Escola Politécnica da Universidade de São Paulo Departamento de Engenharia Química

PQI 2409 Laboratório de Operações Unitárias e Reatores

Experiência REATOR DE BATELADA NÃO ISOTÉRMICO

OBJETIVO

O objetivo desta experiência é ilustrar a utilidade do balanço de energia para obter informações úteis de um processo a partir de medições de temperatura. No caso, a partir de dados de temperatura versus tempo em reator de batelada operado de modo não isotérmico, deseja-se obter os parâmetros cinéticos da equação de Arrhenius (fator de frequência k0 e energia de ativação E) de uma reação exotérmica (hidrólise de anidrido acético).

INTRODUÇÃO E DESCRIÇÃO DO EQUIPAMENTO

O reator de batelada a ser usado consiste de um recipiente (que pode ser uma garrafa térmica - frasco de Dewar - ou mesmo um simples béquer), dotado de um agitador (magnético ou mecânico) e um medidor de temperatura (termômetro ou termopar). A reação a ser estudada é a hidrólise de anidrido acético, formando ácido acético e a cinética desta reação é de primeira ordem em relação a cada um dos reagentes:

(CH3CO)2O + H2O → 2 CH3COOH ou A + B → 2 C (-rA ) = k CA CB = k0 exp[-E/(RT)] CA CB

Se o reator pudesse ser considerado adiabático, seria possível combinar as equações de balanço de massa e de energia para um reator adiabático de batelada (Fogler, 1992), para obter uma relação algébrica simples entre a temperatura e a conversão do reagente limitante (o anidrido acético). Assim, seria possível inferir os valores experimentais de conversão a partir de medidas mais simples de temperatura. Isto permitiria fazer o tratamento de dados e obter os parâmetros cinéticos da expressão de Arrhenius, k0 e E.

Se, entretanto, o reator não for adiabático, a relação entre a temperatura experimentalmente medida e a conversão torna-se um pouco mais complicada, sendo necessário avaliar a troca de calor entre o conteúdo do reator e o ambiente externo, e incluí-la explicitamente no balanço de energia. O tratamento de dados no relatório deve considerar estes aspectos.

PROCEDIMENTO EXPERIMENTAL

Medir volumetricamente (ou pesar) os reagentes nas quantidades indicadas pelo professor. Colocar a água no reator e ligar o agitador. Adicionar o anidrido acético no reator (t=0), mantendo o conteúdo do reator sob agitação, iniciando imediatamente as medidas de temperatura em função do tempo. Faça também medidas para avaliar o caráter adiabático do reator (proponha um método e discuta-o previamente com o professor). (Importante! Recomendação de segurança: cuidado ao manipular o anidrido acético, se possível em capela, usando luvas protetoras e óculos de segurança.) RELATÓRIO (a) A partir das equações de balanço de massa e de energia, obtenha a equação que será usada no tratamento

de dados. Deixe claro todas as hipóteses adotadas nesta dedução. (b) O reator usado no experimento é mesmo adiabático? Avalie a partir das medidas experimentais

realizadas. Caso o reator não seja exatamente adiabático, modifique ou adapte adequadamente o tratamento de dados de maneira a levar em conta este efeito, e ainda assim, obter os parâmetros desejados.

(c) Existe algum efeito térmico apreciável caudado pelo agitador? Seria possível avaliar isso experimentalmente?

(d) A partir dos dados experimentais medidos no laboratório, e usando valores conhecidos de entalpia de reação (ΔH, ver Tabela 1) e calor específico dos componentes, obtenha os valores de ko e E para a reação estudada. Compare com os valores reportados na literatura para estes parâmetros (vide Tabela 2). Discuta possíveis causas das eventuais discrepâncias observadas. Compare também os valores de k(25°C).

(e) Caso o valor da entalpia de reação (ΔH) não fosse conhecido, seria possível, a partir dos dados medidos, obter também o valor de ΔH? Se possível, obtenha-o e compare com o valor reportado na Tabela 1.

Tabela 1. Valores reportados na literatura para a entalpia de reação da hidrólise de anidrido acético (extraído de Shatynski & Hanesian, 1993, De Domenico et al, 2001)

Autor ΔH (kcal/mol) Shatynski (1991) média de 4 experimentos -14.4 ± 0.2 Dyne (1967) -14.6 Conn (1942) -14.1 Glasser & Williams (1971) -14.3 DeDomenico et al (2001) -14.5 Média dos valores publicados -14.4 ± 0.3

(f) A inércia do medidor de temperatura pode afetar os resultados? De que modo? O que seria necessário

medir adicionalmente, e/ou modificar o tratamento de dados para levar em consideração este efeito da inércia do medidor de temperatura?

(g) Anidrido acético é bastante higroscópico e, se não armazenado adequadamente, pode absorver (e reagir com) a umidade do ar. Como se poderia quantificar este efeito? Como verificar se este problema afetou os dados obtidos na experiência?

(h) Note que durante o início do experimento, o líquido contido no reator fica “turvo”, mas após um certo tempo, com o consumo de parte do anidrido e aumento da temperatura, torna-se límpido e transparente. O que isso significa ? Isto tem implicações no tratamento dos dados ? De que modo?

(i) Para confirmar a coerência dos parâmetros determinados no relatório, resolva (numericamente) as equações de balanço de massa e de energia no reator, com os parâmetros determinados no tratamento de dados, para prever a variação da temperatura com o tempo T(t) e a conversão com o tempo XA(t) durante o ensaio realizado, e compare com os dados medidos (modelo com linha contínua, dados experimentais com pontos discretos).

