Decomposition of hydrogen peroxide in a catalytic fluidized-bed reactor
Shanshan Chou
1, Chihpin Huang
∗Institute of Environmental Engineering, National Chiao Tung University, Hsinchu 30039, Taiwan Received 25 September 1998; received in revised form 16 February 1999; accepted 6 May 1999
Abstract
The decomposition of H2O2by a novel supported␥-FeOOH catalyst was performed in a continuous fluidized-bed reactor. This catalyst has been successfully used in the treatment of organic contaminants with H2O2in our previous work. In this study, we attempted to determine the effects of pH, H2O2concentration, and catalyst concentration on the decomposition of H2O2. An approach, we regarded this reactor as a continuous-flow stirred-tank reactor, was applied to investigate the kinetic behavior. At low H2O2concentration, the decomposition rate of H2O2was found to be proportional to both H2O2and catalyst concentrations. At high H2O2concentration, however, the rate decreased with the increasing H2O2concentration. This can be explained by the substrate inhibition model. The large difference in the observed first-order rate constants under various pH values was also modeled. The model agreed well with the experimental results. ©1999 Elsevier Science B.V. All rights reserved.
Keywords: Iron oxide; Hydrogen peroxide; Heterogeneous catalysis; Fluidized bed
1. Introduction
Hydrogen peroxide has been found to be useful in wastewater treatment [1,2] and in soil remediation [3,4]. It is a powerful oxidant for contaminants work-ing either alone or in conjunction with a catalyst [4]. The most common homogeneous catalyst is ferrous iron. When combined with H2O2, it is well known as Fenton’s reagent [5]; heterogeneous catalysts in-volve metal oxides, and supported metal oxides [6]. Recently, the application using iron oxide catalyst has been studied extensively [3,6–9]. Goethite, hematite, semicrystalline, and ferrihydrite have been used as
∗Corresponding author. Tel.: +886-3-5726463; fax:
+886-3-5725958; e-mail: [email protected]
1Present address: Union Chemical Laboratories, Industrial
Tech-nology Research Institute, Hsinchu, Taiwan.
catalysts to treat the organic contaminants [3,7,8]. In our previous work, we developed a novel supported
␥-FeOOH catalyst and proved that it can effectively remove benzoic acid and 2,4,6-trichlorophenol [9]. All the results indicate that the removal of contaminants is related to the catalytic decomposition of H2O2 by iron oxide. Due to this important role, the catalytic de-composition of H2O2deserves further investigation.
The continuous-flow stirred-tank reactor (CSTR) has been considered as the most attractive reactor for studying the kinetics of solid catalyzed reaction [10]. Most of the studies mentioned above, however, were performed in the batch mode. To prevent the catalyst from any damage due to mechanical mixing, we se-lected a fluidized-bed reactor (FBR) to conduct exper-iments. The performance in circulating FBR is similar to that in CSTR when the recycle ratio is large enough [10,11]; the method has been extensively applied in 0926-860X/99/$ – see front matter ©1999 Elsevier Science B.V. All rights reserved.
Table 1
Properties of the catalyst
Parameters Value
Iron content (g kg−1) 135
Total surface concentration of irona(g kg−1) 95
Bulk density (g cm−3) 1.11
Dry density (g cm−3) 1.70
Average particle size (mm) 0.564 Specific surface area (m2g−1) 48.3 Surface site (mole g−1) 5.89× 10−4
pKa1 5.3
pKa2 8.8
pHpzc(point of zero charge)b 7.05 aTotal surface concentration of iron on the catalyst = iron content
of catalyst− iron content of support.
bpH
pzc= (pKa1+ pKa2)/2.
heterogeneous catalysis due to its high efficiency in mass transfer [10].
In this study, we attempted to evaluate the perfor-mance of the continuous circulating FBR with the sup-ported ␥-FeOOH catalyst. The effects of pH, H2O2 concentration and catalyst concentration on the de-composition of H2O2were studied.
