Density functional theory applied to thermochemical calculations for phenol reactions

Fluid Phase Equilibria 228–229 (2005) 459–464

Density functional theory applied to thermochemical calculations for phenol reactions Miria H.M. Reisa , Hueder P.M. de Oliveirab , Teresa D.Z. Atvarsb , Liege F.S. Mascoloa , Maria Regina Wolf-Maciela,∗ a

Faculdade de Engenharia Qu´ımica, Universidade Estadual de Campinas, P.O. Box 6066, 13081-970 Campinas, S˜ao Paulo, Brazil b Instituto de Qu´ımica, Universidade Estadual de Campinas, P.O. Box 6154, 13084-971 Campinas, S˜ ao Paulo, Brazil

Abstract Phenol recovery from wastewaters is a crucial task in the chemical process area, for both economical and environmental reasons, since phenol is a high added value product but, also, highly toxic. Reactive distillation is being proposed as an alternative process for eliminating phenol from water. However, before studying the process, it is necessary to derive a suitable phenol reaction and, also, to calculate its equilibrium constants, since no such values are reported in the open literature. In this work, Benson’s method and molecular modeling are applied to calculate thermochemical values for phenol reactions with acetic acid (phenol acylation) and with acetic anhydride (phenol esterification). However, Benson’s method presented limitation for calculation of the thermochemical values for the proposed reactions, because some of the additivity groups are not found in published tables. Using molecular modeling, calculations were carried out at several temperatures. Results from density functional theory (DFT) indicate that the equilibrium constant for phenol esterification is greater than the one for phenol acylation and, thus, the former reaction is more suitable in terms of consumption of phenol. Moreover, it was observed that the acylation reaction reaches high conversions only at high temperatures. © 2004 Elsevier B.V. All rights reserved. Keywords: Molecular simulation; Density functional theory; Chemical equilibria; Phenol acylation; Phenol esterification; Thermochemical data; Reactive distillation

1. Introduction Phenol and its derivatives are high added value products, being widely used in several types of industries, including chemical, petrochemical, and paper industries, as well as in the production of herbicides and insecticides. On the other hand, phenols are frequently found in wastewaters as dilute solutions, which must be purified to attend to environmental restrictions. Phenolic products are toxic to humans and aquatic organisms and they are listed among the most common and serious environmental contaminants [1]. According to the 80/778/EEC Directive [2], the maximum ad∗

Corresponding author. Tel.: +55 19 37883957; fax: +55 19 37883965. E-mail addresses: [email protected] (M.H.M. Reis), [email protected] (M.R. Wolf-Maciel). 0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.08.025

missible concentration (MAC) of phenols in drinking water should not exceed 0.5 pg/l. Thus, recovery of phenol from wastewater is an important task in the separation engineering area. Several processes have been proposed to separate the phenol/water mixture, including liquid–liquid extraction [3], distillation [4], and pervaporation [5]. However, the distillation process is not economical in this case, because of the high costs related to water vaporization, since this component is in high concentration in the mixture and, also, it has high latent heat of vaporization. The pervaporation process requires high investment, a fact that sometimes makes this process unfeasible. Liquid–liquid extraction is the most used process for this kind of separation (dilute solutions), although it presents some limitations, such as the choice of a suitable solvent to guarantee the separability according to the

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environmental restrictions, and the operating and economic viabilities. In this work, an alternative methodology for the separation of phenol from water, based on reactive distillation, is considered. In the last two decades, reactive distillation process has received growing attention due to its potential as a non-conventional separation process for many kinds of liquid-phase systems [6]. The advantages that are achieved by simultaneously performing reaction and separation within the same apparatus lead to an important area of design: process intensification. Moreover, reactive distillation process has some clear benefits relative to the principles of green engineering [7], such as reduced energy and solvent requirements, and higher selectivity. However, prior to proposing a new separation scheme, knowledge of the chemical reactions involved, including stoichiometries, kinetics, and thermodynamic parameters, is necessary. Estimates of reaction thermochemistry may be obtained by the use of Benson’s additivity rules [8], which allow calculation of enthalpies (Hf◦ ) and entropies (S◦ ) for molecules in the gas phase. Nowadays, statistical thermodynamics, coupled with computational quantum chemistry based on molecular theory, also offers the possibility to accurately estimate thermodynamic parameters of an extremely large range of molecules. This is a new and important tool for engineering calculations [9]. The main objective of this work is to determine thermochemical parameters for two reactions for phenol consumption: phenol acylation and phenol esterification.