(j) Uma das aplicações dos conceitos vistos nesta experiência é o uso de reatores calorimétricos, nos quais medidas mais simples e rápidas de temperatura são usadas para monitorar a conversão da reação. Cite alguns exemplos reais deste tipo de procedimento e as limitações deste tipo de inferência (cite a respectiva referência bibliográfica fonte desta informação).

Tabela 2. Valores experimentais de energia de ativação e de ln k0 para a hidrólise de anidrido acético reportados na

literatura (extraído de Asprey et al., 1996, Shatynski & Hanesian, 1993; Hirota et al., 2010) Autor E (kcal/mol) ln k0 Unidades de k0 Rivett & Sidgwick (1910) 10.3 Marek (1954) 13.8 Marmers (1965) 16.4 Dyne (1967) 11.8 King & Glasser (1985) 9.5 9.93 s-1 Bisio & Kabel (1985) 11.1 12.80 s-1 Shatynski & Hanesian (1993) 11.2 ± 0.50 12.74 ± 0.94 s-1 Haji & Erkey (2005) 12.8 15.48 s-1 Glasser & Williams (1971) 10.8 7.95 L/(mol.s) Eldrich & Piret (1950) 10.3 7.53 L/(mol.s) Cleland & Wilhelms (1956) 10.6 7.80 L/(mol.s) Asprey et al (1996) 10.9 ± 0.15 7.66 ± 0.4 L/(mol.s)

Obs.: alguns autores reportaram constantes de pseudo primeira ordem (unidades s-1). Pergunta: Como converter os valores de pseudo-primeira-ordem em valores de segunda ordem ? BIBLIOGRAFIA ASPREY, S.P., WOJCIECHOWSKI, B.W., RICE, N.M. & DORCAS, A. (1996) “Applications of temperature scanning in kinetic

investigations: the hydrolyis of acetic anhydride”, Chem. Eng. Sci., v. 51 n. 20, p. 4681-4692. DE DOMENICO, G.; LISTER, D.G., MASCHIO, G., & STASSI A. (2001) “On-line calibration and determination of the heat of

reaction for laboratory scale heat transfer calorimeters”, J. Thermal Anal.Cal., v. 66, p.815-826. FOGLER, H.S. (1999) Elements of Chemical Reaction Engineering, Prentice-Hall, Englewood Cliffs, 3rd edition. GLASSER, D. & WILLIAMS, D.F. (1971) “The study of liquid-liquid kinetic using temperature as a measured variable”, Ind. Eng.

Chem. Fundam., v. 10, n. 3, p. 516-519. HIROTA, W.H., RODRIGUES, R.B., SAYER, C., & GIUDICI, R. (2010) “Hydrolysis of aceitc anhydride. Non-adiabatic determination

of kinetics and heat exchange”, Chem. Eng. Sci., v. 65, p. 3849-3858. HAJI, S. & ERKEY, C. (2005) “Kinetics of hydrolysis of anhydride by in-situ FTIR spectroscopy”, Chem. Eng. Educ., Winter 2005, p.

56-61 SHATYNSKI, J.J & HANESIAN, D. (1993) “Adiabatic kinetic studies of the cytidine/acetic anhydride reaction by temperature versus

time data”, Ind. Eng. Chem. Res., v. 32, p. 594-599.

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Chemical Engineering Science 65 (2010) 3849–3858

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

� Corr

E-m1 Fa

journal homepage: www.elsevier.com/locate/ces

Hydrolysis of acetic anhydride: Non-adiabatic calorimetric determination ofkinetics and heat exchange

Wilson H. Hirota a, Rodolfo B. Rodrigues a, Claudia Sayer b,1, Reinaldo Giudici a,�

a Universidade de S ~ao Paulo, Escola Politecnica, Departamento de Engenharia Quımica, Av. Prof. Luciano Gualberto, trav. 3, n. 380, CEP 05508-900 S~ao Paulo, Brazilb Universidade Federal de Santa Catarina, Departamento de Engenharia Quımica e de Alimentos, Florianopolis, Brazil

a r t i c l e i n f o

Article history:

Received 14 August 2009

Received in revised form

14 March 2010

Accepted 19 March 2010Available online 24 March 2010

Keywords:

Acetic anhydride

Reaction calorimetry

Hydrolysis

Kinetics

Chemical reactors

Reaction engineering

Mathematical modeling

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.03.028

esponding author. Fax: +55 11 3813 2380.

ail address: rgiudici@usp.br (R. Giudici).

x: +55 48 3331 9687.

a b s t r a c t

A simple calorimetric method to estimate both kinetics and heat transfer coefficients using

temperature-versus-time data under non-adiabatic conditions is described for the reaction of

hydrolysis of acetic anhydride. The methodology is applied to three simple laboratory-scale reactors

in a very simple experimental setup that can be easily implemented. The quality of the experimental

results was verified by comparing them with literature values and with predicted values obtained by

energy balance. The comparison shows that the experimental kinetic parameters do not agree exactly

with those reported in the literature, but provide a good agreement between predicted and

experimental data of temperature and conversion. The differences observed between the activation

energy obtained and the values reported in the literature can be ascribed to differences in anhydride-to-

water ratios (anhydride concentrations).

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

During the early stages of a chemical process development,tasks such as delineating safety conditions and reaction optimiza-tion and control can be carried out only if a reaction model andthe corresponding reaction parameters are known. If the kineticsis not fully understood, several problems may arise, includingrunaway reactions that can lead to the release of environmentallydangerous substances, serious physical equipment damage, oreven the possibility of an explosion. Unfortunately, for themajority of reactions, there is hardly any knowledge about thekinetic, thermodynamic, and physical parameters.

