Kinetic Analysis of the Catalytic Reduction of 4-Nitrophenol by Metallic

Article pubs.acs.org/JPCC

Kinetic Analysis of the Catalytic Reduction of 4‑Nitrophenol by Metallic Nanoparticles Sasa Gu, Stefanie Wunder, Yan Lu, and Matthias Ballauff* Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany

Robert Fenger and Klaus Rademann Department of Chemistry, Humboldt-Universität zu Berlin, Brook-Taylor-Strasse 2, 12489 Berlin, Germany

Baptiste Jaquet Institute for Chemical and Bioengineering, ETH Zürich, Wolfgang-Pauli-Strasse 10/HCI F123 ETH Zürich, CH-8093 Zürich, Switzerland

Alessio Zaccone Physik-Department and Institute of Advanced Study, Technische Universität München, 85748 Garching, Germany S Supporting Information *

ABSTRACT: We present a study on the catalytic reduction of 4-nitrophenol (Nip) to 4-aminophenol (Amp) by sodium borohydride (BH4−) in the presence of metal nanoparticles in aqueous solution. This reaction which proceeds via the intermediate 4-hydroxylaminophenol has been used abundantly as a model reaction to check the catalytic activity of metallic nanoparticles. Here we present a full kinetic scheme that includes the intermediate 4-hydroxylaminophenol. All steps of the reaction are assumed to proceed solely on the surface of metal nanoparticles (Langmuir−Hinshelwood model). The discussion of the resulting kinetic equations shows that there is a stationary state in which the concentration of the intermediate 4-hydroxylaminophenol stays approximately constant. The resulting kinetic expression had been used previously to evaluate the kinetic constants for this reaction. In this stationary state there are isosbestic points in the UV/vis-spectra which are in full agreement with most published data. We compare the full kinetic equations to experimental data given by the temporal decay of the concentration of Nip. Good agreement is found underlining the general validity of the scheme. The kinetic constants derived from this analysis demonstrate that the second step, namely the reduction of the 4-hydroxylaminophenol is the rate-determining step.

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INTRODUCTION

nanoparticles or for a given type of nanoparticle immobilized in different carrier systems. In recent years, the reduction of 4-nitrophenol (Nip) to 4-aminophenol (Amp) by borohydride (BH4−) in aqueous solution has become such a model reaction that meets all criteria of a model reaction.10 It can be monitored easily with high precision by UV−vis spectroscopy.10−13 This is due to the fact that Nip has a strong absorption at 400 nm and the decay of this peak can be measured precisely as the function of time. Moreover, the reaction rate is small enough so that the conversion

Metallic nanoparticles (NP) have been the subject of intense research during the recent years because of their potential use in catalysis.1−6 It is now well-established that even inert metals such as gold may become active catalysts when divided down to nanoscale.7,8 Very often, nanoparticles are attached to a suitable colloidal carrier for easier handling and in order to avoid potential hazards.9 However, these carrier systems may impede the activity of the nanoparticles for a given reaction. Comparing the catalytic activity of nanoparticles bound in various systems hence requires a model reaction, that is, a well-controlled reaction without side reactions.10 Kinetic data and rate constants obtained from such a reaction can be compared for different © 2014 American Chemical Society

Received: June 18, 2014 Revised: July 22, 2014 Published: July 24, 2014 18618

dx.doi.org/10.1021/jp5060606 | J. Phys. Chem. C 2014, 118, 18618−18625

The Journal of Physical Chemistry C

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we have modeled this stationary state in terms of an apparent reaction rate kapp (see Figure 1). We20 and others25 demonstrated that this rate constant can be fully evaluated in terms of a Langmuir−Hinshelwood kinetics: Both reactants, namely Nip and BH4− must be adsorbed on the surface to react. This kinetic model has met with gratifying success when compared to experimental data.19,20 However, the theory presented in refs 19 and 20 only models the decay rate of Nip; no follow-up products are considered. Here we present a full kinetic analysis of the reduction of Nip in the presence of metal nanoparticles. The present analysis aims at a quantitative understanding of the entire kinetics starting just after the delay time and the subsequent transition to the stationary state. We consider the direct route15 that takes place on the surface. The goal of this work is to develop a kinetic model for the entire dependence of the concentration of Nip on time and the comparison of this model with the experimental data given in ref 20. The model is general, however, and applies to reductions catalyzed by other nanoparticles as well. The only prerequisite is that all steps take place at the surface.

