Ind. Eng. Chem. Res. 2008, 47, 8533–8541
8533
Initial Degradation Rate of p-Nitrophenol in Aqueous Solution by Fenton Reaction Meng-Wen Chang, Tai-Shang Chen, and Jia-Ming Chern* Department of Chemical Engineering, Tatung UniVersity, Taipei, 104, Taiwan
Because of environmental concern, wastewater containing nitrophenols must be treated before it is allowed to discharge. In addition to traditional treatment methods, advanced oxidation processes (AOPs) using a powerful hydroxyl radical to decompose organic pollutants in wastewater receive great attraction. Among the many AOPs to degrade nitrophenols, the Fenton reaction was proven to be the most effective and the least expensive method, and the resultant solutions treated by the Fenton reagent were not toxic. However, owing to the complicated mechanism involved in the Fenton reaction, an oversimplified first-order rate equation or empirical rate laws were usually used to model the Fenton reaction. Such oversimplified or empirical kinetics cannot be used confidently in the design and operation of large-scale Fenton processes. A series of experiments were carried out to determine the initial decomposition rates of p-nitrophenol (PNP) at varying initial ferrous ion, hydrogen peroxide, and PNP concentrations. The PNP decomposition rate equations for two proposed mechanisms were derived by the general rate methodology. The rate equation resulting from the reaction mechanism involving the PNP reaction with both hydroxyl and hydroperoxy radicals fits the experimental data well. Introduction Phenolic hydrocarbons including nitrophenols are widely used in pharmaceutical, petrochemical, and other chemical manufacturing processes. Because of their harmful effects, wastewaters containing phenolic compounds must be treated before being discharged into receiving water bodies. The methods to treat wastewaters containing phenolic compounds can be classified into biological methods,1-12 physical methods,13-21 and chemical methods.22-33 The reaction rates of the biological methods are usually slow; thus huge reactor volumes or spaces are usually required. The physical methods only transform the pollutants into other forms; thus new waste disposal problems are generated. The reaction rates of the chemical methods are relatively high and total mineralization is possible if the reaction conditions and reactor is adequately designed. Among the many chemical methods, the advanced oxidation process (AOP) using the hydroxyl radical ( · OH) has been recognized as a promising technology to treat wastewaters containing refractory organic compounds. There are various advanced oxidation processes that can produce hydroxyl radicals, such as Fenton reagent (Fe2+/H2O2), O3/UV, H2O2/UV, and TiO2/UV etc. Goi and Trapido34 compared many AOPs to degrade nitrophenols and concluded that the Fenton reagent was the most effective and the least expensive method for nitrophenol degradation and the resultant solutions treated by the Fenton reagent were not toxic. The Fenton reaction involves the reaction of hydrogen peroxide (H2O2) and ferrous ion (Fe2+) or ferric ion (Fe3+). Walling and his coauthors35-37 investigated the mechanism and kinetics of organic substances reacting with the Fenton reagent. After Walling, various researches studied the characteristics and operating conditions of the Fenton reaction for treating wastewater and the optimal pH range of the Fenton process was found to be between 2 and 4.38-40 There are numerous research activities on the Fenton reaction that can be found in the literature. Many studies just reported the treatment results for certain targeted compounds without mentioning the reaction mechanisms and kinetics. Some studies, although * To whom correspondence should be addressed. E-mail: jmchern@ ttu.edu.tw. Tel.: +886 221822 928 ext 6277. Fax: +886 225861939.