Since several chemical reactions are moderately–highlyexothermic, it is possible to quantify continuously the amountof heat released based only on temperature measurements andenergy balance equations that, in turn, can be used to infer usefulinformation about the progress of the reaction such as thermo-chemical and kinetics parameters, reaction calorimetry becomingan essential tool for data-oriented development of chemicalengineering processes.

Hydrolysis of acetic anhydride is a moderately–highly exothermic,fast reaction, which is ideal for verifying the dynamic response ofa calorimetric reactor. The overall hydrolysis reaction of acetic

ll rights reserved.

anhydride can be represented as

H3C C

H3C C

O

O

O

+ OH2 2 C

OHH3C

O

ð1Þ

The overall reaction mechanism proceeds via three irreversiblesteps: addition, elimination, and proton transfer to solvent(Asprey et al., 1996):

addition

CH3

C

O O

C

O

CH3

+ OH2 CH3 C

O O

H

O+

H

C

O

CH3

ð2Þ

elimination

CH3 C

O O

H

O+

H

C

O

CH3

CH3 C

O

H

O+

H

+ C

O

CH3O

ð3Þ

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proton transfer

ð4Þ

where the addition reaction is the rate-controlling process, andthe resulting kinetics are first-order in each of the reactants(Asprey et al., 1996).

The kinetics of the hydrolysis of acetic anhydride have beenstudied in literature using different techniques for measuring theextent of the reaction and the reaction rate: titration (Orton andJones, 1912; Cleland and Wilhelm, 1956), colorimetry (Oakenfull,1974), conductivity (Rivett and Sidgwick, 1910; Asprey et al.,1996; Kralj, 2007), spectroscopic techniques (Bell et al., 1998;Zogg et al., 2004; Haji and Erkey, 2005), and different calorimetrictechniques (Gold, 1948; Smith, 1955; Janssen et al., 1957; Glasserand Williams, 1971; Regenass, 1985; Shatynski and Hanesian,1993; Ampelli et al., 2003, 2005). More recently, the combinationof calorimetric and spectroscopic techniques was also proposed(Zogg et al., 2003, 2004; Puxty et al., 2005).

Conn et al. (1942) employed calorimetry to measure theenthalpy of hydrolytic reactions at 303 K for a number of straight-chain and cyclic acid anhydrides (acetic, propionic, isobutyric, andtrimethylacetic anhydrides). Gold (1948) analyzed the effect ofsolvent type (water and acetone–water mixtures) and tempera-ture on the kinetics of the hydrolysis of acetic anhydride; first-order rate constants were determined by conductimetry at 5, 15,and 25 1C, and the data analyzed in terms of the parameters of theArrhenius equation; the reaction belongs to the class ofnucleophilic bimolecular (SN2) solvolytic substitution reactionsand, therefore, the hydrolysis of acetic anhydride obeys secondorder kinetics, being first order with respect to both aceticanhydride and water. In order to elucidate the role of waterstructure in the kinetics of hydrolysis, Oakenfull (1974) made acomparative study of the kinetics of hydrolysis of aceticanhydride and the reaction of 4-nitrophenyl acetate withimidazole in mixtures of water with ethanol, t-butyl alcohol,dimethyl sulphoxide, and dioxin; he observed that both rateconstants were always reduced by the addition of organic solvent.Janssen et al. (1957) used calorimetric techniques to study thehydrolysis of acetic anhydride in concentrated acetic acid withoutcatalyst.

Dyne et al. (1967) and King and Glasser (1965) measured thekinetics of hydrolysis of acetic anhydride in diluted solutionsusing an adiabatic calorimetric reactor in which the reactor wallswere electrically heated to be at the same temperature of the fluidinside the reactor. Later, Glasser and Williams (1971) determinedthe kinetic parameters of the hydrolysis of acetic anhydride indilute aqueous solution, from experimental temperature–timecurves by a regression analysis on the differential equationsdescribing the reaction system. A small vessel reactor, working asan isoperibolic calorimeter, was placed in a constant-temperaturebath, and the heat transfer coefficient between reactor and thebath was determined from temperature–time curve obtainedusing a known amount of a hot or cold suitable inert liquid addedin the reactor using a syringe filled with a known quantity of onereactant. In order to eliminate the mixing effects when thereactants are first brought together, the zero of the time scale ofdifferential equations that describe the reactions system waschosen at an arbitrary point after the initial disturbances diedaway. Shatynski and Hanesian (1993) also determined thekinetics of the hydrolysis reactions using temperature data

obtained under adiabatic conditions in a commercial reactioncalorimeter in order to avoid some of the complexities inherent inthe method proposed by Glasser and Williams (1971).

Asprey et al. (1996) used the temperature scanning method toestimate the kinetic parameters of a simple reaction of aceticanhydride hydrolysis carried out in a plug-flow reactor (PFR),continuous stirred tank reactor (CSTR), and batch reactor. Theconversion of acetic anhydride was calculated from conductivitymeasurements using available computer interface boards. Somenoise in the conductivity signal was unavoidably present due tothe electrodes used. The operation of a temperature scanningreactor involves the ramping of the feed temperature whilecollecting composition and temperature data at the output of thereactor. In order to make such data interpretable, the temperatureramping rate must be such that the time between successiveanalyses is much shorter than the time required for a kineticallysignificant increment of the temperature to be induced in the feedto the reactor (Wojciechowski, 1997). As the reactions werecarried out with an excess of water, pseudo-first-order reactionconditions were assumed. Comparison of Arrhenius plot deter-mined by temperature scanning with those found in the literatureshowed that the reaction constant obtained by this method issmaller than those obtained by the methods previously used instudies of acetic anhydride hydrolysis.