can be conveniently monitored over several minutes. The presence of isosbestic points in the UV−vis spectra measured at different time gives clear evidence that Nip is fully reduced to the final product Amp, no byproducts can be detected. The analogous reaction, namely the reduction of nitrobenzene is a well-studied reaction. Since the classical work by Haber,14 the various intermediates are well-known:15 In the so-called direct route nitrobenzene is reduced to nitrosobenzene and then to phenylhydroxylamine. In the final step, phenylhydroxylamine is reduced to aniline. In the condensation route, the intermediates nitrosobenzene and phenylhydroxylamine react to form azoxybenzene which is reduced subsequently to aniline. Recent work has clearly revealed that in the presence of gold particles as catalyst the reduction proceeds only along the direct route, no traces of azoxybenzene and the following products are found.16−20 This finding has been explained by a strong adsorption of all intermediates to the surface of the nanoparticles. Practically all published studies agree on this point and assume that the catalysis takes place on the surface of the nanoparticles. The work of Nigra et al. is the notable exception.21 These authors state that the catalysis of the reduction of Nip in the presence of gold nanoparticles is affected by a soluble species leaching from the metal nanoparticles. The concentration of this soluble gold species must be very low and its catalytic activity in turn very high. However, the reduction of Nip by BH4− is catalyzed by many other noble metals such as Pt,19 Ag,22,23 Pd,24 Ru,25 and alloys.26 Hence, one must postulate soluble species of all these metals with similarly high catalytic activity. Moreover, the recent study by Mahmoud et al.27 has given clear evidence that the reaction is proceeding at the surface. Additional evidence is given in recent experimental work.13,25,27 Recently, we have analyzed the kinetics of this reaction in great detail.19,20 Figure 1 shows a typical absorbance spectra measured

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KINETICS In analogy to the well-studied case of the reduction of nitrobenzene,15−17 we formulate the reaction in terms of the direct route15,16 shown in Figure 2.28 Two intermediates may be

Figure 2. Proposed mechanism (direct route) of the reduction of 4-nitrophenol by metallic nanoparticles: In step A, 4-nitrophenol (Nip) is first reduced to the nitrosophenol which is quickly converted to 4-hydroxylaminophenol (Hx). This compound is the first stable intermediate. Its reduction to the final product, namely 4-aminophenol (Amp), takes place in step B, which is the rate-determining step. There is an adsorption/desorption equilibrium for all compounds in all steps. All reactions take place at the surface of the particles.

identified, namely 4-nitrosophenol and 4-hydroxylaminophenol. The first stable intermediate is the 4-hydroxylaminophenol as is well borne-out of the studies done on nitrobenzene.15−17 Thus, we have three compounds that adsorb and desorb during the reaction cycle, namely 4-nitrophenol (Nip), 4-hydroxylaminophenol (Hx) and 4-aminophenol (Amp). We assume furthermore that all three compounds compete for a fixed number of surface sites on the surface of the nanoparticles. Let cNip, cHx, and camp be the actual concentrations of Nip, 4-hydroxylaminophenol, and of Amp, respectively. The surface coverage θNip of Nip is modeled in terms of a Langmuir− Freundlich isotherm.19 Hence, we have

Figure 1. Typical time dependence of the absorption of 4-nitrophenolate ions at 400 nm. The blue portion of the line displays the linear section, from which kapp is taken. The induction period t0 which 20 s in this case is marked with the black arrow.

as the function of time. At first, there is a delay time in which no reaction takes place. The induction period t0 was related to a surface restructuring of the nanoparticles before the catalytic reaction starts.19,20 Hence, a rearrangement of the surface atoms seems to be necessary to create catalytically active sites as, e.g., corners or edges on the surface. Subsequently, the reaction starts and after an intermediate period a stationary state is reached that may last for many minutes. In our previous work,

θNip =

(KNipcNip)n 1 + (KNipcNip)n + KHxcHx + KBH4c BH4

(1)

where KNip, KHx, and KBH4 are the Langmuir adsorption constants of the respective compounds, and n is the Langmuir− Freundlich exponent. Following ref 19, n was set to 0.5. The coverage θHx and θBH4 of 4-hydroxylaminophenol, and of 18619