3. Group additivity results Benson’s approach [8] can be used to determine Hf◦ of a molecule by adding the Hf◦ of the various groups in the molecule. A group is defined as an atom and its ligands. Hf◦ of each group was calculated from experimentally determined Hf◦ of compounds that contain that group. Then, Hf◦ for a new molecule is obtained by simply adding together the contributions from each group. There are several published tables [8,10,11] from which values for Hf◦ and S◦ at 298.15 K and for heat capacity values (Cp◦ ) at several temperatures for each ligand can be taken. Thermodynamic properties can be estimated at different temperatures using an average value for heat capacity, assuming a linear function of Cp within the temperature range (Eq. (1)). In order to calculate enthalpy and entropy values, Eqs. (2) and (3) can be applied. Cp◦ m = 21 (Cp◦ (T ) + Cp◦ (298.15 K))

(1)

Hf◦ (T ) = Hf◦ (298.15 K) + Cp◦ m (T − 298.15)
 T Sf◦ (T ) = Sf◦ (298.15 K) + Cp◦ m ln 298.15

(2) (3)

Eq. (4) shows how the entropy of formation of each compound (Sf◦ (298 K)) can be calculated from its chemical elements at 298.15 K [12]:  Se◦ (298.15 K) (4) Sf◦ (298.15 K) = S ◦ (298.15 K) −

Acylation reactions are widely employed in the fine chemical industry, producing a variety of synthetic fragrances and pharmaceutical products. The principal route to obtain acylaromatics is the acylation of aromatics, which is, generally, carried out using Br¨onsted or Lewis acid catalysts. In this work, phenol acylation with acetic acid is proposed (Scheme 1), producing phenyl acetate and water. Another known way to produce phenyl acetate is heating phenol with excess acetic anhydride with addition of either a basic catalyst (fused sodium acetate, pyridine, triethylamine) or an acid catalyst (sulfuric acid, boron fluoride etherate). This reaction, phenol esterification (Scheme 2), will also be considered as a process to consume phenol from an aqueous stream.

where Se◦ (298.15 K, H2 ) = 134.86 J mol−1 K−1 ; Se◦ (298.15 K, C) = 5.70 J mol−1 K−1 ; Se◦ (298.15 K, O2 ) = 205.15 J mol−1 K−1 . Tables 1–4 present the groups of phenol, acetic acid, phenyl acetate, and acetic anhydride, respectively, with their respective values of Hf◦ and S◦ at 298.15 K and Cp◦ at temperatures equal to 300, 400, 600, and 800 K. It is important to mention that there were no published values for some groups, mainly for Cp , which makes the calculation of chemical equilibrium at different temperatures from 298.15 K difficult. Moreover, the group additivity model does not permit molecules with less than two non-hydrogen atoms. Thus, it was impossible to predict the thermochemical values for water by Benson’s method. The following calculations will be carried out only for phenol esterification at 298.15 K since, in this reaction, water is neither product nor reagent. In order to calculate Gibbs free energy for each compound, Eq. (5) is applied. The Gibbs free

Scheme 1. Reaction for phenol acylation.

Scheme 2. Reaction for phenol esterification.

2. Proposed reactions

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Table 1 Benson’s group contributions for phenol Center

Ca-ring Ca-ring O

Attachment

H O Ca-ring H

Quantity

5 1 1

Hf◦ (kJ mol−1 )

S◦ (J mol−1 K−1 )

Cp◦ (J mol−1 K−1 ) 300 K

400 K

600 K

800 K

18.59 22.19 18.42

26.38 27.63 21.90

31.57 28.89 25.20

13.82 −3.77 −158.68

48.27 −42.66 121.84

13.57 16.33 18.00

Table 2 Benson’s group contributions for acetic acid Center

Attachment

Quantity

Hf◦ (kJ mol−1 )

S◦ (J mol−1 K−1 )

Cp◦ (J mol−1 K−1 ) 300 K

400 K

600 K

800 K

C C O O

HHH CO C OH

1 1 1

−42.71 −146.96 −243.25

127.32 61.96 102.58

25.92 25.12 15.91

32.82 28.05 20.93

45.18 33.49 26.38

54.51 37.26 30.14

S◦ (J mol−1 K−1 )

Cp◦ (J mol−1 K−1 )