2. Experimental 2.1. Catalyst preparation
A novel catalyst, iron oxide on a brick grain support, was developed in the following manner [12]. The brick grains were packed in a 6.1 l (6.8 cm× 170 cm-H) FBR as carriers. To maintain a low supersaturation condition for heterogeneous nucleation of iron oxide, 3.5 mM H2O2(Union Chemical) and 7.0 mM FeSO4 (Merck) were fed continuously into the reactor bottom at 24 (± 4)◦C. The pH of the solution was controlled at 3.5 to prevent Fe(OH)3precipitation. The crystals were allowed to grow on the surfaces of brick grains for 1 week. Table 1 lists the properties of the catalyst prepared from FBR. The number of fluoride-binding surface sites (mole g−1) was determined following the method of Sigg and Stumm [13]. Intrinsic acidity con-stants (Ka1 and Ka2) were obtained from graphic ex-trapolation of transformed acid/base titration data to zero surface charge conditions [14]. The major com-ponent coated on the catalyst surface was identified as␥-FeOOH with a Mössbauer spectrometer (Austin S-600).
Fig. 1. The schematic diagram of the fluidized-bed reactor.
2.2. Catalytic experiments
All the catalytic experiments were conducted at room temperature (24± 4◦C). The schematic appa-ratus is shown in Fig. 1. Two bench-scale FBRs were packed with 4 and 2 mm of glass beads on the bottom separately, and then the desired amount of supported␥-FeOOH catalyst grains. The smaller one (2 cm-× 100 cm-H) was applied for most of the experiments and the larger one (3 cm× 200 cm-H) was used only in part of Section 4.2. The recycle ratio of FBR was kept between 1.5 and 10 (normally above 4) except for trials studying the mixing effect. The superficial velocity was maintained at 40–60 m h−1 with circulation. The applied flow rate and H2O2 concentration were determined from the residence time (τ) and the desired H2O2 dosage, respectively. To maintain a stable pH during the reaction, pH was controlled by regulating the pH of H2O2 feed before the experiment. The effluent was collected after 5τs to insure that the reaction was at steady state [15]. The sample was filtered and titrated with KMnO4 (Union Chemical) for the analysis of H2O2.
3. Theory
In the earlier literature [7,16,17], the catalytic de-composition of hydrogen peroxide with metals or metal oxides has been described by the Weiss
mech-Table 2
Mechanism proposed for decomposition of H2O2on goethite [18]
≡FeIIIOH + H 2O2 k1 ⇔ k1aH2O2–S (II.1) H2O2–S k2 ⇔ k2a(≡Fe II•O2H) + H2O (II.2) (≡FeII•O 2H) k3 ⇔ k3a ≡Fe II+ HO 2• (II.3) ≡FeII+ H 2O2 k4 → ≡FeIIIOH +•OH + H 2O (II.4) HO2•⇔ H++ O2•− (II.5) ≡FeIIIOH + HO
2•/O2•−→ ≡FeII+ H2O/OH−+ O2 (II.6)
≡FeII+•OH→ ≡FeIIIOH (II.7)
anism, in which the major reaction is:
H2O2+ S →•OH+ OH−+ S+ (1)
where S denotes the active site on the catalyst sur-face and S+represents the oxidized site. Recently, Lin and Gurol [18] has regarded that the Weiss mecha-nism cannot appropriately explain the decomposition of H2O2 by granular goethite. Based on the surface complexation of iron oxide, they proposed another re-action mechanism which is similar to the Fenton-like reaction of Fe3+/H2O2 system [19]. The H2O2 de-composition rate (RH) can be expressed as Eq. (2) ac-cording to the new reaction mechanism proposed in Table 2: RH = kST [H2O2] 1+ KH[H2O2] (2) where k = 2k1k2k3/k0, KH= k1(k3+ k2a)/k0, k0= k3 (k1a+ k2) + k1ak2a, ST is the total concentration of the surface sites, and [H2O2] represents the H2O2 concentration in the batch reactor. This equation resembles the classic Langmuir–Hinshelwood equa-tion (L–H equaequa-tion) [20] in heterogeneous catalysis, where k and KH correspond to the rate constant and equilibrium binding constant [8]. The kinetic model has been verified at pH 7 between 1.1 and 11 mM of [H2O2]. When KH[H2O2] 1, Eq. (2) can be reduced to a second-order kinetic expression verified by Lin and Gurol [18]:
RH = kST[H2O2] (3)
4. Results and discussion
In this study, the catalytic experiments were con-ducted in a circulating FBR, which can be regarded as a CSTR at larger recycle ratio (R). According to
the mass balance of H2O2 in the CSTR, the decom-position rate of H2O2(RH) can be determined directly from the inlet and outlet H2O2concentrations; the rate is related to its conversion:
RH=
CHi− CH
τ =
CHiX
τ (4)
where X is the conversion of H2O2, CHi and CH de-note the inlet and outlet H2O2concentrations at steady state, respectively.