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borohydride, respectively, are formulated using the classical Langmuir isotherm, that is, n = 1. The reaction is now modeled in two steps (cf. Figure 2) termed A and B: First Nip is reduced to 4-hydroxylaminophenol in step A. The reduction of the latter compound is done in step B. Hence, the rate of reaction of Nip follows as −

dcNip dt

⎛ dc ⎞ = kappcNip = kaSθNipθBH4 = ⎜ Hx ⎟ ⎝ dt ⎠source

(2)

where S denotes the total surface of all nanoparticles in the solution. This equation follows directly from the fact that SθNip is proportional to the number of all adsorbed molecules in the system while θBH4 denotes the conditional probability to find an adsorbed surface hydrogen atom near to an adsorbed Nip molecule. As a tacit assumption in the entire LH kinetics, the total number of adsorbed molecules is much smaller than the total number of molecules of a given species in solution; that is, adsorption on the surface of the catalyst does not shift the concentration in the system in a detectable way. Moreover, it is assumed that the adsorption equilibrium between the solution and the surface of the catalyst is established quickly. Given these assumptions and prerequisites, the reaction rate for step A follows as −

dcNip dt

= kaS

Figure 3. Idealized time dependence of the concentration of 4-nitrophenol and definition of the different stages of the reaction (see the discussion of eqs 5 to 10). The black line shows the concentration of 4-nitrophenol as the function of time whereas the red dashed line corresponds to the concentration of 4-hydroxylaminophenol. The early stage I, where 4-nitrophenol is reduced to 4-hydroxylaminophenol, is mainly determined by step A of the reaction (see Figure 2) while the concentration of the final product 4-aminophenol is still small. The decay rate in this stage is approximated by kapp,1 given by eq 6. Stage II, starting at time tS (cf. eq 11), is the stationary state characterized by kapp,II that can be approximated by eq 8. Here the concentration of 4-hydroxylaminophenol is approximately constant. In this idealized picture, the stationary concentration cHx,stat of this compound follows from the balance of its generation (step A; cf. Figure 2) and decay (step B; cf. Figure 2) and may be approximated by eq 7. This concentration equals the decay of the concentration of 4-nitrophenol at time tS.

(KNipcNip)n KBH4c BH4 [1 + (KNipcNip)n + KHxcHx + KBH4c BH4]2

⎛ dc ⎞ = ⎜ Hx ⎟ ⎝ dt ⎠source

(3)

nanoparticles and thus slow down the rate of reaction. Moreover, it is evident that 4-hydroxylaminophenol is very strongly adsorbed to the surface of the nanoparticles. This can be argued from the fact that its formation slows down the rate of reaction while not accumulating in solution. The present model does not consider the adsorption/ desorption equilibrium of the final product 4-aminophenol. In principle, a strong adsorption of Amp on the surface of the particles would strongly influence the kinetics of the reaction, at least in the final state when the concentration of Amp has risen. In case of strong adsorption, the reaction rate should decrease markedly since more and more places are blocked by Amp. This is not observed in any study so far. Hence, we disregard this possibility in the present model. A full solution of the kinetic problem thus defined consists in the simultaneous solution of eq 3 and 4 which must be done numerically. This procedure leads to the concentration of nitrophenol cNip as the function of time that can directly be compared to experimental data. However, in first approximation a simple solution may be found: After the initial state, we may postulate a stationary state in which

The intermediate 4-hydroxylaminophenol thus generated is further reduced to the final product Amp in step B and its rate of decay may be formulated through ⎛ dc ⎞ −⎜ Hx ⎟ ⎝ dt ⎠decay = kbS

KHxcHxKBH4c BH4 [1 + (KNipcNip)n + KHxcHx + KBH4c BH4]2

=

dcamp dt

Hence, the full rate equation for the generation and decay of the intermediate 4-hydroxyaminophenol is given by ⎛ dc ⎞ ⎛ dc ⎞ dcHx = ⎜ Hx ⎟ − ⎜ Hx ⎟ ⎝ dt ⎠source ⎝ dt ⎠decay dt = kaS − kbS

(KNipcNip)n KBH4c BH4 [1 + (KNipcNip)n + KHxcHx + KBH4c BH4]2 KHxcHxKBH4c BH4 [1 + (KNipcNip)n + KHxcHx + KBH4c BH4]2

(4)

dcHx =0 dt

Equations 3 and 4 now constitute a set of coupled rate equations that allows us to discuss the entire kinetics of the reaction. In the following we give a brief qualitative discussion of these equations: First of all, it is evident that kA ≫ kB. This can be seen directly from the fact that the initial rate of reaction as determined from the tangent in Figure 1 for t > t0 is much larger than the tangent in the stationary state. Hence, 4-hydroxylaminophenol is formed rather quickly but its further reduction in step B is much slower. When its concentration rises quickly in the early stage of the reaction, it will more and more compete with nitrophenol for the surface places of the

