4-nitrophenol

Kinetic Analysis of the Catalytic Reduction of 4‑Nitrophenol byMetallic NanoparticlesSasa Gu, Stefanie Wunder, Yan Lu, and Matthias Ballauff*

Soft Matter and Functional Materials, Helmholtz-Zentrum Berlin fur Materialien und Energie, Hahn-Meitner-Platz 1,14109 Berlin, Germany

Robert Fenger and Klaus Rademann

Department of Chemistry, Humboldt-Universitat zu Berlin, Brook-Taylor-Strasse 2, 12489 Berlin, Germany

Baptiste Jaquet

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

Alessio Zaccone

Physik-Department and Institute of Advanced Study, Technische Universitat Munchen, 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 metalnanoparticles in aqueous solution. This reaction which proceeds via the intermediate4-hydroxylaminophenol has been used abundantly as a model reaction to check thecatalytic activity of metallic nanoparticles. Here we present a full kinetic scheme thatincludes the intermediate 4-hydroxylaminophenol. All steps of the reaction are as-sumed to proceed solely on the surface of metal nanoparticles (Langmuir−Hinshelwoodmodel). The discussion of the resulting kinetic equations shows that there is astationary state in which the concentration of the intermediate 4-hydroxylamino-phenol stays approximately constant. The resulting kinetic expression had been usedpreviously to evaluate the kinetic constants for this reaction. In this stationary statethere are isosbestic points in the UV/vis-spectra which are in full agreement withmost published data. We compare the full kinetic equations to experimental datagiven by the temporal decay of the concentration of Nip. Good agreement is found underlining the general validity of thescheme. The kinetic constants derived from this analysis demonstrate that the second step, namely the reduction of the4-hydroxylaminophenol is the rate-determining step.

■ INTRODUCTION

Metallic nanoparticles (NP) have been the subject of intenseresearch during the recent years because of their potential usein catalysis.1−6 It is now well-established that even inert metalssuch as gold may become active catalysts when divided down tonanoscale.7,8 Very often, nanoparticles are attached to a suitablecolloidal carrier for easier handling and in order to avoid poten-tial hazards.9 However, these carrier systems may impede theactivity of the nanoparticles for a given reaction. Comparing thecatalytic activity of nanoparticles bound in various systemshence requires a model reaction, that is, a well-controlled reac-tion without side reactions.10 Kinetic data and rate constantsobtained from such a reaction can be compared for different

nanoparticles or for a given type of nanoparticle immobilized indifferent 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 allcriteria of a model reaction.10 It can be monitored easily withhigh precision by UV−vis spectroscopy.10−13 This is due to thefact that Nip has a strong absorption at 400 nm and the decayof this peak can be measured precisely as the function of time.Moreover, the reaction rate is small enough so that the conversion

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

Article

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

pubs.acs.org/JPCC

can be conveniently monitored over several minutes. Thepresence of isosbestic points in the UV−vis spectra measured atdifferent time gives clear evidence that Nip is fully reduced tothe final product Amp, no byproducts can be detected. Theanalogous reaction, namely the reduction of nitrobenzene is awell-studied reaction. Since the classical work by Haber,14 thevarious intermediates are well-known:15 In the so-called directroute nitrobenzene is reduced to nitrosobenzene and then tophenylhydroxylamine. In the final step, phenylhydroxylamine isreduced to aniline. In the condensation route, the intermediatesnitrosobenzene and phenylhydroxylamine react to formazoxybenzene which is reduced subsequently to aniline. Recentwork has clearly revealed that in the presence of gold particlesas catalyst the reduction proceeds only along the direct route,no traces of azoxybenzene and the following products arefound.16−20 This finding has been explained by a strong adsorp-tion of all intermediates to the surface of the nanoparticles.Practically all published studies agree on this point and assumethat the catalysis takes place on the surface of the nanoparticles.The work of Nigra et al. is the notable exception.21 Theseauthors state that the catalysis of the reduction of Nip in thepresence of gold nanoparticles is affected by a soluble speciesleaching from the metal nanoparticles. The concentration ofthis soluble gold species must be very low and its catalyticactivity in turn very high. However, the reduction of Nip byBH4

− is catalyzed by many other noble metals such as Pt,19

Ag,22,23 Pd,24 Ru,25 and alloys.26 Hence, one must postulatesoluble species of all these metals with similarly high catalyticactivity. Moreover, the recent study by Mahmoud et al.27 hasgiven clear evidence that the reaction is proceeding at thesurface. Additional evidence is given in recent experimentalwork.13,25,27