Bell et al. (1998) monitored the hydrolysis of acetic anhydridein a hydrothermal/supercritical water reactor with Ramanspectroscopy to demonstrate the use of in situ spectroscopycombined with mathematical interpretation to estimate kineticsand thermodynamics parameters of an organic reaction carriedout in a challenging medium. From the intensity relationships andthe temperature information, the activation energy of thehydrolysis reaction was estimated and compared to literaturevalues. Besides, the authors also estimated the enthalpic andentropic cost of this reaction for a change in solvation environ-ment of acetic acid at high temperatures. The authors noted thatthe value of activation energy obtained by this method isconsistent with the literature value of acid-catalyzed hydrolysis,but significantly lower than those values reported for noncata-lyzed process. The experiments were carried out in a stainlesssteel high-pressure reactor vessel with internal volume of 10.4 mLusing 2 mL of distilled water and 2 mL of acetic anhydride.

Zogg et al. (2004) proposed a new approach that combines thejoint evaluation of calorimetric and online infrared data toidentify kinetic and thermodynamic parameters of a chemicalreaction. Furthermore, a new weighting principle was developedthat performs an automatic scaling of the infrared and calori-metric data in order to equalize their influence on the estimatedreaction parameters. According to the authors, the evaluation ofthe calorimetric and infrared data is conventionally carried outseparately. This will generally lead to different estimated reactionparameters caused by measurement errors, by unmodeledprocesses with different influences on the two analytical signals,or unequal information content of the two signals. The feasibilityof the new evaluation algorithm was demonstrated based on thehydrolysis of acetic anhydride. The authors noted that thereaction of acetic anhydride with water shows significant heatof mixing, this effect is visible only in the calorimetric signals anddoes not affect the infrared spectrum, and, therefore, theseparated evaluation of the infrared and calorimetric data gavesimilar results only when the dosing phase was excluded from thecalorimetric data. As the reaction was carried out in acid medium,the reactions kinetics was assumed to be pseudo-first-order. Zogget al. (2003) and Visentin et al. (2004) developed a small-scalereaction calorimeter fitted with integrated infrared-attenuatedtotal reflection (IR-ATR), which combines the principles of powercompensation and heat balance. The power compensation was

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W.H. Hirota et al. / Chemical Engineering Science 65 (2010) 3849–3858 3851

used to maintain isothermal conditions and Peltier elements wereimplemented to compensate the change of heat-transfer coeffi-cient during measurements, making time-consuming calibrationunnecessary. The new combined reaction calorimeter has beentested using three chemical reactions: neutralization of sodiumhydroxide with sulfuric acid, hydrolysis of acetic anhydride, andacetylation of a substituted benzopyranol. The hydrolysis of aceticanhydride was analyzed at three different temperature levels andthe total power produced during the reaction and the IR-ATRmeasurements were used to quantify rate constant and activationenergy, respectively. Because the reaction is carried out in quitedilute 0.1 M HCl the reactions kinetics was assumed to be pseudo-first-order. Haji and Erkey (2005) developed a reaction engineer-ing experiment that employs in-situ Fourier transfer infrared(FTIR) spectroscopy for monitoring concentrations of hydrolysis ofacetic anhydride carried out in a batch reactor and isothermally atroom temperature. Since no sampling is required, the analyticaltechnique developed allows the reaction kinetics to be observedwithout disturbing the reaction mixture. Concentrations of aceticanhydride and acetic acid were measured as a function of time,and the reaction order and rate constant were determined by theintegral method of analysis. As the reactions were carriedout in the presence of excess water, its concentration was notmonitored and the reaction kinetics was assumed to be pseudo-first-order. Ampelli et al. (2003) used an isoperibolic reactioncalorimeter combined with an UV–vis absorption spectrometer tostudy the kinetics of hydrolysis of acetic anhydride. An acid–baseindicator is added to the reaction mixture and the change of itscolor as a function of the extent of the hydrolysis reactionis followed by visible spectrum measurements (‘‘optical pHmeasurement’’).

Kralj (2007) determined the kinetics parameters (activationenergy, reaction rate constant, rate order) of hydrolysis of aceticanhydride by measuring the conductivity of the weak electrolyte(acetic acid). The reactions were carried out in a stirred batchreactor at three different temperatures and using the molar ratioof acetic anhydride to water equal to 1:131. The acetic acidconcentration was calculated on the theoretical basis of weakelectrolytes ionization, and the results obtained by the authorsshowed that the hydrolysis of acetic anhydride is a pseudo-first-order reaction.

In view of the foregoing, it can be seem that most classicalmethods for the determination of kinetic parameters of hydrolysisof acetic anhydride have relied mainly on reactors operatedisothermally at several pre-selected temperatures, and on avariety of methods, some very difficult and time consuming, tomeasure concentrations at discrete time intervals and that can beseverely limited when the reaction rates are fairly fast. Purelycalorimetric approaches do not require sampling and chemicalanalysis, but may involve different levels of sophistication in theequipment (reaction calorimeter) and in the data treatment.Under certain conditions, calorimetric methods allow for deter-minination of temperature dependency of the rate constant in asingle experiment.