To verify the applicability of Eq. (4), the mixing effect in FBR was investigated by varying R. The result shows that RH was independent of R at pH 7.0 (CHi= 23.5 mM, τ = 13 min, catalyst concentra-tion = 167 g l−1). It may be due to the turbulent flow of numerous oxygen bubbles caused by higher re-action rate at pH 7.0 (as mentioned later). However, at pH 3.5 and pH 5.0, RH remained constant when
R > 0.9 but gradually decreased when R< 0.9. Since
a R value of 0.9 corresponded to 15 m h−1of superfi-cial velocity under this condition, all of the following experiments were performed at R > 1.5 and superficial velocity > 40 m h−1, which are far above these two critical values (i.e. 0.9 and 15 m h−1).
4.1. Effects of H2O2and catalyst concentrations The decomposition of H2O2 was conducted with various inlet H2O2concentrations (CHi) at pH values of 3.5, 5.0 and 7.5. The relationship between the con-version of H2O2and CHi is shown in Fig. 2(a). The conversion at steady state decreases with increasing
CHiat these three pH conditions. It is also found that, at the same CHi, the conversion at pH 7.5 is far larger than that at pH 3.5. To analyze the kinetics, the decom-position rate of H2O2versus the outlet H2O2 concen-trations (CH) was plotted, as shown in Fig. 2(b). In this figure, RH is presented as a function of outlet H2O2 concentration. It is shown that RH is proportional to
CHat low H2O2concentration, and the catalytic reac-tion is decreased with the excess H2O2after reaching its maximum. Since oxygen is formed in decompos-ing H2O2, it must first be clarified whether the excess oxygen at high H2O2 concentration inhibits the de-composition of H2O2. It seems plausible that the ad-sorption of oxygen would compete with H2O2for the active sites of the catalyst surface, thereby affect the decomposition rate of H2O2. The result of a control
Fig. 2. Effect of H2O2 concentration on (a) the conversion and
(b) the decomposition rate of H2O2. τ = 11.8 min, m = 167 g l−1,
m denotes the catalyst concentration.
experiment performed with introducing additional air by a small air diffuser, however, shows that increas-ing dissolved oxygen does not have any effect on the decomposition rate of H2O2. Therefore, the effect of the holdup of gaseous oxygen on the decomposition of H2O2can be neglected in this reaction system.
Inhibition by excess substrate has been extensively studied in many enzymatic (bio-catalytic) systems [21,22]. Haldane [21] applied a simple model mech-anism with regard to substrate inhibition:
E+ A⇔kel k−elEA
ke2
→E + Products (5)
EA+ Ak⇔e3
k−e3EA2 (dead-end reaction)
(6) where E and A denote enzyme and substrate, respec-tively. A commonly accepted explanation is that two substrate molecules get stuck together in the same active site (that is, we get an ineffective EA2 com-plex). In high substrate concentration, the chance of forming ineffective complexes increases. Therefore, we modified the reaction mechanism proposed by Lin and Gurol (as shown in Table 2) by incorporat-ing the substrate inhibition mechanism of enzyme kinetics [21,22]. To derive the rate equation of H2O2 decomposition in our reaction system, the formation of ineffective H2O2−catalyst surface complex (i.e., (H2O2)2−S) is also included H2O2–S+ H2O2 ki ⇔ k−i(H2 O2)2–S KI= ki k−i (7)
where H2O2–S denotes the effective H2O2–catalyst surface complex, and KI represents the equilibrium binding constant of an ineffective complex (mM−1). The steady state concentration of (H2O2)2–S can be expressed, derived from reaction (7), as:
(H2O2)2–S
= KICH[H2O2–S] (8)
The mass balance equation for the surface sites of the catalyst can be written as Eq. (9) by neglecting the species≡FeII and≡FeII•O2H (as shown in Table 2) due to the fact that≡FeIIis readily oxidized by H2O2 and≡FeII•O2H is only a transitional state.
ST= h ≡ FeIIIOHi+ [H 2O2–S]+ (H2O2)2–S (9) Therefore, RHcan be derived from a modified L–H equation (the detailed derivation is shown in the Ap-pendix A),
RH= kSTCH 1+ KHCH(1 + KICH)
(10) which differs from Eq. (2) only in the term (1 + KICH) of the denominator. Note that CH is used here to de-note the outlet H2O2 concentration of FBR at steady state instead of the time-variant H2O2 concentration in the batch reactor (i.e. [H2O2], as indicated in Eq. (2)). Parameters in Eq. (10) can be replaced by the form used in the substrate inhibition model of enzyme kinetics [22].