(5)

In this approximation, the reaction kinetics after t0 may be divided into two regimes depicted schematically in Figure 3: (i) Early regime, ranging from t0 to a time ts: Here cHx ≈ 0 and − 18620

dcNip dt

≈ kaS

(KNipcNip)n KBH4c BH4 [1 + (KNipcNip)n + KBH4c BH4]2

(6)



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Figure 4. Fit of the concentration of Nip as the function of time by the numerical solution of eq 3 and 4. The concentration of Nip was normalized to the respective starting concentration cNip,0. The experimental data have been taken from ref 20 and refer to a temperature of 10 °C (data points with error bars). The solid lines refer to the fits by the kinetic model.

In this regime, no isosbestic point can be expected since the spectra of 3 compounds varying with time are superimposed.

In this stationary state, the amount of aminophenol generated per unit time is exactly given by the decay rate of nitrophenol. If the stationary concentration of the 4-hydroxylaminophenol is small, the condition for the isosbestic point is restored. Hence, the constants kapp, that is, the tangents of the absorbance as the function of time, are given for the two limiting cases by

(ii) Stationary state (t > ts) in which cHx is approximately constant (see Figure 3): eq 5 leads to the condition that

cHx , stat =

ka(KNipcNip)n kbKHx

(7)

(I) Early regime from t0 to ts:

Thus, −

dcNip dt

= kaS

=

(KNipcNip)n KBH4c BH4 ⎡ n ⎢⎣1 + (KNipcNip) 1 +

(

ka kb

)

⎤ + KBH4c BH4 ⎥ ⎦

kapp , I = kaS 2

(KNip)n (cNip)n − 1KBH4c BH4 [1 + (KNipcNip)n + KBH4c BH4]2

(9)

where tS is the time where stationary state starts (see Figure 3).

dcamp dt

(II) Stationary state for t > ts:

(8) 18621


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n KNip (cNip)n − 1KBH4c BH4

⎡ n ⎢⎣1 + (KNipcNip) 1 +

(

ka kb

)+K

⎤2

BH4c BH4 ⎥ ⎦

(10a)

The concept of a stationary state leads immediately to the conclusion that the stationary concentration of 4-hydroxylaminophenol cHx,stat should be given in good approximation by the amount of nitrophenol that has reacted at t = ts. Thus, we assume that the subsequent conversion to the Hx has not taken place to a notable degree. Hence, with cNip,0 being the concentration of nitrophenol at t = 0, we get for the time ts where the stationary state has been reached cNip ,0 − cHx , stat ln = − kapp , I(ts − t0) cNip ,0 which may be approximated through ts − t0 =

cHx , stat cNip ,0kapp , I

=

[1 + (KNipcNip ,0)n + KBH4c BH4]2 kbSKBH4c BH4KHx (11)

Equations 7 and 11 give the predictions for the onset of the stationary state. Figure 3 summarizes all stages of this kinetic scheme together with temporal evolution of the concentrations of all reactants expected from this model. It is interesting to compare this result to the previous version of theory that did not take into account explicitly the intermediates. With this simplification we obtained for the stationary state (see eq 3a of ref 19 or eq 5 of ref 20) kapp , II = kaS

Figure 5. Fit of the concentration of Nip as the function of time by the numerical solution of eq 3 and 4. The concentration of Nip was normalized to the respective starting concentration cNip,0. The experimental data have been taken from ref 20 and refer to a temperature of 30 °C (data points with error bars).The solid lines refer to the fits by the kinetic model.

n KNip (cNip)n − 1KBH4c BH4

[1 + (KNipcNip)n + KBH4c BH4]2

(10b)

which differs from eq 10a only by a factor 1 + ka/kb in the denominator. The adsorption constant KHx does not appear in eq 10a because of the stationary state condition of eq 5. There are two limiting cases that can be derived from eq 10a: (i) ka ≪ kb, that is, 4-hydroxylaminophenol reacts much faster than 4nitrophenol. In this case, eq 10b is a good approximation and the reduction of 4-nitrophenol is the rate-determining step. (ii) ka ≫ kb. Now the reduction of 4-hydroxylaminophenol becomes the rate-determining step, and the reaction is slowed down due to the additional factor in the denominator of eq 10b.

