Kinetics of Ethyl Acetate Synthesis Catalyzed by Acidic Resins

LABORATORY EXPERIMENT pubs.acs.org/jchemeduc

Kinetics of Ethyl Acetate Synthesis Catalyzed by Acidic Resins Bruno M. Antunes, Sim~ao P. Cardoso, Carlos M. Silva, and Inês Portugal* Department of Chemistry, CICECO, University of Aveiro, Campus Universitario de Santiago, 3810-193 Aveiro, Portugal

bS Supporting Information ABSTRACT: A low-cost experiment to carry out the second-order reversible reaction of acetic acid esterification with ethanol to produce ethyl acetate is presented to illustrate concepts of kinetics and reactor modeling. The reaction is performed in a batch reactor, and the acetic acid concentration is measured by acidbase titration versus time. The experimental data are used to optimize the specific rate constant of the direct reaction, which is the unique parameter of the model; the rate constant for the inverse reaction is expressed in terms of the equilibrium constant. Good representations are generally obtained: the absolute average relative deviation found in this work is only 2.86%. After the experiment, students may carry out simulations for distinct operating conditions. The experimental data for short times are also analyzed approximately by using the classical approach for irreversible second-order reactions. KEYWORDS: Upper-Division Undergraduate, Chemical Engineering, Laboratory Instruction, Physical Chemistry, Computer-Based Learning, Hands-On Learning/Manipulatives, Equilibrium, Esters, Kinetics, Laboratory Equipment/ Apparatus

E

sters are an important class of organic compounds with application in a variety of products such as solvents, plasticizers, pharmaceuticals, pesticides, and fragrances1 and as intermediaries in chemical syntheses.2 They are essentially produced by the reaction of carboxylic acids with alcohols. These reactions are slow and reversible; hence, catalysts are usually required. Amberlyst 15 is one of the most active resins used in this type of reaction due to the acidic nature of the sulfonic groups. According to Calvar et al.,3 the reaction time under equivalent experimental conditions reduces from dozens of days to just some hours after the introduction of catalyst. The esterification of acetic acid with ethanol to produce ethyl acetate is a simple reaction that can be used to illustrate concepts of kinetics and reactor modeling to undergraduate chemical and chemical engineering students. Accordingly, an esterification experiment is carried out in the laboratory course intended to provide hands-on experience on separations, reaction, and control. The laboratory course meets 6 h each week. Students, divided into groups of three, perform the lab exercise in the first week, and in the second week, they finalize calculations and simulations in the computer room. The esterification of acetic acid with ethanol is conducted in a batch reactor in the presence of Amberlyst 15, and the conversion is followed by acidbase titration. The reaction model is proposed, and the experimental results are used to determine its unique parameter, namely, the specific rate constant of the direct reaction. Although many undergraduate kinetic experiments are available for Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.

instructors, they usually do not deal with reversible reactions or use them under conditions where they perform almost irreversibly.4 This experiment intends to fulfill this gap, giving the students an opportunity to improve skills in this subject.

’ THEORETICAL BACKGROUND The esterification of acetic acid (A) with ethanol (B) to produce ethyl acetate (C) and water (D) is a second-order reversible reaction that may be represented by the following chemical equation: AþB a CþD Accordingly, the expression for the rate law, r, is 1 CC CD ð1Þ r ¼ kdir CA CB kinv CC CD ¼ kdir CA CB KC where kdir and kinv are the kinetic constants of the direct and inverse reactions, respectively; Cj is the molar concentration of species j; and KC = kdir/kinv is the equilibrium constant expressed in concentrations.5 When the reaction is carried out in a batch reactor but the volume of the withdrawn samples is significant, the process should be modeled as semicontinuous to include volume variation. For instance, sampling may be represented approximately by a continuous volumetric flow rate Q. Accordingly, Published: June 02, 2011 1178

dx.doi.org/10.1021/ed100471j | J. Chem. Educ. 2011, 88, 1178–1181

Journal of Chemical Education

LABORATORY EXPERIMENT

the necessary materials balances are5 rj W ¼ QCj þ

d ðCj V Þ dt

ð2Þ

dV dt

ð3Þ

0¼Qþ

where rj = νjr is the rate of formation of component j, whose stoichiometric coefficient is νj (positive for products, negative for reactants, and null for inert components), V is the reacting fluid volume, and W is the mass of catalyst in the reactor. The previous equations may be combined to give dCj 1 W ð4Þ ¼ νj kdir CA CB CC CD KC V dt For the reaction under study, the four material balances reduce to dCA 1 W ð5Þ ¼ kdir CA CB CC CD KC V dt CA CA0 ¼ CB CB0 ¼ CC0 CC ¼ CD0 CD