The aim of the present work is to explore the usefulness ofcalorimetry as a tool to obtain information about liquid-phasekinetics during the hydrolysis of acetic anhydride using tempera-ture as the only measured variable in a very simple experimentalsetup. Temperature versus time curves were used to determinethe frequency factor (k0), activation energy (E), and the global heatexchanged (UA) for three reactions carried out under non-isothermal and non-adiabatic conditions (isoperibolic conditions).The predicted conversion and reactor temperatures were alsodetermined for each reaction. The hydrolysis of acetic anhydridewas chosen as a test reaction because it is simple and severalliterature references are available.

2. Methodology

In the present work the kinetics of hydrolysis of aceticanhydride was studied using simple isoperibolic calorimetry,under non-isothermal conditions. The experiment is very simple,employing only an arbitrary vessel (e.g., laboratory glassware)and a digital thermocouple for measuring the variation oftemperature. Data treatment involves the use of mass and energybalances to extract information regarding the kinetic parametersof the reaction. As the reactor is not adiabatic, it is necessary toinclude in the data treatment the determination of heat transfercoefficient between the reactor and the surroundings .

2.1. Mass and energy balances

For a homogeneous reaction carried out in a liquid-phase,constant-volume, non-adiabatic batch reactor, the mass andenergy balance equations, taking acetic anhydride (species A) asthe limiting reactant, are given by

NA0dXA

dt¼ ð�rAÞV ð5Þ

ðmCpÞrdTr

dt¼ ð�rAÞVð�DHÞ�UAðTr�TambÞ ð6Þ

It is important to note that the value of (mCp)r in Eq. (6)accounts for the heat capacity of the chemical components, aswell as for the contribution from heat capacities of the reactorwall, stirrer, and components:

ðmCpÞr ¼ ðmCpÞreactorþX

j

mjCp,j ð7Þ

The effect of stirring was neglected in the energy balance.Previous experiments without reaction (only water inside thereactor, agitation turned on, and temperature measured for timeslonger than the typical duration of the experiment with reaction)have shown no detectable changes in temperature, so that theheat generated by stirring was considered negligible.

The hydrolysis of acetic anhydride follows second-orderkinetics (first order with respect to each reactant):

ð�rAÞ ¼ kCACW ð8Þ

where k is the rate constant, which is temperature-dependentaccording to the Arrhenius equation:

k¼ k0e�ðE=RTr Þ ð9Þ

In Eq. (8), the molar concentrations of acetic anhydride (CA)and water (CW) may be written in terms of the conversion of thelimiting reactant as follows:

CA ¼NA0

Vð1�XAÞ ð10Þ

CW ¼NA0

V

NW0

NA0�XA

� �ð11Þ

Besides the initial amounts of water and acetic anhydride (NA0,NW0), the room temperature (Tamb) and the temperature inside thereaction (Tr(t)) are the only measured variables during theexperiment. The calculation procedure described below allowsone to estimate the evaluation of conversion (XA(t)) and thekinetic (ko and E) and heat transfer (U) parameters.

For other reactions also studied by reaction calorimetry, suchas polymerizations, the heat transfer coefficient U could changedue to an increase in the viscosity of the reaction medium (e.g.,Poc-o et al., 2010). In general, changes in viscosity during thereaction should be a concern in other reactions (e.g., polymeriza-tion reactions), because the heat transfer coefficient varies withliquid viscosity. However, in the reaction under study (hydrolysis

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of acetic anhydride) the changes in viscosity are not so intense;therefore a constant value of the heat transfer coefficient can beused throughout the reaction.

2.2. Determining the kinetic parameters, conversion and global heat

coefficient from the energy and mass balances for a non-adiabatic

system

In a non-adiabatic reactor, changes in temperature are relatedto the rate of heat release by the exothermic reaction and to heatexchange between the reactor and surroundings. After completeconversion of the limiting reactant (acetic anhydride), tempera-ture decreases due to heat exchange between the reactor andsurroundings. In the simple experimental setup used here, thereactor is allowed to cool by heat exchange to air at ambienttemperature (this is called isoperibolic calorimetry).

Hence, the global heat transfer coefficient can be obtainedfrom an analysis of the transient during the temperature decreasebecause the change of temperature occurs due to thermalexchange between the reactor and the environment, since alllimiting reactant has been consumed. For this temperaturedecrease, the governing equation is

ðmCpÞrdTr

dt¼�UAðTr�TambÞ ð12Þ

Using the integrated form of Eq. (12), the slope of a plot ofln(Tr�Tamb) versus t corresponds to –UA/(mCp)r, from which theglobal heat transfer coefficient can be determined.

Thus, given UA and the known parameters (�DH) and (mCp)r,the conversion of acetic anhydride can also be estimated bycombining the mass and energy balances and integrating theresulting equation from t0 to tf assuming that the conversion oflimiting reactant is equal to 100% at the end of the experiment.Therefore, the experimental values of conversion of aceticanhydride are given by the following recursive relationship:

XiA ¼ Xiþ1

A �ðmCpÞrðTr,iþ1�Tr,iÞþUA

R tiþ 1

tiðTr�TambÞdt

ð�DHÞNA0ð13Þ

Table 2Reactants and reactors: volume and masses.

Volume (mL) Mass (g)

Deionized water 150

Acetic anhydride 90

Cylindrical plastic vessel – 6.68

Volumetric flask – 80.10

Thermal bottle – 23.59

Magnetic stirrer – 4.40

Table 3Constants for specific heat capacity of reactants and products.

A (J/mol K) B (J/mol K2)

Water 92.053 �3.995�10�2

Acetic anhydride 71.831 8.888�10�1

Acetic acid �18.944 1.0971

Table 1Room temperature.