Table 3 Benson’s group contributions for phenyl acetate Center

C Ca-ring Ca-ring C O O

Attachment

HHH H O CO Ca-ring C O

Quantity

1 5 1 1 1

Hf◦ (kJ mol−1 )

300 K

400 K

600 K

800 K

32.82 18.59 22.19 28.05

45.18 26.38 27.63 33.49

54.51 31.57 28.89 37.26

−42.71 13.82 −3.77 −146.96 −153.66

127.32 48.27 −42.66 61.96 42.71

25.92 13.57 16.33 25.12

Table 4 Benson’s group contributions for acetic anhydride Center

Attachment

Quantity

Hf◦ (kJ mol−1 )

S◦ (J mol−1 K−1 )

Cp◦ (J mol−1 K−1 ) 300 K

400 K

600 K

800 K

C C O O

HHH CO C OC O

2 2 1

−42.71 −146.96 −194.69

127.32 61.96 35.80

25.92 25.12

32.82 28.05

45.18 33.49

54.51 37.26

energy of reaction is obtained taking the appropriate sums and difference between reactants and products (Eq. (6)): G◦f = Hf◦ − TSf◦   (G◦f )prod − (G◦f )reac r G◦ (T ) =

(5) (6)

Table 5 shows the thermochemical values (Hf◦ , Sf◦ , and G◦f ) calculated using the group additivity model for all the reactants and products of the phenol esterification reaction. Using Eq. (6) and the values reported in Table 5, the calculated value for r G◦ is equal to −41.57 kJ mol−1 , at 298.15 K. The equilibrium constant (K) is calculated by the following equation: ln K(T ) =

G◦ (T )

−r RT

(7)

For phenol esterification, K is equal to 1.93 × 107 at 298.15 K. This permits to conclude that phenol esterification can be an appropriate reaction to consume phenol, since the forward reaction is faster than the inverse one.

Sobrinho et al. [12] calculated the equilibrium constant for phenol acylation at several temperatures using Benson’s method. These authors calculated the group contribution for phenyl acetate by Benson’s method, and for the other compounds (phenol, acetic acid and water) the thermochemical values were taken from Stull et al. [13]. For the additivity groups which are not reported in the published tables, the authors considered them equal to zero. They concluded, from the high K values, that phenol acylation reaches high conversions only at high temperatures. Therefore, following this approach, phenol acylation is not a suitable reaction to consume phenol. Table 5 Calculated thermochemical values, using Benson’s group contributions, for all components of phenol esterification reaction at 298.15 K Compound

Hf◦ (kJ mol−1 ) Sf◦ (J mol−1 K−1 ) G◦f (kJ mol−1 )

Phenol Acetic anhydride Phenyl acetate Acetic acid

−93.37 −574.01 −278.00 −432.92

314.76 390.34 415.79 282.73

−187.15 −690.32 −401.89 −517.15

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Table 6 Thermochemical data of components present in phenol acylation and esterification reactions at several temperatures and 101.32 kPa Components

Phenol Acetic acid Phenyl acetate Water Acetic anhydride

Sum of electronic and thermal free energies (ε0 + Gcorr ) (×105 kJ mol−1 ) T = 50 K