presenting some kinetic data, did not elucidate the reaction mechanisms and their corresponding rate equations. Some studies did propose simplified reaction mechanisms, but did not derive rigorous rate equations from their proposed mechanisms. Probably due to its complexity, the reaction mechanism and kinetics of the Fenton reaction are seldom investigated in detail. Therefore many studies used the power-law type or simple firstorder rate equation form to describe the Fenton reaction.38,39 The apparent first-order rate constants were not really constants; they were influenced by the reaction conditions, for example, the coreactant concentrations. The empirical power-law type or simple first-order rate equation may be adequate to fit some experimental data, but cannot be used confidently for rector design. On the contrary, a reliable kinetic model resulting from the reaction pathway and mechanism can be used more confidently for reactor design, scale-up, and optimization. For the kinetic studies involved of the reaction mechanism in batch reactors, elementary reaction steps were proposed and a system of ordinary differential equations (ODEs) was set up to solve for all the species concentrations. For example, a 24step mechanism,41 a 28-step mechanism,42 and a 49-step mechanism43 were proposed to model the reaction kinetics of organic compound degradation by the Fenton or Fenton-like reactions, respectively. The calculated species concentrations were compared with the measured ones and the rate coefficients were adjusted to best fit the experimental data. Solving a system of ODEs and then minimizing the sums of squares of the errors between the calculated and experimental data is not a problem since many subroutines are available. The problem is to determine the single set of best-fit rate coefficients. Because many rate coefficients appeared in the proposed mechanisms, the order of magnitude of one rate coefficient was usually varied while keeping all others constant to test the sensitivity of that reaction step on the overall result. In general, such numerical integration plus error minimization leads to multiple best-fit parameters that need careful statistical judgment. To reduce the system of ODEs and avoid such ambiguous situation, rate equations with a less number of lumped coefficients while retaining mathematical correctness are highly desired. This study
10.1021/ie8003013 CCC: $40.75 2008 American Chemical Society Published on Web 10/18/2008
[
8534 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
Figure 1. A snowflake type reaction network with fully reversible, simple, 10-ended, 8-node with 17 reduced reversible steps.44
therefore aims at elucidating the reaction kinetics of pnitrophenol degradation by the Fenton reaction using an effective kinetic modeling methodology based on the Bodenstein approximation for trace-level intermediates.44 According to the numerical simulation, the free radicals indeed remain at trace level.41 Therefore, the effective kinetic modeling methodology is applicable. In most studies involved with the reaction mechanism of organic compound degradation by Fenton reaction, only the reaction between organic compound with the hydroxyl radical ( · OH) was considered; the reaction between organic compound with the hydroperoxyl radical (HO2 · ) was neglected. There is no reason to assume that organic compound reacts with the hydroxyl radical only. The hydroperoxyl radical may also play an important role in the degradation of organic compound. However, it is not easy to identify the importance of the reaction with the hydroperoxyl radical by the traditional method. The initial rate equations for organics degradation involving both reaction steps are quite different; they can be easily derived by the effective kinetic modeling methodology and thus be used to discriminate the two reaction mechanisms easily. Because the main purpose of this study is to illustrate the application of the methodology, only the initial PNP degradation rates under varying experimental conditions were measured in a small UV cell; the experimental and modeling results for the product and intermediates in a batch reactor will be presented in a separate publication. To facilitate understanding how to use the methodology, the algorithm for deriving the rate for multinode reaction with branches will be briefly described below. General Algorithm for Snowflake-Type Network. The rate law of formation of any product Pj (or of consumption of any reactant Pj) in a single- or multinode simple network of arbitrary configuration can be derived by the general algorithm. Consider an example shown in Figure 1, a fully reversible, simple, 10ended, 8-node with 17 reduced reversible steps. The rate law rP1 is composed of 9 contributions of net reaction rates between P1 and the other 9 members P2, P3,..., P10. As an example of compilation of the contribution of P5 T P1 has the form rP5TP1 )
{
(Π51[P5] - Π15[P1])|M51| |M|
with
∏
∏
) ΛP5,5Λ53Λ32Λ21Λ1,P1 ) ΛP1,1Λ12Λ23Λ35Λ5,P5 15 S1 ) Λ1,P1 + Λ1,P2 + Λ12 S2 ) Λ21 + Λ23 + Λ26 S3 ) Λ32 + Λ34 + Λ35 S4 ) Λ4,P3 + Λ4,P4 + Λ43 S5 ) Λ5,P5 + Λ5,P6 + Λ53 S6 ) Λ62 + Λ67 + Λ68 S7 ) Λ7,P7 + Λ7,P8 + Λ76 S8 ) Λ8,P9 + Λ8,P10 + Λ86
51
and matrix M, M51 defined as
(1)
}
(2)
]
S1 Λ12 0 0 0 0 0 0 Λ21 S2 Λ23 0 0 Λ26 0 0 0 0 0 Λ32 S3 Λ34 Λ35 0 0 0 0 0 0 0 Λ43 S4 M) (3) S5 0 0 0 0 0 Λ53 0 S6 Λ67 Λ68 0 Λ62 0 0 0 0 0 0 0 0 Λ76 S7 0 S8 0 0 0 0 0 Λ86 0 S4 0 0 0 0 S6 Λ67 Λ68 (4) M51 ) 0 Λ76 S7 0 S8 0 Λ86 0 M is the characteristic matrix of the entire network; it is an n × n square matrix, with n being the number of nodes, with elements Si (i ) 1-n) along its diagonal, with Λij at position row i and column j for all Xi and Xj connected directly, and with zero in all other elements. M51 is the characteristic matrix of the pathway P5 T P1 that is compiled similarly to M, but with the mth rows and mth columns omitted, where all m’s are the indices of all node intermediates on the path from P5 to P1. If there exist loops in the reaction networks, such as two or more parallel pathways between Pi and Pj, the contribution of all parallel pathways to an affected rates Pi T Pj are additive. It is important to note that all the reduced reversible steps between the nodes in Figure 1 can contain an arbitrary number of steps Xj
Xj+1
T
]
[
...