Reactor Room temperature Tamb (K)

1 294.65

2 295.15

3 294.45

The integral of Eq. (13) was calculated for each interval of timeusing the trapezoidal rule. Hence, the values of experimentalconversion were obtained from the final time for completeconversion of A backward to the starting time.

Knowing the value of UA, the rate of reaction of the limitingreactant can be determined experimentally from the thermalbalance as follows:

ð�rAÞ ¼ðmCpÞrðdTr=dtÞþUAðTr�TambÞ

Vð�DHÞð14Þ

Once (�rA) is determined, the values of the rate constant ateach time can be calculated from Eq. (8) as

k¼ð�rAÞ

CACWð15Þ

where CA and CW are calculated from Eqs. (10) and (11),respectively.

Finally, the values of the frequency factor (k0) and theactivation energy (E) are obtained, respectively, from the interceptand the slope of the straight line adjusted to the plot of ln(k)versus 1/Tr:

lnðkÞ ¼ lnðk0Þ�E

R

1

Trð16Þ

In Eq. (14), the values of the derivative dTr/dt are calculated byfinite difference method, using the following 2nd order centralfinite difference or three-point differentiation formulas:

initial point

dTr

dtt0

¼�3Trðt1Þþ4Trðt2Þ�Trðt3Þ

2Dt

�����ð17Þ

interior points

dTr

dttj

¼Trðtjþ1Þ�Trðtj�1Þ

2Dt

������ð18Þ

last point

dTr

dttn

¼Trðtn�2Þ�4Trðtn�1ÞþTrðtnÞ

2Dt

�����ð19Þ

3. Experimental

The hydrolysis of acetic anhydride was carried out with excess ofwater and in three different non-adiabatic vessels: (a) a cylindricalplastic vessel (reactor 1), (b) a volumetric flask (reactor 2), and (c) athermal bottle or Dewar flask (reactor 3). Throughout the whole

C (J/mol K3) D (J/mol K4) Ref.

�2.211�10�4 5.347�10�7 Yaws (1999)

�2.653�10�3 3.350�10�6 Yaws (1999)

�2.892�10�3 2.93�10�6 Yaws (1999)

Table 4Specific heat capacity of materials of reactors and stirrer.

Cp (J/g K) Ref.

Cylindrical plastic vessel 1.79 Ullmann (1985)

Volumetric flask 0.75 Ullmann (1985)

Thermal bottle 0.75 Ullmann (1985)

Magnetic stirrer 0.65 Westrum and Grønvold (1969)

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Table 6Initial conversions.

Reactor XA at t¼0 (%)

W.H. Hirota et al. / Chemical Engineering Science 65 (2010) 3849–3858 3853

reaction, the reaction medium was kept well stirred by a magneticstirrer, and the reactor surrounds were at room temperature. As thereactions were carried out on different days, the room temperatureswere different for each type of reactor and are reported in Table 1.

Fig. 1. Graphical estimation of global heat transfer for the cooling region for:

(a) reactor 1, (b) reactor 2, and (c) reactor 3.

Table 5Experimental heat transfer coefficient.

Reactor UA (W/K)

1 0.424

2 0.280

3 0.0846

1 6.33

2 4.94

3 5.72

Fig. 2. Arrhenius plot for the data taken from: (a) reactor 1, (b) reactor 2, and

(c) reactor 3.

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As already mentioned, the heating effect of stirring was evaluated inexperiments with water (no reaction) for longer periods and nodetectable change in temperature was measured. Thus, the heatingeffect of stirring was neglected.

The first two systems were used to simulate a non-adiabaticreactor while reactor 3 simulated a non-ideal adiabatic reactor.These systems were chosen to allow the implementation of thisstudy as an experiment for the undergraduate laboratory. Thetemperatures were recorded every 30 s using a digital thermo-meter with a sheathed thermocouple.

Acetic anhydride having a minimum assay of 95% anddeionized water were used and the volumes of both are shownin Table 2 along with masses of the vessels and the magneticstirrer (magnetite—Fe3O4).

The specific heat capacity of the reactants and products wascalculated by

Cp ¼ AþBTþCT2þDT3 ð20Þ

The constants A–D are presented in Table 3. Specific heatcapacities of the reactor wall and the magnetic stirrer arepresented in Table 4 and the heat of reaction for the hydrolysisof acetic anhydride was assumed to be (�DH)¼58,994.4 J/mol(Conn et al., 1942).

In Table 1 the mass of the thermal bottle was calculateddisregarding the external wrapper and considering that the massof glass ampoule corresponds to 10% of the total mass of thebottle. The external wrapper was not considered because weconsider that only the internal wall of the ampoule reaches thesame temperature of the liquid inside the reactor. The specificheat capacities of the volumetric flask and glass ampoule (Table 3)are related to the specific heat capacity of an alloy composed 96%of silicon oxide.

Table 7Experimental activation energy and ln(k0) values for the hydrolysis of acetic

anhydride.

Reactor ln(k0) (L/mol s) E (kJ/mol)

1 16.25 68.9

2 15.28 66.5

3 15.15 66.3

Table 8Kinetic parameters for hydrolysis of acetic anhydride reported in the literature.

Ref. Acetic anhydride concentration

(mol/L)

M

King and Glasser (1965) n.r. C

Eldridge and Piret (1950) n.r. T

Takashima et al. (1971) Infinite dilution n

Cleland and Wilhelm (1956) 0.02–0.06 T

Dyne et al. (1967) 0.17 C

Bisio and Kabel (1985) 0.22 C

Glasser and Williams (1971) 0.25 C

Takashima et al. (1971) 0.25 n

Shatynski and Hanesian (1993) 0.27 C

Wilsdon and Sidgwick (1913) 0.34 C

Kralj (2007) 0.41 C

Rivett and Sidgwick (1910) 0.54 C

Haji and Erkey (2005) 0.66 F

Asprey et al. (1996) 1.0 C

Wilsdon and Sidgwick (1913) 1.10 C

Marek (1954) 1.34 n

Marmers (1965) Equimolar concentration n

n.r.¼not reported.

