Ind. Eng. Chem. Res. 1996, 35, 3759-3762
3759
Infinite Dilution Activity Coefficients Predicted from UNIFAC Model. New Experimental Data for the Solvolytic Reactions of 2-Chloro-2-methylpropane in Methanol/Ethanol, Methanol/ 2-Methoxyethanol, and Ethanol/2-Methoxyethanol Lı´dia C. Albuquerque,* Ana N. Simo˜ es, Cristina M. Ventura, and Raquel C. Gonc¸ alves Grupo de Estrutura e Reactividade Quı´mica (GERQ), Faculdade de Cieˆ ncias da Universidade de Lisboa, Calc¸ ada Bento da Rocha Cabral, 14, 1250 Lisboa, Portugal
Euge´ nia A. Macedo* Laborato´ rio de Processos de Separac¸ a˜ o e Reacc¸ a˜ o (LSRE), Faculdade de Engenharia do Porto, Rua dos Bragas, 4099 Porto Codex, Portugal
The UNIFAC group contribution method was used to calculate the infinite dilution activity coefficients (γ∞) of 2-chloro-2-methylpropane (t-BuCl) in the binary mixtures methanol/ethanol, methanol/2-methoxyethanol, and ethanol/2-methoxyethanol at 298.15 K. For each system, nine different compositions of the solvent mixtures were considered. The modified Flory-Huggins equation in the combinatorial term was used, as well as the group contribution parameters from the vapor-liquid equilibrium parameter table in the residual term, due to the nonavailability of specific γ∞ UNIFAC interaction parameters for the relevant groups. The γ∞ values were combined with a set of new and experimentally determined kinetic parameters of the solvolytic reactions of the same substrate in the same solvents to describe quantitatively the contributions of the initial state and the transition state to the solvent effect. By using this approach, the Gibbs energies of transfer of the reactants and the activated complex were obtained, which allows us to better understand the reaction mechanism and to influence reaction rates through a coherent selection of solvents. Introduction The utility of infinite dilution activity coefficients (γ∞) has been well recognized in different areas such as separation processes, phase equilibrium behavior, and many others. Recently, Macedo et al. (1995) showed the important contribution of infinite dilution activity coefficient (γ∞) values to the calculation of Gibbs energies of transfer and, consequently, to the study of reaction mechanisms by using solvent variation. The application of predictive models for the calculation of thermodynamic properties, such as the γ∞, is very common. The most widely used model is the UNIFAC method (Fredenslund et al., 1975) due to the availability of large group interaction parameter tables. The examination of solvent effects on the rate constants (k) or on the Gibbs energy of activation (∆qG), through the calculation of the transfer Gibbs energy of activation (δ∆qG), the transfer Gibbs energy of the reactants (δGi), and the transfer Gibbs energy of the activated complex (δGt), allows us to express solutesolvent interactions quantitatively, as stated before (Abraham et al., 1985, 1988; Gonc¸ alves et al., 1993a,b; Macedo et al., 1995). In fact, thermodynamic transfer energies take into account the effect of changes resulting from the sucessive replacement of the molecules of one solvent by those of a second solvent in the coordination sphere of the solute. Moreover, binary alcoholic mixtures seem to induce preferential solvation, which is particularly relevant in many industrial chemical processes. Preferential solvation affects the variations in all of the transfer parameters in mixed solvent systems. In this work we present new calculated values for infinite dilution activity coefficients of 2-chloro-2-methylpropane (t-BuCl) in nine methanol/ethanol, methanol/ * Authors to whom correspondence should be addressed.