Recently, we have analyzed the kinetics of this reaction in greatdetail.19,20 Figure 1 shows a typical absorbance spectra measured

as the function of time. At first, there is a delay time in whichno reaction takes place. The induction period t0 was related toa surface restructuring of the nanoparticles before the catalyticreaction starts.19,20 Hence, a rearrangement of the surfaceatoms seems to be necessary to create catalytically active sitesas, e.g., corners or edges on the surface. Subsequently, the reac-tion starts and after an intermediate period a stationary state isreached that may last for many minutes. In our previous work,

we have modeled this stationary state in terms of an apparentreaction rate kapp (see Figure 1). We20 and others25 demon-strated that this rate constant can be fully evaluated in terms ofa Langmuir−Hinshelwood kinetics: Both reactants, namelyNip and BH4

− must be adsorbed on the surface to react. Thiskinetic model has met with gratifying success when comparedto experimental data.19,20 However, the theory presented inrefs 19 and 20 only models the decay rate of Nip; no follow-upproducts are considered.Here we present a full kinetic analysis of the reduction of Nip

in the presence of metal nanoparticles. The present analysisaims at a quantitative understanding of the entire kineticsstarting just after the delay time and the subsequent transitionto the stationary state. We consider the direct route15 that takesplace on the surface. The goal of this work is to develop akinetic model for the entire dependence of the concentration ofNip on time and the comparison of this model with the experi-mental data given in ref 20. The model is general, however, andapplies to reductions catalyzed by other nanoparticles as well.The only prerequisite is that all steps take place at the surface.

■ KINETICSIn analogy to the well-studied case of the reduction of nitro-benzene,15−17 we formulate the reaction in terms of the directroute15,16 shown in Figure 2.28 Two intermediates may be

identified, namely 4-nitrosophenol and 4-hydroxylaminophe-nol. The first stable intermediate is the 4-hydroxylaminophenolas is well borne-out of the studies done on nitrobenzene.15−17

Thus, we have three compounds that adsorb and desorb duringthe reaction cycle, namely 4-nitrophenol (Nip), 4-hydroxylami-nophenol (Hx) and 4-aminophenol (Amp). We assume further-more that all three compounds compete for a fixed number ofsurface 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 surfacecoverage θNip of Nip is modeled in terms of a Langmuir−Freundlich isotherm.19 Hence, we have

θ =+ + +

K c

K c K c K c

( )

1 ( )NipNip Nip

n

Nip Nipn

Hx Hx BH BH4 4 (1)

where KNip, KHx, and KBH4are the Langmuir adsorption con-

stants of the respective compounds, and n is the Langmuir−Freundlich exponent. Following ref 19, n was set to 0.5. Thecoverage θHx and θBH4

of 4-hydroxylaminophenol, and of

Figure 1. Typical time dependence of the absorption of4-nitrophenolate ions at 400 nm. The blue portion of the line displaysthe linear section, from which kapp is taken. The induction period t0which 20 s in this case is marked with the black arrow.

Figure 2. Proposed mechanism (direct route) of the reduction of4-nitrophenol by metallic nanoparticles: In step A, 4-nitrophenol(Nip) is first reduced to the nitrosophenol which is quickly convertedto 4-hydroxylaminophenol (Hx). This compound is the first stableintermediate. Its reduction to the final product, namely 4-aminophenol(Amp), takes place in step B, which is the rate-determining step. Thereis an adsorption/desorption equilibrium for all compounds in all steps.All reactions take place at the surface of the particles.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp5060606 | J. Phys. Chem. C 2014, 118, 18618−1862518619

borohydride, respectively, are formulated using the classicalLangmuir isotherm, that is, n = 1. The reaction is now modeledin two steps (cf. Figure 2) termed A and B: First Nip is reducedto 4-hydroxylaminophenol in step A. The reduction of thelatter compound is done in step B. Hence, the rate of reactionof Nip follows as

θ θ− = = =⎛⎝⎜

⎞⎠⎟

c

tk c k S

ct

d

dd

dNip

app Nip a NipHx

sourceBH4

(2)

where S denotes the total surface of all nanoparticles in thesolution. This equation follows directly from the fact that SθNipis proportional to the number of all adsorbed molecules in thesystem while θBH4

denotes the conditional probability to find anadsorbed surface hydrogen atom near to an adsorbed Nipmolecule. As a tacit assumption in the entire LH kinetics, thetotal number of adsorbed molecules is much smaller than thetotal number of molecules of a given species in solution; that is,adsorption on the surface of the catalyst does not shift theconcentration in the system in a detectable way. Moreover, it isassumed that the adsorption equilibrium between the solutionand the surface of the catalyst is established quickly.Given these assumptions and prerequisites, the reaction rate

for step A follows as

− =+ + +

=⎛⎝⎜

⎞⎠⎟

c

tk S

K c K c

K c K c K c

ct

d

d

( )