first input for KNip, KBH4, ka, kb, and n. Then every theoretical cNip,th as the function of time was compared to the corresponding experimental data cNip,exp. The calculation is repeated until most of calculated data of cNip,th match the corresponding experimental data sets cNip,exp. Second, the reaction rate of steps A and B (ka, kb) may be different at different initial reaction concentrations, so the values of ka and kb were reoptimized using MatLab routine II (see Supporting Information). This routine can only analyze one cNip,exp at one time. The values of ka and kb were changed while keeping KNip, KBH4, KHx, and n obtained by routine I constant until full agreement was reached. Third, the error bars of these parameters were also checked by MatLab routine II. Changing one parameter at one time, cNip,th was compared to the corresponding experimental data cNip,exp to check whether the value was within the error bars. Evidently, the consumption of the Hx intermediate cannot be measured directly and the fit values for kb and KHx are less precise to get from this fit than the other parameters.

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NUMERICAL SOLUTION OF THE KINETIC EQUATIONS All data analyzed here have been taken from ref 20. In all cases, the delay time t0 has been subtracted as discussed previously.19,20 The concentration of Nip as the function of reaction time, cNip,exp, was then analyzed by a numerical solution of eq 3 and 4 by two MatLab routines (see the full sheets in the Supporting Information). The Matlab routines were used to calculate the theoretical Nip concentration cNip,th as the function of time for a given values of KNip, KBH4, KHx, ka, kb, and n. These data are compared to the experimental results and the constants are changed until agreement with the experiment is reached. In the following we give the details of this procedure. First, all cNip,exp data obtained for a given temperature were put into MatLab routine I (see the Supporting Information). Routine I calculates cNip,th for a given set of values of KNip, KBH4, KHx, ka, kb and n. The parameters from ref.20 were used as a

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RESULTS AND DISCUSSION Figure 4 and 5 display examples of the fits of the experimental data at temperature of 10 °C (Figure 4) and 30 °C (Figure 5) obtained by a simultaneous numerical solution of eq 3 and 4. The concentration of Nip normalized to the respective concentration cNip,0 at t = 0 is plotted as the function of time for different initial concentrations of Nip and BH4−. To ensure a 18622



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Figure 6. Kinetic constants ka and kb obtained from the comparison of theory and experiment for (a, b) 10 and (c, d) 30 °C, respectively. The dashed lines give the average value of the constants.

Table 1. Constants Derived from the Fits of the Measurements at Different Temperatures temp [°C] 10 20 25 30

average ka [10‑4mol/m2 s] 4.2 9.4 9.7 11.5

± ± ± ±

0.9 2.6 2.9 3.9

average kb [10‑5mol/m2 s] 2.1 5.6 7.8 7.1

± ± ± ±

0.9 1.4 1.7 1.5

KNip [L/mol] 2700 3700 4600 5200

± ± ± ±

500 900 1200 1500

KBH4 [L/mol] 30 50 62 86

± ± ± ±

2 4 6 10

KHx [L/mol]

n

± ± ± ±

0.5 0.5 0.5 0.5

150000 160000 175000 200000

10000 15000 20000 25000

intermediates compete for free places at the surface of Au nanoparticles, and the reaction can occur only between species adsorbed on the surface. If most places are occupied by a single species, such as Hx, the reaction will be slowed down. For this reason the accumulation of Hx slows down the apparent reaction rate when the reaction approaches stage II. Figure 6 gathers the reaction rates of steps A and B derived from fitting at 10 and 30 °C. The rate constants ka and kb scatter around a mean values indicated by a dashed line in Figure 6. It should be noted that the constant kb is derived in an indirect fashion since the experiment measures only the decay of Nip. Given the various uncertainties of the analysis, the agreement of theory and experiment may be regarded as satisfactory. Table 1 gathers the resulting constants. Figure 6 shows that kb is much smaller than ka. Moreover, the adsorption constant of intermediate Hx is considerably greater than that of the other components. Evidently, the reduction of Hx is rate-determining step of the reaction and the accumulation of Hx on the surface slows down the reaction when stage II is reached. This strong adsorption of Hx on the surface of the particles precludes the formation of other products as e.g. the substituted azoxybenzenes. The formation of the latter compounds requires the presence of a sufficient concentration of