T = 298.15 K

T = 400 K

T = 600 K

T = 800 K

−8.07559 −6.01726 −12.0849 −2.00723 −10.0267

−8.07626 −6.01786 −12.0857 −2.00766 −10.0275

−8.07659 −6.01815 −12.0861 −2.00787 −10.0279

−8.07735 −6.01877 −12.087 −2.00829 −10.0288

−8.07822 −6.01945 −12.0881 −2.00874 −10.0298

4. Molecular modeling results Results from molecular modeling were obtained using Gaussian software (Gaussian 98, Rev A.11.2) and density functional calculations. This software requires an input file containing the molecular structure and the key words for the required computation. The structures of the molecules were built up using HyperChem software (HyperCube) and preoptimized using a semi-empirical quantum mechanical calculation with the approximate Hamiltonian AM1. This preoptimized geometry is the input for the functional density calculation that employs functional B3LYP and 6-31G** basis set, available in the Gaussian package. This “ab initio” quantum mechanical method recalculates the molecular geometry and computes thermochemical data for all the compounds involved in both reactions (Scheme 1). These two steps were performed within the same route section. Simulations were carried out at atmospheric pressure and at several temperatures (50, 298.15, 400, 600, and 800 K), in order to fill the gaps of such data in the open literature. Table 6 shows the sum of the electronic and thermal free energy values for the components in both reactions. In order to obtain the free energy values for the reactions, Eq. (8) was used.   r G◦ (T ) = (ε0 + Gcorr )prod − (ε0 + Gcorr )reac (8) where the terms (ε0 + Gcorr ) correspond to the sum of the electronic and thermal free energies. It is important to mention that Gaussian output provides the sum of electronic and thermal free energies, so that it is not possible to compare these values with those calculated by Benson’s method. However, this sum of energies, instead of the energy of formation, works properly, since the number of atoms of each element is the same on both sides of the reaction and, therefore, all atomic information cancels out [14]. Fig. 1 shows the calculated values of r G◦ for phenol acylation and esterification at several temperatures. The data can be adjusted to a linear fit, corresponding to Eq. (9), for phenol acylation, and (10), for phenol esterification. Correlation coefficients (R values) are 0.98 and 0.99, respectively. r G (phenol acylation) = 67.332 + 0.01958T r G (phenol esterificaton) = 2.838 + 0.04941T

(9) (10)

Fig. 1. Values of r G as a function of temperature for phenol acylation and esterification reactions.

Table 7 shows K values calculated for both reactions using Eq. (7). For process design purposes, the most important conclusion that can be taken from the calculated values of equilibrium constants is that the reaction of phenol esterification is more appropriate to consume phenol than is phenol acylation, since K values for the former reaction are higher than for the second one, at moderate temperatures. Moreover, phenol acylation reaches higher conversion rates only at high temperatures. This conclusion is in agreement with Sobrinho et al. [12]. Analyzing values of ln K versus temperature (Fig. 2), it is possible to observe that the phenol esterification reaction presents ln K values that are practically constant from 298.15 to 800 K. Moreover, above 400 K, both reactions converge to approximately the same K values. This behavior indicates that both reactions are suitable at high temperatures, although Table 7 Equilibrium constant values for phenol acylation and for phenol esterification reactions at several temperatures and 101.32 kPa Temperature (K)

K (reaction (1))

K (reaction (2))

50.00 298.15 400.00 600.00 800.00

1.23067E−70 9.74849E−14 1.14131E−10 1.26835E−07 4.4491E−06

1.10943E−08 0.001697423 0.001947623 0.001686498 0.001295916

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sion rate at useful conditions of temperatures. Based on these results, further work will be performed to simulate the reactive distillation for the esterification reaction. List of symbols heat capacity (J mol−1 K−1 ) Cp G Gibbs free energy (J mol−1 ) H enthalpy (J mol−1 ) K equilibrium constant R universal gas constant (J mol−1 K−1 ) S entropy (J mol−1 K−1 ) T absolute temperature (K)

Fig. 2. Values of ln K as a function of temperature for phenol acylation and esterification reactions. Table 8 Comparison between entropy values calculated by Benson’s method and molecular modeling at 298.15 K Components

S◦ (J mol−1 K−1 ) Benson’s method

Molecular modeling

Difference

Phenol Acetic acid Phenyl acetate Water Acetic anhydride

314.764 282.735 415.791 – 390.335

312.218 270.827 368.246 194.661 372.370

2.546 11.907 47.545 – 17.966

this condition is not interesting on an industrial scale, because of the high costs. Results obtained by Benson’s method and molecular modeling agree qualitatively well. An effective way to compare both methodologies is through the entropy values (Table 8), since these values can be directly taken from Gaussian output. Higher differences are observed for phenyl acetate and acetic anhydride, probably because these molecules are more complex. Benson’s method requires some corrections in the sum of entropies, using the symmetry number and the number of possible optical isomers, nevertheless these numbers were not taken into account, since they were not available in the consulted tables [8,10–11] for the studied compounds. It is important to mention that only with molecular modeling it was possible to compute the thermochemical values at several temperatures for both reactions. These results have been used in a new process proposal for separating phenol from wastewater [15].

5. Concluding remarks Quantum mechanical calculations are an effective methodology for predicting thermochemical data. Based on the results from DFT calculations, it was possible to conclude that the esterification reaction is more properly indicated to carry out the reactive distillation process for treating phenol wastes, since this reaction presents better chemical conver-

Greek symbols  variation (ε0 + Gcorr ) sum of electronic and thermal free energies, taken from Gaussian output (J mol−1 ) Superscript 0 standard Subscript e elements f formation m average value prod products r reaction reac reactants

Acknowledgements We gratefully acknowledge FAPESP and CNPq for financial support and fellowships.

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