4. Results and discussion

In order to determine experimental values of activation energyand frequency factor, the global heat transfer coefficient must beknown. This coefficient can be experimentally inferred fromanalysis of temperature variations during the temperaturedecrease where no reaction occurs due to complete conversionof the limiting reactant. Taking the integrated form of Eq. (12), UA

can be readily estimated from the slope of a plot of ln(Tr–Tamb)versus t (Fig. 1). The global heat capacity of the reactor, used inEq. (12), was computed by considering the heat capacity of thereactor and the magnetic stirrer plus the average heat capacities ofwater and acetic acid produced by complete conversion of aceticanhydride. The estimated values of UA are presented in Table 5.The correlation coefficients in Fig. 1 ranged from 0.997 to 0.999.

Comparing the estimated values of heat transfer coefficientspresented in Table 5, it can be seen that the value of UA for thevolumetric flask is slightly lower than that obtained for reactor 1.This occurs because the heat transfer resistance of reactor 2 isgreater than that of the polystyrene cup. Besides, the long neck ofthe volumetric flask makes heat exchange between the reactionmedium and the environment difficult.

It is important to note that while heat exchange through thedouble walls of the thermal bottle is minimal, reactor 3 presents anonzero value of the heat transfer coefficient, because the thermalbottle was kept open throughout the reaction, allowing for someheat exchange though the open top of the bottle.

Using the estimated values of UA, the experimental profile forconversion can be obtained by recursive application of Eq. (13).Because all reactions were carried out with an excess of deionizedwater, conversions were computed from the final point, where theconversion of acetic anhydride was assumed to be equal to 100%.Values of the initial conversion cannot be assumed to be zerobecause the purity of the acetic anhydride is not well known.

Table 6 lists the initial conversion for each system. It can beseen that the experimental conversions at t¼0 are very differentfrom zero. Therefore, apparently the actual purity of the aceticanhydride used during the reactions is slightly smaller than thenominal purity provided by manufacturer. The decrease in puritymay be caused by the duration of storage of the reagent or contactwith the environment since acetic anhydride reacts with moisturein air.

Regarding the kinetic parameters, using the experimentalvalues of temperature, global heat transfer coefficient (Table 5),

easuring techniques E (kJ/mol) ln(k0) Units of k0

alorimetry 39.8 9.93 s�1

itration 43.2 7.53 L/(mol s)

.r. 33.6 – –

itration 44.4 7.80 L/(mol s)

alorimetry 49.4

alorimetry 46.5 12.80 s�1

alorimetry 45.3 7.95 L/(mol s)

.r. 49.4 18.1 s�1

alorimetry 46.9 12.74 s�1

onductivity 50.6 18.52 s�1

onductivity 50.1 14.21 s�1

onductivity 43.2

TIR 53.6 15.48 s�1

onductivity 45.7 7.66 L/(mol s)

onductivity 56.2 20.45 s�1

.r. 57.8

.r 68.7

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and conversion, both k0 and E can be easily computed graphicallyvia Eq. (16). Fig. 2 shows a typical Arrhenius plot according toEq. (16), where the slope is equal to (�E/R) and the intercept (at1/Tr¼0) is ln(k0). As can be seen from Fig. 2, the data fall on areasonably straight line with correlation coefficients above 0.99.The kinetic parameters (k0 and E) obtained for each system aresummarized in Table 7. The literature values for the activationenergy and frequency factor for the hydrolysis of acetic anhydrideare listed in Table 8, based on the values reported by Asprey et al.(1996) and Shatynski and Hanesian (1993) and complemented

Fig. 3. Arrhenius plot for comparing the rate constant for the hydrolysis of acetic

anhydride obtained in this work with those reported in the literature: (a) reactor 1,

(b) reactor 2, and (c) reactor 3.

with additional literature information. It is important to note that,in Table 8, some frequency factors were obtained under thehypothesis of pseudo-first-order reaction conditions. Therefore,for comparison purposes, these parameters should be convertedto second-order constants by dividing the pseudo-first-orderconstant by the concentration of water, when available.

Comparing the kinetic parameters presented in Table 7obtained in the present work, it can be observed that the valuesare very similar, regardless of the reactor used. However, whenthe values of Table 7 are compared with those found in theliterature (Table 8), it can be seen that the values of activationenergy and frequency factor obtained are always higher thanthose reported in Table 8. It is well known that small differencesin activation energy causes large differences in ln(k0), as this valueis obtained by extrapolation of the Arrhenius plot far from thestudied range of temperature. Therefore, it is sounder to comparedirectly the values of k obtained at different temperatures, asshown in Fig. 3. The obtained values of k are within the range ofliterature values for higher temperatures, and larger deviationsare found for the low temperature range. A possible explanationfor these deviations is that, for low temperatures, solubility ofacetic anhydride in water is not complete. The excess of aceticanhydride is first dispersed as droplets, and then completelydissolves over time, favored by the increase of temperature andthe formation of some acetic acid from the reaction. Indeed, in theexperiments in glass reactor 2, it was possible to see that thereaction mixture was initially turbid due to the presence of smalldroplets, a clear indication of a partially immiscible system (if thestirring was stopped, droplet coalescence and phase separationcould be observed). When the temperature is higher than about35 1C, the appearance of the mixture suddenly changes to a clearsolution, indicating a completely miscible system from this pointon. Thus, at first only the data taken after this full solubilizationpoint should be considered.