T
T Xj+i
...
T
T Xk (5)
with the “segment coefficients” Λ calculated by i)k-1
Λjk )
i)k-1
Π λi,i+1
i)j
Λkj )
and
Djk
Π λi+1,i
i)j
(6)
Djk
where the λ coefficients are the pseudo-first-order rate coefficients of quasi-single molecular steps that are the products of the actual rate coefficients and the concentrations of any coreactants of the respective steps. For example, for the step X0 + A T X1, λ01 ) k01[A] and λ10 ) k10. The Djk operator in the denominator of eq 6 can be expressed in a compact form as k
Djk ) Σ
i-1
k-1
(Πλ
i)j+1 m)j+1
m,m-1
Π λm,m+1
m)i
)
(7)
(products Π ) 1 if lower index exceeds upper). More easily, Djk is generated as the sum of the products of the rows of the square matrix of order n with elements 1 along the diagonal, with rate coefficients of mth step in the mth column, and with forward rate coefficients above and reverse rate coefficients below the diagonal:
[
1 λj+1,j λj+1,j ... λj+1,j λj+1,j
λj+1,j+2 1 λj+2,j+1 ... λj+2,j+1 λj+2,j+1
λj+2,j+3 λj+2,j+3 1 ... λj+3,j+2 λj+3,j+2
... ... ... ... ... ...
λk-2,k-1 λk-2,k-1 λk-2,k-1 ... 1 λk-1,k-2
λk-1,k λk-1,k λk-1,k ... λk-1,k 1
]
(8)
Taking j ) 0 and k ) 4 for example, D04 can be easily obtained from eq 8 as λ12λ23λ34 + λ10λ23λ34 + λ10λ21λ34λ10λ21λ32. Experimental Details Since the Fenton reaction is a free radical reaction, trying to measure the concentrations of ferrous ion, ferric ion, and
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8535
hydrogen peroxide in real time is very difficult. We only measured the concentration of PNP (reagent grade, Fluka Chemical Co. Japan) by an UV-vis spectrophotometer (JASCO, model V-560) continuously. The model organic compound, PNP was diluted to desired concentration by deionized water. The iron(II) sulfate (Reagent grade, Nihon Shiyaku Industries, Ltd. Co. Japan) solution was prepared by deionized water. After mixing the PNP and Fe(II) solutions, the pH of the mixed solution was adjusted to 3.0 by sulfuric acid (reagent grade, Yakuri Pure Chemicals Co. Japan) for suitable reaction condition. For the ease of online real-time measurement, all the reaction solutions were placed in an UV cell directly. The hydrogen peroxide (reagent grade, Nihon Shiyaku Industries Ltd. Japan) was diluted by deionized water to a desired concentration and injected to the cell to initiate the reaction. Then the concentration of PNP was continuously measured by the UV-vis spectrophotometer at 318 nm wavelength for 10 min. To reduce the influence of mass transfer resistance in the UV cell, we used low initial concentrations of the reactants and only the initial rates of reaction were used to find the kinetic parameters. The initial rates were calculated from the initial slopes of the residual PNP concentration versus time plots. All the experiments were conducted in an air-conditioned room with the temperature controlled at 25 ( 1 °C. The initial rate data were found to be comparable with those obtained in a stirred reactor from which samples were withdrawn and analyzed by HPLC (Thermoseparation Products: column, hypersil C-18; pump, Spectra series P100; UV detector, Spectra series UV150). Results and Discussion 1. Effect of PNP Concentration. The first series of experiments were conducted at constant Fe2+ concentration (0.1 mM) and H2O2 concentration (5.0 mM) while the PNP concentration was varied from 0.1 to 0.4 mM. As shown by Figure 2a, the initial PNP decomposition rate increases with increasing PNP concentration. However, the decomposition rate is not proportional to the PNP concentration. The degradation of PNP starts with the reaction of hydroxyl radical with PNP: PNP + · OH f intermediate f product (9) Although most studies used the following pseudo-first-order model to describe the kinetics in a batch reactor the apparent rate coefficient kapp obtained was found to be dependent on the initial PNP concentration. d[PNP] ) k[·OH][PNP] ) kapp[PNP] (10) dt This approach is very questionable; the hydroxyl radical concentration [ · OH] should depend on the reactant concentrations including [PNP]. It is not appropriate to first assume the apparent rate coefficient kapp is a constant, integrate eq 10, use a ln[PNP] versus t plot to find the slope (-kapp), and finally conclude that kapp depends on the initial PNP concentration. If the kapp depends on the PNP concentration, the variable separation method cannot be used to integrate eq 10 directly to lead to a linear plot of ln[PNP] versus t. Figure 2b shows the plot of reciprocal rate versus reciprocal PNP concentration. Because the reciprocal rate can be adequately correlated as a linear function of the reciprocal PNP concentration, we can use the following empirical equation for the PNP decomposition rate at constant H2O2 and Fe2+ concentrations: -rPNP ) -