S0888-5885(96)00052-8 CCC: $12.00
2-methoxyethanol, and ethanol/2-methoxyethanol binary mixtures. They were obtained by the UNIFAC group contribution method, using the modified Flory-Huggins equation in the combinatorial expression. The group interaction parameters used for these calculations are from the VLE parameter table (Fredenslund et al., 1977; Skjold-Jorgensen et al., 1979; Gmehling et al., 1982; Macedo et al., 1983; Tiegs et al., 1987; Hansen et al., 1991). We also extend our kinetic studies, by using a conductimetric technique (Gonc¸ alves et al., 1990), of the unimolecular decomposition of t-BuCl. In fact, k values were determined at the same mole fractions as the binary solvent mixtures and at the same temperature, 298.15 K. By assuming the transition state theory, ∆qG is given by eq 1, where R, h, and kB are the gas, Planck, and Boltzmann constants, respectively, and T is the temperature in kelvin:
∆qG ) - RT ln(hk/kBT)p
(1)
According to Abraham et al. (1985) and Gonc¸ alves et al. (1993a,b), the transfer Gibbs energies of the reactants are given by
δGi ) RT ln(γ∞j/γ∞r)
(2)
The relationship that correlates the various transfer Gibbs quantities is defined by eq 3, where j refers to a chosen binary mixture of solvents and r refers to the reference solvent (ethanol, in this case):
δGt ) δGi + δ∆qG ) δGi + ∆qGj - ∆qGr
(3)
The results are interpreted and compared with previous results concerning these kinds of reactions in other alcohol/alcohol mixtures. These data contribute to a better understanding of the solute-solvent interactions © 1996 American Chemical Society
3760 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 Table 1. UNIFAC Groups for Each Component
Table 4. Infinite Dilution Activity Coefficients and Rate Constants (s-1) for t-BuCl in Alcohol/Alcohol Mixtures at 298.15 K
component
groups
t-BuCl methanol ethanol 2-methoxyethanol
3 CH3, 1 CCl 1 CH3OH 1 CH3, 1 CH2, 1 OH 2 CH2, 1 OH, 1 CH3O
Table 2. Volume (R) and Surface Area (Q) Parameters for Each Group group
R
Q
CH3 CH2 OH CH3OH CCl CH3O
0.9011 0.6744 1.0000 1.4311 1.0060 1.1450
0.848 0.540 1.200 1.432 0.724 1.088
Table 3. UNIFAC Group Interaction Parameters aij (K) CH3;CH2 OH CH3OH CCl CH3O
CH3;CH2
OH
CH3OH
CCl
CH3O
0 156.4 16.51 91.46 83.36
986.5 0 249.1 562.2 237.7
697.2 -137.1 0 529.0 238.4
35.93 75.62 -38.32 0 301.1
251.5 28.06 -128.6 225.4 0
during the kinetic process, as well as problems specifically involving binary solvent mixtures. Experimental Section The conductimetric technique was applied to obtain the solvolytic rate constants of t-BuCl in the alcohol mixtures. Conductance measurements were recorded in a Wayne-Kerr B905 bridge, and at least three experiments were performed for each system. The temperature control was better than 0.01 degree. The Kezdy-Swinbourne method (Swinbourne, 1971) was applied to obtain the first-order k values at 298.15 K. The experimental error in k is always less than 2%. Other details of the experimental procedure have been described previously (Gonc¸ alves et al., 1990). Alcohols were from BDH and Merck. They were dried over appropriate molecular sieves to keep the content of water less than 0.02%. tert-Butyl chloride was from BDH. The purity of the reagents was estimated to be >99%. UNIFAC Method. In this work the infinite dilution activity coefficients of t-BuCl in the different binary mixtures of solvents were calculated by using the UNIFAC group contribution method (Fredenslund et al., 1975, 1977), due to the nonavailability of experimental data. For the combinatorial term, the modified FloryHuggins equation in the Staverman-Guggenheim expression (Kikic et al., 1980) was used. For the residual term, group interaction parameters from the UNIFAC VLE parameter table (Fredenslund et al., 1977; SkjoldJorgensen et al., 1979; Gmehling et al., 1982; Macedo et al., 1983; Tiegs et al., 1987; Hansen et al., 1991) were used. The reason for this is the nonavailability of specific γ∞ UNIFAC interaction parameters for the relevant groups (Bastos et al., 1988). Tables 1-3 give the different groups for each component, volume and surface area parameters (R and Q) for each group involved, and the UNIFAC interaction parameters used in the calculations, respectively. The typical average error for the families of compounds involved in this work is less than 12% with UNIFAC VLE interaction parameters (Bastos, 1987). Table 4 presents the infinite dilution activity coefficients of t-BuCl in the alcohol/alcohol mixtures for nine different compositions of solvents at 298.15 K.