Table 9Experimental activation energy and ln(k0) values for the hydrolysis of acetic

anhydride without mixing effects.

Reactor ln(k0) (L/mol s) E (kJ/mol)

1 17.57 73.74

2 16.65 70.14

3 16.19 69.12

0

20

40

60

80

100

0initial concentration of acetic anhydride (mol/L)

E (k

J/m

ol)

literature data

present work

present work, consideringonly the data for T > 35 C

2 4 6 8 10

Fig. 4. Effect of initial concentration of acetic anhydride on activation energy of

the hydrolysis reaction. Each point corresponds to one work from the literature,

according to Table 8.

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In order to eliminate the above mentioned effect of incompletemixture during the beginning of the experiment, the kineticparameters were also computed using the temperatures mea-sured only after the initial disturbances disappeared (Tr435 1C).The new kinetic parameters thus estimated are summarized inTable 9.

Comparing the values of activation energy and ln(k0) pre-sented in Tables 7 and 9, it can be seen that the results are verysimilar, implying that solubility is not mainly responsible for thevariability in reaction rates. In fact, Golding and Dussault (1978)noted that data in the literature indicated that in the case ofexcess of either reactant there is deviation from second order

Fig. 5. Experimental and predicted values of temperature for: (a) reactor 1,

(b) reactor 2, and (c) reactor 3.

kinetics, and both frequency factor and activation energy increasewith increasing acetic anhydride concentration. Consequently, forthe anhydride concentration range studied in the literature(0.291–1.47 mol/L) no unique value of either ln(k0) or E could betaken. Besides, Janssen et al. (1957) noted a decrease in the rateconstant in the presence of concentrated acetic acid. This fact canbe attributed to the formation of hydrates of acetic acid, as quotedby Plyler and Barr (1935). According to these authors, thehydration of some of the water with acetic acid formed probablykeeps the water from having a part in the reaction and thepresence of acetic acid also decreases the number of collisions in agiven time between the anhydride and water molecules. On the

Fig. 6. Experimental and predicted values of conversion for: (a) reactor 1,

(b) reactor 2, and (c) reactor 3.

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other hand, Golding and Dussault (1978) also observed that theeffect of acetic acid on reaction rate reported in the literature hasbeen conflicting.

Fig. 4 shows the variation of activation energy obtained bydifferent authors, as a function of the initial concentration ofacetic anhydride. It is quite evident that, for smallerconcentrations, activation energy increases with increasingconcentration of acetic anhydride. Our results, obtained forrelatively higher initial concentration of acetic anhydride, arealso included in this plot and follow reasonably well the trends ofchanges of E with temperature.

Finally, in order to test the values obtained for the 3parameters (U, k0, and E), they were used in the energy and massbalances to simulate the evaluation of temperature and conver-sion. Figs. 5 and 6 show a comparison between the experimentalvalues of the reactor temperature (Fig. 5) and the conversion(Fig. 6) with those predicted by the energy and mass balancesusing the estimated values of UA and kinetic parameters (k0 and E)for each case analyzed. For all cases, a good agreement betweenexperimental and predicted values was found despite values ofactivation energy and frequency factor obtained being alwayshigher than those reported in literature.

5. Conclusions

This work shows that both kinetic parameters and heattransfer coefficient of reactor contents can be easily determinedfor hydrolysis of acetic anhydride using temperature-versus-timedata under non-adiabatic, isoperibolic conditions. The maindifference of this work in relation to other previously publishedworks in the literature is that the kinetic data were obtainedunder non-adiabatic conditions, where the heat transfer coeffi-cient must be known in order to determine these parameters. Theresults shows that the estimates obtained for activation energyand frequency factor of the hydrolysis of acetic anhydride areapparently affected by excess of either reactant and, therefore, nounique value of either ln(k0) or E could be taken. Despite theobserved differences between estimates of k0 and E and thosereported in the literature, experimental and predicted values oftemperature and conversion show good agreement.

As a final comment, the simplicity of the experimental setupand the calculations used in this investigation allows one to usethem as an experiment for undergraduate laboratories toillustrate the application of the non-adiabatic calorimetricmethod to infer state variables.

Notation

CA

concentration of acetic anhydride, mol/L CW concentration of water, mol/L Cp specific heat capacity, J/mol K or J/g K E activation energy, J/mol k specific reaction rate constant, L/mol s k0 pre-exponential factor or frequency factor, L/mol s (mCp)r total heat capacity of reactor and contents, J/K MW molecular weight, g/mol NA0 moles of acetic anhydride initially fed to reactor, mol NW0 moles of water initially fed to reactor, mol R gas constant, J/mol K (�rA) rate of disappearance of component A, mol/L s t0 initial instant, s tf final instant, s Tamb environment temperature, K Tr reactor temperature, K UA heat transfer coefficient, J/K s

V

total volume of reactants added to reactor, L XA conversion of component A

(�DH)

heat of hydrolysis of acetic anhydride, J/mol

r

density, g/L

Acknowledgements

The financial supports from FAPESP—Fundac- ~ao de Amparo �aPesquisa do Estado de S~ao Paulo, CNPq—Conselho Nacionalde Desenvolvimento Cientıfico e Tecnologico, and CAPES—

Coordenac- ~ao de Aperfeic-oamento de Pessoal de Nıvel Superiorare gratefully appreciated.

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