-rPNP )
k1[PNP] 1 + k2[PNP]
(11)
Figure 2. Effect of initial PNP concentration on the initial decomposition rate.
where k1 and k2 are empirical constants. According to eq 11, the reaction is first order with respect to PNP in a low PNP concentration range and becomes zeroth order in a high PNP concentration range. 2. Effect of H2O2 Concentration. The second series of tests were conducted at constant PNP concentration (0.4 mM) and Fe2+ concentration (0.1 mM) while the H2O2 concentration was varied from 2 to 20 mM. As shown by Figure 3a, the initial PNP decomposition rate first increases with increasing H2O2 concentration but seems to approach a plateau at high H2O2 concentration. Because the degradation of PNP starts with the attack of the hydroxyl radicals that are generated from the H2O2 reaction with Fe2+ ion k01
H2O2 + Fe2+ 98 Fe3+ + OH- + · OH
(12)
more H2O2 molecules added to the system will generate more · OH radicals and thus increase the PNP decomposition rate. However, too high H2O2 concentration will consume the · OH radicals via the following reaction: k12
H2O2 + · OH 98 H2O + HO2 ·
(13)
The resultant HO2 · radical is less powerful than the · OH radicals; the PNP decomposition rate is thus decreased. Figure 3b shows the plot of reciprocal rate versus reciprocal H2O2 concentration. Because the reciprocal rate can be adequately correlated as a linear function of the reciprocal H2O2 concentration, we can use the following empirical equation for the PNP decomposition rate at constant PNP and Fe2+ concentrations:
8536 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
-rPNP )
k1 ′ [H2O2] 1 + k2 ′ [H2O2]
(14)
where k1′ and k2′ are empirical constants. According to eq 14, the PNP decomposition rate is first- and zeroth orders with respect to H2O2 in a low and high H2O2 concentration ranges, respectively. 3. Effect of Fe2+ Concentration. The third series of tests were conducted at constant PNP concentration (0.4 mM) and H2O2 concentration (5.0 mM) while the Fe2+ concentration was varied from 0.1 to 0.8 mM. As shown by Figure 4a, the initial PNP decomposition rate first increases with increasing Fe2+ concentration but also approaches a plateau at high Fe2+ concentration. A higher Fe2+ concentration favors the formation of the · OH radicals according to eq 12, but too high Fe2+ concentration will consume part of the · OH radicals: k12 ′
Fe2+ + • OH 98 Fe3+ + OH-
(15)
The PNP decomposition rate is thus decreased due to the consumption of the · OH radicals by Fe2+. Figure 4b shows the plot of reciprocal rate versus reciprocal Fe2+ concentration. Because the reciprocal rate can be adequately correlated as a linear function of the reciprocal Fe2+ concentration, we can use the following empirical equation for the PNP decomposition rate at constant PNP and H2O2 concentrations: -rPNP )
k1 ″ [Fe2+] 1 + k2 ″ [Fe2+]
By combining eqs 11, 14, and 16, we can propose the following empirical equation to describe the PNP decomposition rate as a function of the PNP, H2O2, and Fe2+ concentrations: -rPNP )
ka[H2O2][Fe2+][PNP] [H2O2] + kb[Fe2+] + kc[PNP]
(17)
where ka, kb, and kc are lumped rate coefficients. 4. Reaction Mechanism and Kinetic Model. 4.1. PNP Decomposed by •OH Radical Only. The simplest mechanism proposed for PNP decomposition involves PNP reaction with · OH radical only. In addition to reactions 12, 13, and 15, more reaction steps are commonly cited in the literature: k23
HO2 · 98 H+ + O2· k32
H+ + O2 · 98 HO2 · k34
2+ Fe3+ + O2 · 98 O2 + Fe
k34 ’
3+ 2H+ + Fe2+ + O2 · 98 H2O2 + Fe
k23 ’
Fe3+ + HO2 · 98 H+ + Fe2+ + O2
(18)
(19)
(20)
(21)
(22)
(16)
where k1 and k2 are empirical constants.