RH = kHKHCH 1+ KHCH(1 + KICH)
(11) where kH= kST/KH (mM s−1). The number of the ac-tive sites on the catalyst surface is reduced by the for-mation of ineffective complexes, which limit the de-composition of H2O2. Three parameters (kH, KH, and
KI) in the model equation at pH values of 3.5, 5.0 and 7.5 can be determined via the linear transformation of Eq. (11), and the results are listed in Table 3.
CH RH = 1 kHKH + 1 kHCH+ KI kHC 2 H (12)
It shows that kH at pH 3.5 (e.g. 0.0355 mM s−1) is much lower than those at pH 5.0 and pH 7.5 (e.g. 0.267 and 0.445 mM s−1, respectively). Furthermore,
KH increases but KI decreases with increasing pH. It is observed in Fig. 2(b) that the maxima of RH at these pH values all occurred at 36–51 mM of H2O2 concentration (CH,max), which can also be calculated using: dRH dCH = 0, C H, max = 1 √ KHKI (13) This model seems to contradict to other obser-vations [6,8,23,24] in which RH follows a simple first-order relationship with respect to H2O2 concen-tration. As a matter of fact, the reaction rate with respect to H2O2was found to follow first-order at relatively low CH in our previous study [9]. The H2O2 concentration that we applied in this study (i.e., 0–120 mM) was much higher than those used in other studies, therefore, inhibition on RH at higher
CH occurred.
To simplify the kinetic behavior, we use a pseudo-first-order relationship to describe the reac-tion at constant catalyst amount when CH< CH,max. The observed first-order rate constant, k0obs(s−1), can be calculated from the following equation:
k0 obs= RH CH = CHi− CH CHτ (14) Furthermore, experiments were conducted with dif-ferent catalyst amounts in FBR. The result, shown in Fig. 3, demonstrates that k0obsand the catalyst concen-tration have a good linear relationship. Therefore, we have concluded that RH is proportional to both H2O2
Fig. 3. Relationship between catalyst concentration and k0obs.
CHi= 24.4 mM, m = 167 g l−1, pH = 4.8.
and catalyst concentrations at low CH, which corre-sponds to Eq. (3). The iron content of the catalyst sur-face is believed to be the key factor in catalyzing the decomposition of H2O2[6,18]. We thus define kobsas below, because the iron content is proportional to the catalyst concentration: kobs= k 0obs [≡ Fe]T = CHi− CH CH[≡ Fe]Tτ (15) where [≡Fe]T denotes the total surface concentration of iron on the catalyst per volume of FBR.
4.2. Effect of pH
According to Eq. (15), kobscan be more accurately estimated by performing experiments under different τs. The change in (CHi− CH)/CH/[≡Fe]T with in-creasing τ at different pH conditions is depicted in Fig. 4, in which a good linear relationship between the two is shown. These slopes (kobs) are listed in Ta-ble 4, showing that kobsincreased with increasing pH and became much larger when pH exceeded 5.5. As indicated in Table 2,≡FeIIIOH was used to denote the active site of catalyst surface to simplify the reaction mechanism. As a matter of fact, the iron oxide con-tain three surface species:≡FeIIIOH+2,≡FeIIIOH and
≡FeIIIO−. The equilibrium of surface chemistry [25] concerning these three species can be expressed as:
≡ FeOH+2 ⇔≡ FeOH + H+ K
a1 (16)
Table 3
Three kinetic parameters in Eq. (11)a
pH kH (mM s−1) KH(mM−1) KI (mM−1) CH,max (mM) α+ α0 α−
3.5 0.0355 1.16× 10−2 3.36× 10−2 51 0.984 0.016 7.82× 10-8
5.0 0.267 1.95× 10−2 3.16× 10−2 40 0.666 0.334 5.29× 10-5
7.5 0.445 2.60× 10−2 2.99× 10−2 36 0.006 0.947 0.047
aCalculation ofα+,α0, andα−is based on pK
a1= 5.3 and pKa2= 8.8, as shown in Table 1.
Fig. 4. Relationship between (CHi− CH)/CH/[≡Fe]T andτCHi=23.5 mM, m = 167 g l−1, [≡Fe]T= 167 g l−1× 0.095 g Fe/g catalyst = 15.9 g
Fe/l = 0.283 M.