[1 ( ) ]

dd

Nipa

Nip Nipn

Nip Nipn

Hx Hx

Hx

source

BH BH

BH BH2

4 4

4 4

(3)

The intermediate 4-hydroxylaminophenol thus generated isfurther reduced to the final product Amp in step B and its rateof decay may be formulated through

−

=+ + +

=

⎛⎝⎜

⎞⎠⎟

ct

k SK c K c

K c K c K c

c

t

dd

[1 ( ) ]

d

d

Hx

decay

bHx Hx

Nip Nipn

Hx Hx

ampBH BH

BH BH2

4 4

4 4

Hence, the full rate equation for the generation and decay ofthe intermediate 4-hydroxyaminophenol is given by

= −

=+ + +

−+ + +

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

ct

ct

ct

k SK c K c

K c K c K c

k SK c K c

K c K c K c

dd

dd

dd

( )

[1 ( ) ]

[1 ( ) ]

Hx Hx

source

Hx

decay

aNip Nip

n

Nip Nipn

Hx Hx

bHx Hx

Nip Nipn

Hx Hx

BH BH

BH BH2

BH BH

BH BH2

4 4

4 4

4 4

4 4 (4)

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

nanoparticles and thus slow down the rate of reaction.Moreover, it is evident that 4-hydroxylaminophenol is verystrongly adsorbed to the surface of the nanoparticles. This canbe argued from the fact that its formation slows down the rateof reaction while not accumulating in solution.The present model does not consider the adsorption/

desorption equilibrium of the final product 4-aminophenol. Inprinciple, a strong adsorption of Amp on the surface of theparticles would strongly influence the kinetics of the reaction, atleast in the final state when the concentration of Amp has risen.In case of strong adsorption, the reaction rate should decreasemarkedly since more and more places are blocked by Amp.This is not observed in any study so far. Hence, we disregardthis 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 donenumerically. This procedure leads to the concentration ofnitrophenol cNip as the function of time that can directly becompared to experimental data. However, in first approx-imation a simple solution may be found: After the initial state,we may postulate a stationary state in which

=c

td

d0Hx

(5)

In this approximation, the reaction kinetics after t0 may bedivided into two regimes depicted schematically in Figure 3:

(i) Early regime, ranging from t0 to a time ts: Here cHx ≈ 0and

− ≈+ +

dc

dtk S

K c K c

K c K c

( )

[1 ( ) ]Nip

aNip Nip

n

Nip Nipn

BH BH

BH BH2

4 4

4 4 (6)

Figure 3. Idealized time dependence of the concentration of4-nitrophenol and definition of the different stages of the reaction(see the discussion of eqs 5 to 10). The black line shows the concen-tration of 4-nitrophenol as the function of time whereas the red dashedline corresponds to the concentration of 4-hydroxylaminophenol. Theearly stage I, where 4-nitrophenol is reduced to 4-hydroxylaminophenol,is mainly determined by step A of the reaction (see Figure 2) while theconcentration of the final product 4-aminophenol is still small. Thedecay 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 characterizedby kapp,II that can be approximated by eq 8. Here the concentration of4-hydroxylaminophenol is approximately constant. In this idealizedpicture, the stationary concentration cHx,stat of this compound followsfrom the balance of its generation (step A; cf. Figure 2) and decay (stepB; cf. Figure 2) and may be approximated by eq 7. This concentrationequals the decay of the concentration of 4-nitrophenol at time tS.



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

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

=ck K c

k K

( )Hx stat

a Nip Nipn

b Hx,

(7)

Thus,

− =+ + +

=

⎡⎣⎢

⎤⎦⎥( )

c

tk S

K c K c

K c K c

c

t

d

d

( )

1 ( ) 1

d

d

Nipa

Nip Nipn

Nip Nipn k

k

amp

BH BH

BH BH

2a

b

4 4

4 4

(8)

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

(I) Early regime from t0 to ts:

=+ +

−

k k SK c K c

K c K c

( ) ( )

[1 ( ) ]app I aNip

nNip

n

Nip Nipn,

1BH BH

BH BH2

4 4

4 4 (9)

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

(II) Stationary state for t > ts:

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 normalizedto the respective starting concentration cNip,0. The experimental data have been taken from ref 20 and refer to a temperature of 10 °C (data pointswith error bars). The solid lines refer to the fits by the kinetic model.