Figure 3. Effect of initial H2O2 concentration on the initial decomposition rate.
k02
H2O2 + Fe3+ 98 Fe2+ + H+ + HO2 ·
(23)
Figure 4. Effect of initial Fe2+ concentration on the initial decomposition rate.
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8537 k20
Fe2+ + H+ + HO2 · 98 H2O2 + Fe3+
(24)
Unlike eq 9 that considers PNP decomposition in two steps, we consider the following sequential steps leading to final mineralization products: k12 ″
PNP + · OH 98 X1 + P1
(25)
Fe2+
PNP
H2O2 98 · OH 98 · · · f products Fe3+, OH-
k″23
X1 + R1 98 X2 + P2
(26)
k″n+1,n+2
Xn-1 + Rn-1 98 Xn + Pn
H2O2 + Fe2+ + PNP f · · · f Fe3+ + OH- + products Applying eq 1 to eq 4 leads to
k″n+1,n+2
(28)
Reactions 12, 13, 15, and 18 -28 constitute the reaction network of PNP decomposition by the Fenton reagent. It is important to note that all the radical recombination steps are neglected. In reactions 25 -28, all the Xi represents unstable intermediates; all the Ri represent the coreactants; and all the Pi represents stable intermediate products such as various organic acids after ring opening steps. Reaction steps 25 -28 can be rewritten as following linear segment: ·OH f X1 f X2 f ... f Xn-1 f Xn f products
(29)
with coreactants and coproducts not shown. By applying eqs 6 -8, we can replace the multistep segment by a reduced single step · OH f products with the following segment coefficients: and
The overall reaction in this pathway is
(27)
Xn + Rn 98 CO2 + H2O + NO3
Λ•OHfP ) k01[PNP]
reaction network with the coreactants shown above the arrows and the coproducts shown below the arrows. This network contains three nodes with pseudo-first-order in the intermediates. Although the general rate equation of the snowflake type network can be applied to obtain all the pathway rate equations, the PNP decomposition rate is of primary concern in this study. The reaction pathway involving PNP decomposition is
ΛPf·OH ) 0
(30)
Equation 30 shows that any reaction steps, reversible or
P1) have no contribution to the kinetic rate. Figure 5 shows the
2
+
32
-rPNP )
|
S1 k12[H2O2] 0 k23 S2 0 + 0 k32[H ] S3
or -rPNP )
23 3
|
k01k12″[H2O2][Fe2+][PNP] S1
(31)
(32)
where S1 is the sum of the pseudo-first-order rate coefficients of all the steps stemming from · OH: S1 ) k12[H2O2] + k12 ′ [Fe2+] + k12″[PNP]
(33)
Combining eqs 32 and 33 leads to -rPNP )
k12″
irreversible, after an irreversible step (PNP + · OH 98 X1 +
|k S[H ] kS |
k01k12″[PNP][H2O2][Fe2+]
k01k12″[H2O2][Fe2+][PNP] k12[H2O2] + k12 ′ [Fe2+] + k12″[PNP]
k12″ [H O ][Fe2+][PNP] k12 2 2 ) k12″ k12 ′ 2+ [Fe ] + [PNP] [H2O2] + k12 k12 k01
)
ka[H2O2][Fe2+][PNP] [H2O2] + kb[Fe2+] + kc[PNP]
{
(34)
where ka, kb, and kc are lumped rate coefficients: k12 ″ k12 k12 ′ kb ) k12 k12″ kc ) k12
Figure 5. Proposed mechanism 1 for pollutant decomposition by Fenton reaction; (a) original reaction networks with the coreactants shown above the arrows and the coproducts shown below the arrows, (b) reaction network in X notations (intermediates) and P notations (reactants or products).