Table 4
Various kobs values under different pH values
pH kobsa(M−1s−1) pH kobsb 2.8 3.77× 10-4 2.8 2.13× 10-4 3.7 5.30× 10-4 3.5 3.87× 10-4 5.5 2.44× 10-3 5.0 2.04× 10-3 6.7 7.15× 10-3 7.0 1.01× 10-2 7.5 1.10× 10-2 aCalculated from Fig. 4.
bExperiments were conducted in the larger FBR with 590 gl−1of
catalyst (CHi= 23.5 mM,τ = 33.3 min).
Thus, [≡FeIIIOH+2] and [≡FeIIIO−] can be expressed in terms of [≡FeIIIOH] without considering the electrostatic interaction, as shown in Eqs. (18) and (19) h ≡ FeIIIOH+ 2 i =hFeIIIOH i ×H+/Ka1 (18) h ≡ FeIIIO−i=h≡ FeIIIOHi× K a2/ H+ (19) The variation in kobswith pH may be explained by the changes in the proportion of these three different surface species. Since each species maintains a differ-ent level of binding strength with H2O2, according to the surface complexation theory [25,26], the binding strength between H2O2and␥-FeOOH may be altered when pH is changed.
Next, experimental results were modeled using an approach similar to that of Butler and Hayes [27]. As-suming that three surface species have different reac-tion rates with respect to the decomposireac-tion of H2O2,
Fig. 5. Model fitting for H2O2 decomposition at different pH
values. The experimental conditions are the same as in Table 4. The solid line represents the model prediction.
we can write the rate equation as: RH= kobs[≡ Fe]TCH= k+h≡ FeIIIOH+ 2 i +k0h≡ FeIIIOHi+ k−h≡ FeIIIO−iC H (20) where k+, k0, and k−represent the rate constants as-sociated with≡FeIIIOH+2,≡FeIIIOH, and≡FeIIIO−, respectively. Eq. (20) can be transformed to:
kobs= k+α++ k0α0+ k−α− (21) where α+= [≡FeIIIOH+2]/[≡Fe]T, α0= [≡FeIIIOH]/ [≡Fe]T, and α−= [≡FeIIIO−]/[≡Fe]T. These three ionization fractions (α+,α0,α−) of surface hydroxyl group can be calculated from Eqs. (18) and (19). The
kobsvalues in Table 4 were fitted with Eq. (21) using multiple regression of statistical techniques. Three rate constants with large differences were obtained:
k+= 8.67× 10−5M−1s−1, k0= 6.75× 10−3M−1s−1 and k−= 0.109 M−1s−1 (r2= 0.953). To test the sig-nificance of regression, we calculated the statistic
F from the analysis of variance. Since F (=40.1)
> F0.05,(3,5) (=5.4), we conclude thatα+,α0andα− contribute significantly in predicting kobs. The exper-imental result fitted with model parameters is shown in Fig. 5, which indicates that the model agrees well with the experimental results. The change of KR (Ta-ble 3) also demonstrates that H2O2 favors the sites bearing negative charge. This can be explained by the
conclusion of Wallace [28]: H2O2 may form strong complexes with weak base sites such as≡FeIIIO−.
5. Conclusions
From Section 4 we have come to the following con-clusions.
1. The decomposition rate of H2O2is proportional to both CHand catalyst concentration at low CH, but decays at high CH, which can be interpreted using the modified Langmuir–Hinshelwood equation by incorporating the substrate inhibition model. 2. The effect of pH on kobs can be attributed to
the large differences in reaction rates between H2O2and three surface species of iron oxide, i.e.
≡FeIIIOH+
2,≡FeIIIOH, and≡FeIIIO−.