meaningful comparison, all curves are plotted up to a conversion of 30%. The results of other fits taken at different concentrations and temperatures are given in the Supporting Information. The solid lines are the fits by theory. It is clear that the early stage and the transition to the state II which is clearly seen for the data taken at 10 °C (Figure 4) are wellmodeled by the kinetic scheme given in Figure 2. In general, cNip,th deviates from cNip,exp more for higher Nip concentrations. These deviations are clearly seen at longer reaction time. Partial hydrolysis of BH4− is an unavoidable side reaction, in particular at higher temperatures, and will shift its concentration during the measurements. Moreover, the model assumes the strict validity of the Langmuir adsorption isotherm which may not be fully valid anymore when going to higher concentration of 4-nitrophenol. The resulting fit parameters are plotted in Figure 6 and are summarized in Table 1. Obviously, a single set of constants KNip, KBH4 and KHx is capable of describing the experimental data at a given temperature, at least in the early stage up to conversions of ca. 30%. The much larger value of KHx proves that intermediate hydroxylamine is much stronger adsorbed on the surface of the nanoparticles than the other components. In the Langmuir−Hinshelwood model, the reactants and 18623



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Figure 7. Dependence of the adsorption constants KNip of Nip (a), the adsorption constants KBH4 of borohydride (b), the adsorption constants KHx of 4-hydroxyaminophenol (c), the reaction rate of step A ka (d) on the inverse of temperature.

the nitroso- and the hydroxylamino compounds which is not the case. Figure 7 displays that the adsorption constants and reaction rate ka increase with an increasing temperature which can be determined as a function of temperature. The enthalpies and entropies for the adsorption of Nip, BH−4 and Hx can be obtained from the dependence of the adsorption constants on temperature through ln K = −

Table 2. Summary of Enthalpy and Entropy Values of the Adsorption of Nip, BH4−, and Hx ΔH[kJ/mol] ΔS[J/mol K]

KNip

KBH4

KHx

24 ± 3 150 ± 12

37 ± 2 158 ± 6

10 ± 1 133 ± 3

ΔH ΔS + RT R

Table 2 summarized the value of thermodynamic parameters. All adsorption processes are endothermic. Here the compound with larger adsorption constants has smaller enthalpy. The ΔH and ΔS of the adsorption process of Nip and BH4− are larger than those obtained from previous version of theory20 that did not take into account the intermediates. The activation energy for the reduction of Nip to Hx obtained from an Arrhenius plot of ka, is 36.1 ± 3.3 kJ/mol.

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DISCUSSION OF THE STATIONARY STATE ASSUMPTION Figure 8 displays the temporal evolution of the concentration of 4-hydroxylaminophenol as calculated from the numerical solution in comparison to the decay of 4-nitrophenol. Quite evidently, the concentration of this main intermediate is rising steadily throughout the time 300 s used for the evaluation of the data. After reaching the maximum the concentration of 4-hydroxylaminophenol decreases slowly. For the range in

Figure 8. Calculated concentrations of Nip and Hx as the function of time. The initial concentrations of Nip and BH4− are 0.04 mM and 5 mM, respectively.

which ln(cNip) varies linearly with time, the assumption of a stationary state may be regarded as satisfactory. But clearly the full kinetic scheme as developed here is superior and leads to a more consistent description of all the data and should be preferred for the analysis. 18624



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CONCLUSION A kinetic scheme for the reduction of Nip by BH4− catalyzed by metal nanoparticles in aqueous solution has been presented. The analysis is based on the reaction shown in Figure 2: 4-nitrophenol is first reduced to 4-hydroxylaminophenol which subsequently is reduced to the final product 4-aminophenol. The kinetic scheme leads to the coupled differential eqs 3 and 4 that upon numerical solution describe the decay of Nip with time. Good agreement between theory and experiment is found. In particular, the entire temporal evolution of the concentration of Nip can be described while the earlier approach19,20 was only capable of describing the stationary state. Moreover, the analysis of the stationary state used in earlier analysis of this reaction can be derived directly from this model. An isosbestic point is predicted for the stationary state which is observed indeed for the great majority of the published experimental data.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of parameters from the simulation by MATLAB and optimized ka and kb values and figures showing the fits of the concentration of Nip and kinetic constants ka and kb, and the MATLAB routine. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(M.B.) E-mail address: Matthias.Ballauff@helmholtz-berlin.de. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.Z. gratefully acknowledges financial support of the IAS at TUM via the Moessbauer Fellowship.

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REFERENCES

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Kinetic Analysis of the Catalytic Reduction of 4-Nitrophenol by Metallic

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