ka ) k01
(35)
Comparing eqs 17 and 34, we can find that the proposed mechanism gives the same rate equation as the empirical one. To find the best values for the lumped parameters, a nonlinear regression method was used to minimize the sum of squares of the errors between the experimental initial rate and the rate predicted by eq 35. We first treated the three lumped parameters as adjustable ones and the nonlinear regression gave pretty good data fitting to eq 35. This suggests that the proposed mechanism is quite reasonable to describe the PNP decomposition kinetics.
8538 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
S2 ) k23 + k23 ′ [Fe3+] + k20[Fe2+][H+] + k23 ″ [PNP] (39) S3 ) k32[H+] + k34[Fe3+] + k34 ′ [Fe2+][H+]2
(40)
Combining eqs 38-40 leads to r2 )
AB C(D + E + F)
(41)
where A ) k01k12k23″[H2O2]2[Fe2+][PNP] B ) k32[H+] + k34[Fe3+] + k34 ′ [Fe2+][H+]2 C ) k12[H2O2] + k12 ′ [Fe2+] + k12 ″ [PNP] D ) k32[H+](k23 ′ [Fe3+] + k20[Fe2+][H+] + k23 ″ [PNP]) E ) k34[Fe3+](k23 + k23 ′ [Fe3+] + k20[Fe2+][H+] + k23 ″ [PNP]) F ) k34 ′ [Fe2+][H+]2(k23 + k23 ′ [Fe3+] + k20[Fe2+][H+] + k23 ″ [PNP]) The third pathway is Figure 6. Proposed mechanism 2 for pollutant decomposition by Fenton reaction: (a) original reaction networks with the coreactants shown above the arrows and the coproducts shown below the arrows; (b) reaction network in X notations (intermediates) and P notations (reactants or products).
4.2. PNP Decomposed by · OH Radical and HO2 · Radical. Although the oxidation potential of the hydroperoxy radical (HO2 · ) is less than that of the hydroxyl radical, the probability of reaction between HO2 · radical and PNP cannot be excluded. We can assume a similar PNP decomposition pathway by HO2 · radical with the rate coefficient of the reaction between HO2 · radical and PNP being k23: k23 ″
PNP + HO2 · 98 X1 + P1
(36)
With this additional PNP decomposition pathway, the reaction network is modified and shown in Figure 6. In this proposed mechanism, three pathways must be considered to obtain the PNP decomposition rate. The first pathway remains the same: Fe2+
Fe3+
Fe3+, OH-
The overall reaction for this pathway is H2O2 + Fe3+ + PNP f Fe2+ + H+ + product Applying eq 1 to eq 4 leads to r3 )
(
)
(43)
where G ) k01kb[PNP][H2O2][Fe2+] H ) [H2O2] + ka[Fe2+] + kb[PNP] kc I ) [H2O2] + (1 + kd[Fe2+][H+]) kb
k12″ [H O ][Fe2+][PNP] k12 2 2 -r1 ) k12 ′ 2+ k12″ [H2O2] + [Fe ] + [PNP] k12 k12 k01
J ) [Fe2+][H+]+kc[PNP]
(37)
K ) kd[Fe2+][H+](ke + [Fe2+][H+]+kc[PNP]) where the lumped rate coefficients are
The second pathway is -
H2O2
ka )
PNP
H2O2 98 · OH 98 HO2 · 98 products H2O
2H2O2 + Fe2+ + PNP f H2O + OH- + Fe3+ + product Applying eq 1 to eq 4 leads to k01k12k23″[H2O2]2[Fe2+][PNP]S3 S1(S2S3 - k23k32[H+])
k12′ k12
kb )
k12 ″ k12
kc )
k23 ″ k20 kd )
The overall reaction for this pathway is
where
G I 1+ H J+K
PNP
The reaction rate in the above pathway is also the same:
r2 )
(42)
S2S3 - k23k32[H+]
-rPNP )
Fe3+, OH-
Fe3+, OH-
k02′k23 ″ [H2O2][Fe3+][PNP]S3
We now can add the rate contributions from the three pathways to obtain the PNP decomposition rate, that is, -rPNP ) r1 + r2 + r3. Since the initial concentration of [Fe3+] is zero, r3 ) 0, all the terms involving [Fe3+] in r2 are also zero. Thus the PNP decomposition rate becomes
H2O2 98 · OH- 98 · · · f products
Fe2+
PNP
H2O2 98 HO2 · 98 products
(38)
k34′ k32
ke )
k23 (44) k20
We treated k01, ka-ke as six adjustable parameters and used the nonlinear regression method to give very good data fitting to eq 43. Although both eq 34 and eq 43 can be used to fit the experimental data quite well if all the lumped parameters are treated as adjustable ones, actually many rate coefficients can be found in the literature. Therefore, we cannot arbitrarily adjust all the lumped parameters to minimize the sum of squares of the errors.
Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008 8539 Table 1. Kinetic Parameters of the Fenton Reaction rate coefficient (M-1 s-1)
reaction step
7.6 × 10
k12
2.7 × 10
Buxton et al.45
1.58 × 105
Bielski et al.46
1 × 10
Bielski et al.46
5 × 107
Rothschild and Allen47
1 × 10
Rush and Bielski48
H2O2 + Fe2+ 98 Fe3+ + OH- + · OH k23
HO2 · 98 H+ + O2- ·
Walling37
10
k32
H+ + O2- · 98 HO2 · k34
Fe3+ + O2- · 98 O2 + Fe2+
7
k34
2H+ + Fe2+ + O2- · 98 H2O2 + Fe3+
3 × 108
k12
Fe2+ + · OH 98 Fe3+ + OH-
Walling37
3.1 × 10
Rush and Bielski48
1 × 10-2
Walling and Goosen35
1.2 × 10
Jayson et al.49
k11
5.3 × 10
Walling37
k12
9.05 × 106
5
k23
Fe3+ + HO2 · 98 H+ + Fe2+ + O2 k02
H2O2 + Fe3+ 98 Fe2+ + H- + HO2 ·
6
k20
Fe2+ + H+ + HO2 · 98 H2O2 + Fe3+
9
· OH + · OH 98 H2O2 · OH + PNP 98 intermediate
1.50 × 10
k23
From mechanism 2.
Table 2. Fit Results of the PNP Decomposition Rate Coefficients parameter
mechanism 1
mechanism 2
unit
k12 k23 R2 SSQ
9.97 × 10 0.854 200
9.05 × 10 1.50 × 10-6 0.961 54
-1
6
this studya
-6
HO2 · + PNP 98 intermediate
6
M s-1 M-1 s-1 µM2 s-2
4.3. Model Discrimination. The PNP decomposition rate equations for the two proposed mechanisms have been derived using the general rate equation approach. The experimental initial rate data were first fitted to eq 34 using k12 as the only one adjustable parameter; the data were also fitted to eq 43 using k12 and k23 and as the only two adjustable parameters. All the other rate coefficients in the proposed mechanisms can be found in the literature and are listed in Table 1. The nonlinear regression results for the two proposed rate equations are shown in Table 2. Using the known rate coefficients in the literature, the k12 in mechanism 1 is 9.97 × 106 M-1 s-1 and its 95% confidence interval is 9.25 × 106 e k12 e 10.69 × 106. The k12 in mechanism 2 is 9.05 × 106 M-1 s-1 and its 95% confidence interval is 8.61 × 106 e k12 e 9.49 × 106; the k23 in mechanism 2 is 1.50 × 10-6 M-1 s-1 and its 95% confidence interval is 1.10 × 10-6 e k23 e 1.90 × 10-6. Many different initial guesses of the rate coefficients lead to the same and unambiguous results. Although the rate coefficient of PNP reacting with the HO2 · radical is much smaller than that of PNP reacting with the · OH radical, taking into account the reaction of PNP with the HO2 · radical gives a larger R2 and a smaller sum of squares of the errors between the model and data. This suggests the rate equation corresponding to mechanism 2 is more reasonable. The parity plots shown in Figure 7 also reconfirm that mechanism 2 is more adequate to describe the PNP decomposition kinetics by the Fenton reagents. 4.4. Effect of Radical Recombination. In the derivation of the rate equations of the proposed mechanisms, the free radical recombination step is neglected. We need to re-examine if this assumption is justified. The · OH free radical concentration can be readily derived from eq 37: [·OH] )
1 7
H2O2 + · OH 98 H2O + HO2 ·
a
reference
k01
k01[H2O2][Fe2+] k12[H2O2] + k12 ′ [Fe2+] + k12″[PNP]
(45)
For given reactant concentrations, [ · OH] can be calculated. Therefore, the reaction rates of the competitive steps involving the · OH free radical can be calculated and compared.