6. Notation
CHi, CH inlet and outlet H2O2 concentra-tions of FBR at steady state (mM)
CH,max outlet H2O2 concentration where maximum RH occurs (mM) [≡Fe]T total surface concentration of iron
on the catalyst per volume of FBR (M)
ST total concentration of active surface sites (mM)
k chemical reaction rate constant in Eqs. (2) and (10) (mM s−1)
k+, k0, k− rate constants associated with [≡FeIIIOH+2], [≡FeIIIOH], and [≡FeIIIO−] (M−1s−1)
kH chemical reaction rate constant in Eq. (11) (mM s−1)
k0obs observed first-order rate constant in decomposing H2O2(Eq. (14)) (s−1)
kobsk0obs/[≡Fe]T (M−1s−1)
KI equilibrium binding constant of an ineffective surface complex in reac-tion (7) (mM−1)
KH equilibrium constant in Eqs. (2), (10) and (11) (mM−1)
m catalyst weight per volume of solu-tion (g l−1)
RH decomposition rate of H2O2
α+ [≡FeIIIOH+
2]/[≡Fe]T
α0 [≡FeIIIOH]/[≡Fe]
T α− [≡FeIIIO−]/[≡Fe]
T
τ residence time of FBR (min)
Acknowledgements
The authors would like to thank Dr. Y.-H. Huang of Union Chemical Laboratories, ITRI, and Dr. J.R. Pan of Chiao Tung University for their helpful discussion.
Appendix A. (detailed derivation of Eq. (10)) Since the modified mechanism incorporates the sub-strate inhibition model with the mechanism proposed by Lin and Gurol [18], both reaction (7) and reactions (II.1)–(II.7) (as shown in Table 2) are included in this study. The assumptions given by Lin and Gurol [18] were used in simplifying the derivation of the kinetic equations. According to the modified mechanism, the major reactions responsible for the decomposition of H2O2are reactions (II.1), (7), and (II.4). The decom-position rate of H2O2, RH, can be accordingly pre-sented as: RH= k1 h ≡ FeIIIOHiC H− k1a[H2O2–S] +ki[H2O2–S]CH− k−i[(H2O2) S] +k4 h ≡ FeIIiC H (A.1)
The steady state concentration of (H2O2)2–S can be derived from reaction (7) as:
ki[H2O2–S]CH = k−i
(H2O2)2–S
(A.2) Accordingly, Eq. (A.1) can be simplified to RH= kl h ≡ FeIIIOHiC H− k1a[H2O2− S] +k4 h ≡ FeIIiC H (A.3)
The steady state concentration of H2O2–S can be derived from reactions (II.1), (7), and (II.2) as:
[H2O2–S]= k1 ≡ FeIIIOHC H+ k2a ≡ FeII•O 2H (k1a+ k2) (A.4)
Since KI= ki/k−i, Eq. (A.2) can be further simplified to Eq. (8). At steady state,≡FeII•O2H is given by Eq. (A.5) based on reactions (II.2) and (II.3).
h ≡ FeII•O 2H i =k2[H2O2–S] k3+ k2a (A.5) Eq. (A.4) can be transformed into Eq. (A.6) by in-troducing Eq. (A.5).
[H2O2− S] = k1(k3+ k2a) ≡ FeIIIOHC H k3(k1a+ k2) + k1ak2a (A.6) From reactions (II.3) and (II.4), the≡FeIIat steady state condition is:
h ≡ FeIIi= k3 ≡ FeII•O 2H k4CH = k3k2[H2O2–S] k4(k3+ k2a) CH (A.7) Substituting Eqs. (A.6) and (A.7) into Eq. (A.3), one will obtain:
RH= 2k1k2k3 ≡ FeIIIOHC H k3(k1a+ k2) + k1ak2a (A.8) Since ≡FeII is oxidized rapidly by H2O2 and
≡FeII•O
2H is only a transitional state, [≡FeII] and [≡FeII•O2H] are expected to be very low. The mass balance equation for the surface sites of the catalyst can be shown to be h ≡FeIIIOHi=S T− [H2O2–S]+ (H2O2)2–S (A.9) Substituting Eqs. (8) and (A.6) into Eq. (A.9), one will obtain:
[≡ FeIIIOH]= ST
1+ KHCH(1 + KICH)
(A.10) where KH= k1(k3+ k2a)/k0and k0= k3(k1a+ k2)+k1ak2a. Finally, Eq. (A.8) can be transformed into Eq. (10) by introducing Eq. (A.10).
RH= kSTCH 1+ KHCH(1 + KICH)
(10) where k = 2k1k2k3/k0.
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![Fig. 4. Relationship between (C Hi − C H )/C H /[ ≡Fe] T and τC Hi =23.5 mM, m = 167 g l −1 , [ ≡Fe] T = 167 g l −1 × 0.095 g Fe/g catalyst = 15.9 g](https://thumb-ap.123doks.com/thumbv2/9libinfo/7536962.120580/6.918.238.665.241.600/fig-relationship-hi-fe-τc-fe-fe-catalyst.webp)