=+ + +

−

⎡⎣⎢

⎤⎦⎥( )

k k SK c K c

K c K c

( )

1 ( ) 1app II a

Nipn

Nipn

Nip Nipn k

k

,

1BH BH

BH BH

2a

b

4 4

4 4

(10a)

The concept of a stationary state leads immediately to theconclusion that the stationary concentration of 4-hydroxylami-nophenol cHx,stat should be given in good approximation by theamount of nitrophenol that has reacted at t = ts. Thus, weassume that the subsequent conversion to the Hx has not takenplace to a notable degree. Hence, with cNip,0 being the concen-tration of nitrophenol at t = 0, we get for the time ts where thestationary state has been reached

−= − −

c c

ck t tln ( )Nip Hx stat

Nipapp I s

,0 ,

,0, 0

which may be approximated through

− = =+ +

t tc

c k

K c K c

k SK c K

[1 ( ) ]s

Hx stat

Nip app I

Nip Nipn

b Hx0

,

,0 ,

,0 BH BH2

BH BH

4 4

4 4

(11)

Equations 7 and 11 give the predictions for the onset of thestationary state. Figure 3 summarizes all stages of this kineticscheme together with temporal evolution of the concentrationsof 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 inter-mediates. With this simplification we obtained for the stationarystate (see eq 3a of ref 19 or eq 5 of ref 20)

=+ +

−

k k SK c K c

K c K c

( )

[1 ( ) ]app II aNipn

Nipn

Nip Nipn,

1BH BH

BH BH2

4 4

4 4 (10b)

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

■ NUMERICAL SOLUTION OF THE KINETICEQUATIONS

All data analyzed here have been taken from ref 20. In all cases,the delay time t0 has been subtracted as discussed previ-ously.19,20 The concentration of Nip as the function of reactiontime, cNip,exp, was then analyzed by a numerical solution of eq 3and 4 by two MatLab routines (see the full sheets in theSupporting Information). The Matlab routines were used tocalculate the theoretical Nip concentration cNip,th as the functionof time for a given values of KNip, KBH4

, KHx, ka, kb, and n. Thesedata are compared to the experimental results and the constantsare changed until agreement with the experiment is reached. Inthe 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

first input for KNip, KBH4, ka, kb, and n. Then every theoretical

cNip,th as the function of time was compared to the corre-sponding experimental data cNip,exp. The calculation is repeateduntil most of calculated data of cNip,th match the correspondingexperimental data sets cNip,exp.Second, the reaction rate of steps A and B (ka, kb) may be

different at different initial reaction concentrations, so thevalues of ka and kb were reoptimized using MatLab routine II(see Supporting Information). This routine can only analyzeone cNip,exp at one time. The values of ka and kb were changedwhile keeping KNip, KBH4

, KHx, and n obtained by routine I con-stant 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 datacNip,exp to check whether the value was within the error bars.Evidently, the consumption of the Hx intermediate cannot bemeasured directly and the fit values for kb and KHx are lessprecise to get from this fit than the other parameters.

■ RESULTS AND DISCUSSIONFigure 4 and 5 display examples of the fits of the experimentaldata 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 concen-tration cNip,0 at t = 0 is plotted as the function of time fordifferent initial concentrations of Nip and BH4

−. To ensure a

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



meaningful comparison, all curves are plotted up to a conver-sion of 30%. The results of other fits taken at different concen-trations and temperatures are given in the SupportingInformation. The solid lines are the fits by theory. It is clearthat the early stage and the transition to the state II which isclearly seen for the data taken at 10 °C (Figure 4) are well-modeled 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. Partialhydrolysis of BH4

− is an unavoidable side reaction, in particularat higher temperatures, and will shift its concentration duringthe measurements. Moreover, the model assumes the strictvalidity of the Langmuir adsorption isotherm which may not befully valid anymore when going to higher concentration of4-nitrophenol.The resulting fit parameters are plotted in Figure 6 and are

summarized in Table 1. Obviously, a single set of constantsKNip, KBH4

and KHx is capable of describing the experimentaldata at a given temperature, at least in the early stage up toconversions of ca. 30%. The much larger value of KHx provesthat intermediate hydroxylamine is much stronger adsorbed onthe surface of the nanoparticles than the other components.In the Langmuir−Hinshelwood model, the reactants and

intermediates compete for free places at the surface of Au nano-particles, and the reaction can occur only between speciesadsorbed on the surface. If most places are occupied by a singlespecies, such as Hx, the reaction will be slowed down. For thisreason the accumulation of Hx slows down the apparentreaction 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 kbscatter around a mean values indicated by a dashed line inFigure 6. It should be noted that the constant kb is derived in anindirect fashion since the experiment measures only the decayof Nip. Given the various uncertainties of the analysis, theagreement of theory and experiment may be regarded assatisfactory. 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 greaterthan that of the other components. Evidently, the reduction ofHx is rate-determining step of the reaction and the accumulationof Hx on the surface slows down the reaction when stage II isreached. This strong adsorption of Hx on the surface of theparticles precludes the formation of other products as e.g. thesubstituted azoxybenzenes. The formation of the latter com-pounds requires the presence of a sufficient concentration of

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. Thedashed lines give the average value of the constants.