{
this study
For example, if [H2O2] ) [Fe2+] ) [PNP] ) 0.1 mM, [ · OH] ) 2.13 × 10-11 M and the competitive rates are k12[·OH][H2O2] ) 5.76 × 10-8 M/s for step · OH + H2O2 f HO2 ·
k12 ′ [·OH][Fe2+] ) 6.83 × 10-7 M/s for step 3+ · OH + Fe2+ 2 f OH + Fe
k12″[·OH][PNP] ) 1.93 × 10-8 M/s for step · OH + PNP f products k11[·OH]2 ) 2.41 × 10-12 M/s for step · OH + · OH f H2O2
(46)
Obviously, the rate of · OH free radical recombination is much smaller than those of the other steps considered in the proposed mechanism. Considering the orders of magnitude of the competitive rates, the · OH free radical recombination step can be reasonably neglected in the kinetic analysis. 4.5. Effect of Intermediate Products. As proposed by Gallard and De Laat,41 the intermediate products can serve as the scavengers of the hydroxyl radical and thus influence the PNP degradation rate. Consider, for example, if we add the following reaction steps in mechanism 1, kPi
Pi + · OH 98 products
i ) 1, 2,n
(47)
then S1 in eq 33 becomes n
S1 ) k12[H2O2] + k12 ′ [Fe2+] + k12″[PNP] +
∑k
Pi[Pi]
(48)
i)1
Substituting this S1 into eq 34, the PNP degradation rate becomes a function of the intermediate concentration. However, the intermediate products have no influence on the initial degradation rate of PNP because at t ) 0, [Pi] ) 0 for all the intermediate products. To model the concentration histories of the reactants and intermediate products, the general algorithm for snowflake networks is still applicable if all the reactions between intermediates and free radicals are considered. Conclusions A series of experiments were carried out to study the initial decomposition rates of p-nitrophenol by the Fenton reaction
8540 Ind. Eng. Chem. Res., Vol. 47, No. 22, 2008
Figure 7. Comparison of the experimental and predicted initial rates for the two mechanisms.
at varying operating conditions. The rate equations of two proposed mechanisms for PNP decomposition were derived by the general rate equation method. Application of the general rate equation method is quite straightforward and the rate equations reflecting the elementary reaction steps can be derived by direct substitution and collection of the rate coefficients. The initial rate data with varying initial ferrous ion, hydrogen peroxide and PNP concentrations were used to discriminate the two proposed mechanisms and to determine the rate coefficient for the reaction of PNP with hydroxyl and hydroperoxy radicals, respectively. Although the proposed mechanism involving PNP reaction with hydroxyl radical only gives satisfactory agreements between the experimental rates and the predicted results, the rate equation considering PNP reacting both with hydroxyl and hydroperoxy radicals gives better fit to the experimental data. In the future, the same general rate equation method will be used to find the pathway reaction rates with which the concentration histories of PNP and intermediate products can be calculated. Acknowledgment We would like to thank Ms. S.-W. Wang and Mr. C.-C. Wei for performing part of experimental work. The financial support from National Science Council of Taiwan under grant NSC962221-E-036-023 is highly appreciated. Literature Cited (1) Arcangeli, J.-P.; Arvin, E. Biodegradation rates of aromatic contaminants in Biofilm reactors. Water Sci. Technol. 1995, 31, 117–128.
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ReceiVed for reView February 20, 2008 ReVised manuscript receiVed August 31, 2008 Accepted September 4, 2008 IE8003013