ð6Þ

where CA0, CB0, CC0, and CD0 are the initial concentrations of each species. Equations 3, 5, and 6, with initial values CA0 and V0, may be numerically solved to obtain all concentrations and volume over time. The unique parameter of the model is kdir, because KC may be obtained from thermodynamic principles (see the Supporting Information). The equilibrium concentrations Cj,eq may be predicted with the model for high reaction times. Alternatively, they can be obtained from the equilibrium expression and eq 6 by first computing CA,eq from KC ¼ ¼

CC, eq CD, eq CA, eq CB, eq ðCC0 þ CA0 CA, eq Þ ðCD0 þ CA0 CA, eq Þ CA, eq ðCB0 CA0 þ CA, eq Þ

ð7Þ

’ EXPERIMENTAL SECTION The reactions are performed in a 0.250 dm3 isothermic batch reactor schematically presented in Figure 1. In a typical experiment, using equimolar concentration of both reactants (8.53 mol/dm3), ethanol (0.082 dm3) and 18.00 g of Amberlyst 15 (wet) catalyst (Rohm and Haas, 39389-20-3) are added to the reactor and heated to the desired temperature (78 °C). Stirring speed is adjusted to 900 rpm and preheated acetic acid (0.080 dm3) is added to the reactor. This instant is taken as time zero and the reaction is followed by titration of unreacted acetic acid in 1 cm3 aliquots, using NaOH and phenolphthalein as indicator. The concentration of the sodium hydroxide solution is adjusted during experiment to reduce errors. To ensure the absence of external mass-transfer resistances, a stirring speed of 900 rpm was used. An average particle diameter of 0.463 mm is sufficient to eliminate internal mass-transfer resistances.3,6 Catalyst mass was chosen to reach equilibrium concentration in a 3 h period. At the end of the experiment, the resin was recovered by decantation, washed with acetone and water, and regenerated with a solution of HCl (1 mol/dm3) for 1 h; finally, it was washed with water until neutral.

Figure 1. Schematic representation of the experimental setup.

’ HAZARDS Acetic acid (CAS#: 64-19-7) is corrosive and causes severe irritation and burns. Proper attention and caution should be taken when handling ethanol (CAS#: 64-17-5), as it is flammable and irritating to eyes, respiratory system, and skin. Ethyl acetate (CAS#: 141-78-6) is harmful if swallowed, is irritant and vapors may cause drowsiness. NaOH (CAS registry number: 1310-732) is very corrosive, which causes severe burns in skin and eye damage; harmful by ingestion or by inhalation of dust. HCl (CAS registry number: 7647-01-0) is extremely corrosive, causes serious burns; toxic, harmful by inhalation, ingestion, and through skin contact. Gloves and safety glasses are needed during the lab exercise. Students must review the materials safety data sheet for each chemical before starting the experiment and are instructed to collect wastes in specific tanks to be subsequently treated. ’ RESULTS AND DISCUSSION Students plot the acetic acid concentration in the reactor versus time (Figure 2). Note that these results were found for an initial equimolar mixture of acetic acid and ethanol with CA0 = 8.53 mol/dm3. From this figure, students are able to draw some typical conclusions and discuss equilibrium compositions. The experimental data are monotonically decreasing, because acetic acid is a reactant and no products were introduced initially in the reactor. Moreover, complete conversion cannot be attained, because this is an equilibrium reaction. Students must be aware that, although Amberlyst 15 speeds up the reaction, it never determines the endpoint of the esterification, which is governed by thermodynamics. Hence, the final acetic acid concentration may be predicted by a simple equilibrium calculation. From Figure 2, CA,eq = 3.20 mol/dm3, which coincides with the value computed from eq 7. Also, from experimental data one obtains KC = 2.67, which is very close to the calculated theoretical value, KC = 2.76 (see the Supporting Information). These values at 1179

dx.doi.org/10.1021/ed100471j |J. Chem. Educ. 2011, 88, 1178–1181



value, kdir = 4.35 105 dm6/(mol min g) (only 18.2% inferior). Despite the clearly approximated nature of the calculations, such rate constant may be taken as a first guess of the real value.