Table 1. Constants Derived from the Fits of the Measurements at Different Temperatures

temp [°C] average ka [10‑4mol/m2 s] average kb [10

‑5mol/m2 s] KNip [L/mol] KBH4[L/mol] KHx [L/mol] n

10 4.2 ± 0.9 2.1 ± 0.9 2700 ± 500 30 ± 2 150000 ± 10000 0.520 9.4 ± 2.6 5.6 ± 1.4 3700 ± 900 50 ± 4 160000 ± 15000 0.525 9.7 ± 2.9 7.8 ± 1.7 4600 ± 1200 62 ± 6 175000 ± 20000 0.530 11.5 ± 3.9 7.1 ± 1.5 5200 ± 1500 86 ± 10 200000 ± 25000 0.5



the nitroso- and the hydroxylamino compounds which is notthe case.Figure 7 displays that the adsorption constants and reaction

rate ka increase with an increasing temperature which can bedetermined as a function of temperature. The enthalpies andentropies for the adsorption of Nip, BH4

−and Hx can be ob-tained from the dependence of the adsorption constants ontemperature through

= − Δ + ΔK

HRT

SR

ln

Table 2 summarized the value of thermodynamic parameters.All adsorption processes are endothermic. Here the compoundwith larger adsorption constants has smaller enthalpy. The ΔHand ΔS of the adsorption process of Nip and BH4

− are largerthan those obtained from previous version of theory20 that didnot take into account the intermediates. The activation energyfor the reduction of Nip to Hx obtained from an Arrhenius plotof ka, is 36.1 ± 3.3 kJ/mol.

■ DISCUSSION OF THE STATIONARY STATEASSUMPTION

Figure 8 displays the temporal evolution of the concentration of4-hydroxylaminophenol as calculated from the numericalsolution in comparison to the decay of 4-nitrophenol. Quiteevidently, the concentration of this main intermediate is risingsteadily throughout the time 300 s used for the evaluation ofthe data. After reaching the maximum the concentration of4-hydroxylaminophenol decreases slowly. For the range in

which ln(cNip) varies linearly with time, the assumption of astationary state may be regarded as satisfactory. But clearly thefull kinetic scheme as developed here is superior and leads to amore consistent description of all the data and should bepreferred for the analysis.

Figure 7. Dependence of the adsorption constants KNip of Nip (a), the adsorption constants KBH4of borohydride (b), the adsorption constants KHx

of 4-hydroxyaminophenol (c), the reaction rate of step A ka (d) on the inverse of temperature.

Table 2. Summary of Enthalpy and Entropy Values of theAdsorption of Nip, BH4

−, and Hx

KNip KBH4KHx

ΔH[kJ/mol] 24 ± 3 37 ± 2 10 ± 1ΔS[J/mol K] 150 ± 12 158 ± 6 133 ± 3

Figure 8. Calculated concentrations of Nip and Hx as the functionof time. The initial concentrations of Nip and BH4

− are 0.04 mM and5 mM, respectively.



■ 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 whichsubsequently is reduced to the final product 4-aminophenol.The kinetic scheme leads to the coupled differential eqs 3 and 4that upon numerical solution describe the decay of Nip withtime. Good agreement between theory and experiment is found.In particular, the entire temporal evolution of the concentrationof Nip can be described while the earlier approach19,20 was onlycapable of describing the stationary state. Moreover, the analysisof the stationary state used in earlier analysis of this reaction canbe derived directly from this model. An isosbestic point ispredicted for the stationary state which is observed indeed forthe great majority of the published experimental data.

■ ASSOCIATED CONTENT

*S Supporting InformationTables of parameters from the simulation by MATLAB andoptimized ka and kb values and figures showing the fits of theconcentration of Nip and kinetic constants ka and kb, and theMATLAB routine. This material is available free of charge viathe Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*(M.B.) E-mail address: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

A.Z. gratefully acknowledges financial support of the IAS atTUM via the Moessbauer Fellowship.

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