. Therefore, no “general” LFER exists that can provide the same high level of accuracy in estimating rate constants for all polyNBs and/or o-NBs as can be achieved for mono-, non-oNBs. Nonetheless, the rate constants for all of the compounds can be estimated with sufficient accuracy (within approximately an order of magnitude of kexpt) with a single LFER established using NB and/or mono-, non-o-NBs. Reduction rate constant data for poly-NBs and/or o-NBs are scarce, and given the scatter in the mono-, o-NB data, the linear correlations between EAcalc and log kexpt would not be as strong as for the mono, non-o-NBs even if additional data became available. Hence, we do not recommend developing separate LFERs based on mono-, o-NBs or polyNBs. Given these considerations, we recommend the use of the LFERs in Table 1 for estimating rate constants for all of the substituted nitrobenzenes in the respective reduction systems in cases where data needed for environmental fate modeling are unavailable. The ability to identify a single LFER that can be (sufficiently) accurately applied to all of the compounds is a powerful result in terms of providing a simple method to estimate rate constants for NAC reduction. The advantage of using LFERs based on EA rather than measured EoH values is that the method is not limited by the availability of experimental data. The circular approach of using values of EoH estimated from one LFER to make predictions for another reduction system is also avoided. The new correlations with EAcalc that we have reported
here and in ref 19 provide a simple and accurate method to independently check previously reported values of EoH and k. Measured values of EA are more readily available than EoH,expt values for substituted nitrobenzenes, and EA values are generally reported with lower experimental uncertainties (19). EA values can also be calculated with high accuracy and efficiency, such that the LFER approach can be applied to either the measured or calculated EA values. Insofar as the coefficients a and b in eq 1 can be considered to offer mechanistic insights, this information is also available from EA-log k LFERs, since the (approximate) relationship between a and b and R and β is known based on the empirical relationship between EA and EoH that we reported in ref 19. Estimating New Reduction Rate Constants. The LFERs in Table 1 have been used to estimate rate constants in each of the reducing systems for all 23 NACs examined in this work. Estimated k values are listed in SI Table S4. We report a total of 169 estimated reduction rate constants in cases for which no measurements are available, representing 23 NACs in nine different reducing systems. In the cases where measurements are available, the deviation between the measured and estimated k values is reported as an indication of the accuracy of the LFERs, discussed above. Applications to Environmental Fate Modeling for NACs. We have demonstrated here that linear correlations exist between (QM-calculated) EA values and log k values that can be used to estimate rate constants for the reduction of substituted nitrobenzenes in a range of homogeneous reducing systems. In cases where no measured rate constant data are available, the LFERs we have reported (Table 1) and the k values estimated from them (SI Table S4) can be used to estimate the half-lives for NACs in natural or engineered environments resembling those reducing systems. The approach may also be applied to other NACs (e.g., musk xylene) and to homogeneous reduction systems not examined in this work. Caution should be exercised in utilizing the LFER approach in cases where data have not been shown to support the existence of a linear correlation between EoH or EA and log k, as some mechanistic aspects of NAC reduction remain unknown. These findings may also be applicable to heterogeneous systems (5, 9), however, other processes not directly linked to NAC reduction, such as biological regeneration of reactive surface sites (5), may limit the reaction rates. To establish LFERs in new reduction systems, only measured k values for as few as two simple mono-, non-osubstituted nitrobenzenes or NB are needed. Once LFERs have been established for a particular reaction system, no additional experimental data are required to estimate k values for other compounds. Therefore, we have provided a relatively simple, accurate and general procedure to estimate halflives for NACs in reducing environments.
Acknowledgments This material is based upon work supported by the National Science Foundation under Grant GOALI-0853685. We thank the anonymous reviewers for their comments, which led to significant improvements in the manuscript.
Supporting Information Available Table S1 lists measured rate constants, along with values of EAcalc and EoH,expt. Classifications for each of the compounds (e.g., ortho-substituted) are provided in Table S2. Table S3 summarizes LFERs reported in the literature for the homogeneous reduction of substituted nitrobenzenes. Table S4 lists LFERs and estimated k values determined in this work. Figures S1-S13 are plots of the EAcalc-log kexpt values and LFERs for the reduction systems lawsone/H2S, NOM/H2S at
various pH values, AHQDS, Fe(II) porphyrin-cysteine, Fe(II)tiron, Fe(II)-thioglycolate, Fe(II)-cysteine, and the (CH3)2COH radical. This material is available free of charge via the Internet at http://pubs.acs.org.
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