’ HOMEWORK EXERCISE Students are asked to answer the following questions at home or on the second week of the lab exercise. 1. Derive eqs 5 and 6. 2. Neglect the variation of the reacting volume due to sampling (i.e., Q = 0) and recalculate kdir. Compare and discuss results. 3. Simulate the reaction for different catalyst load and reacting volume. 4. Simulate the reaction for different initial concentrations of all species.

Figure 2. Concentration of acetic acid versus time.

Figure 3. Slope of the linear fitting to the initial points (five points).

78 °C are within those found in the literature at 80 °C, namely, 2.252 and 3.45.3 Concerning modeling, the results graphed in Figure 2 prove that the initial value problem given by eqs 3, 5, and 6 represents data accurately. The rate constant, kdir, has been fitted to the experimental data by simultaneous optimization and numerical integration to yield kdir = 4.35 105 dm6/(mol min g) with an average absolute relative deviation AARD = 2.86%. Instructors and students can utilize the Matlab code provided in the Supporting Information to carry out all calculations. The objective function adopted for the optimization is Fobj ¼

nX data i¼1

exp

2 ðCcalc A, i CA, i Þ

ð8Þ

It is interesting and pedagogically useful to discuss with the class the possibility of interpreting the experimental data by the well-documented approach for irreversible second-order reactions. In fact, because initially CA, CB . CC, CD, one may consider r = kdirCACB (see eq 1). For an equimolar feed mixture, it reduces to r = kdirCA2, giving rise to the classical analytical solution:5 1 1 W ¼ þ kdir t CA CA0 V

ð9Þ

Therefore, by plotting the foremost experimental points in 1/CA versus t coordinates, it is possible to determine kdir approximately by the slope of the linear fitting. In this work, five points have been tested, from which kdir = 3.56 105 dm6/(mol min g) is obtained; from the data in Figure 3, the slope = kdirW/V = 3.95 103 dm3/(mol min). It is worth noting the reliable result obtained when compared with the former non-approximated

’ CONCLUSIONS A low-cost experiment where the esterification of acetic acid with ethanol is catalyzed by Amberlyst 15 in a batch reactor is presented to analyze the trend of concentrations versus time, determine the specific rate constant of the direct reaction (kdir), and simulate the reaction for different operating conditions. The experimental results are interpreted using the rigorous model for the reversible second-order reaction. Calculated results are in good agreement with experimental points, as the absolute average relative deviation is 2.86%; the rate constant obtained at 78 °C is kdir = 4.35 105 dm6/(mol min g). For comparison, kdir is also obtained approximately by assuming that the reaction is irreversible of second-order, which is only true for very short times. In the whole, this work gives the students an opportunity to deal with catalytic heterogeneous reversible reactions, and develop modeling and simulation skills. ’ ASSOCIATED CONTENT

bS

Supporting Information Table with properties and constants of all components; calculation of both thermodynamic and mass-action law equilibrium constants; notes about titration; pictures of the experimental setup; equipment list; Matlab computer codes (version 7.8.0) for the optimization of the rate constant (kdir_opt.m) and for the reaction simulation for distinct experimental conditions (simul.m). This material is available via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Bruno M. Antunes wishes to express his gratitude to Fundac-~ao para a Ciência e Tecnologia (Portugal) for the grant provided (SFRH/BD/66805/2009). ’ REFERENCES (1) Lilja, J.; Murzin, D. Y.; Salmi, T.; Aumo, J.; Arvela, P. M.; Sundell, M. J. Mol. Catal. A: Chem. 2002, 182, 555–563. 1180




(2) Kirbaslar, S. I.; Baykal, Z. B.; Dramur, U. Turk. J. Eng. Environ. Sci. 2001, 25, 569–577. (3) Calvar, N.; Gonzalez, B.; Dominguez, A. Chem. Eng. Process. 2007, 46, 1317–1323. (4) Smith, J. B.; Byrd, H.; O’ Donnell, S. E.; Davis, W. J. Chem. Educ. 2010, 87, 845–847. (5) Fogler, H. S. Elements of Chemical Reaction Engineering, 4th ed.; Prentice Hall: Upper Saddle River, NJ, 2009; pp 1141. (6) Popken, T.; Gotze, L.; Gmehling, J. Ind. Eng. Chem. Res. 2000, 39, 2601–2611.

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Kinetics of Ethyl Acetate Synthesis Catalyzed by Acidic Resins

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