methanol/ ethanol/ methanol/ethanol 2-methoxyethanol 2-methoxyethanol x1a
γ∞
106k
γ∞
106k
γ∞
106k
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
4.94 5.24 5.94 7.39 9.68 10.4 11.9 12.7 13.6
0.0851 0.309 0.589 1.082 1.530 1.453 1.251 1.129 0.871
7.68 8.06 8.84 10.2 11.8 12.2 12.9 13.3 13.6
0.423 0.585 0.728 0.919 0.996 1.013 0.977 0.944 0.871
7.68 7.39 6.85 6.11 5.46 5.32 5.11 5.02 4.94
0.423 0.538 0.858 1.000 1.035 0.771 0.733 0.449 0.0851
a
Mole fraction of the first component of the alcoholic mixture.
Table 5. Gibbs Energies of Activation (kJ mol-1) for the Solvolytic Reaction of t-BuCl in Alcohol/Alcohol Mixtures at 298.15 K ∆qG x1a
methanol/ ethanol
methanol/ 2-methoxyethanol
ethanol/ 2-methoxyethanol
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
113.37 109.98 108.58 107.08 106.22 106.35 106.72 106.97 107.62
109.41 108.60 108.06 107.48 107.28 107.24 107.33 107.42 107.62
109.41 108.81 107.65 107.27 107.19 107.92 108.04 109.26 113.37
a
Mole fraction of the first component of the alcoholic mixture.
Results and Discussion The experimental mean values of the rate constants of the solvolytic reactions for t-BuCl in the three alcohol/ alcohol mixtures under study are also presented in Table 4. Table 5 summarizes the Gibbs energies of activation, calculated according to eq 1. Table 6 gives the values obtained for the Gibbs energies of transfer for the activated process, initial state, and transition state according to eqs 2 and 3. We illustrate the behavior of the transfer Gibbs functions against the mole fraction of the binary solvents in Figure 1. As noted earlier (Macedo et al., 1995), the composition dependence of the Gibbs energies of transfer in alcohol/ alcohol mixtures seems to be a continuous function. However, the observed dependence of δ∆qG and δGt on the three binary mixtures presented in this paper differs from that observed on methanol (ethanol or 2-methoxyethanol)/ethane-1,2-diol, as illustrated by the minima (0.7 < x1 < 0.8) shown in Figure 1 and the plot in Figure 2. Values in Figure 2 were obtained from Gibbs energies of transfer presented by Macedo et al. (1995), using ethanol as the reference solvent, for comparative purposes. This is a very interesting situation and we will consider the significance of this point in more detail in the following. The transfer functions for the initial state are always positive, while those for the activated process and the transition state are negative. δGi values increase with the mole fraction in methanol/ethanol and methanol/2methoxyethanol, are almost constant in methanol/ ethane-1,2-diol, but decrease in the other mixtures studied, indicating a significant relation between the chosen alcohol and the mole fraction composition. Another significant feature is that δ∆qG values exhibit marked differences from δGi behavior, and, conversely, the concentration dependence of δ∆qG and δGt
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3761 Table 6. Transfer Gibbs Energies (kJ mol-1) for the Solvolytic Reaction of t-BuCl in Alcohol/Alcohol Mixtures at 298.15 K (Reference Solvent: Ethanol) methanol/ethanol
methanol/2-methoxyethanol
ethanol/2-methoxyethanol
x1a
δ∆qG
δGi
δGt
δ∆qG
δGi
δGt
δ∆qG
δGi
δGt
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
0 -3.20 -4.79 -6.30 -7.16 -7.03 -6.66 -6.41 -5.76
0 0.15 0.46 1.00 1.67 1.85 2.19 2.35 2.52
0 -3.05 -4.34 -5.30 -5.49 -5.18 -4.47 -4.06 -3.24
-3.97 -4.78 -5.32 -5.90 -6.10 -6.14 -6.05 -5.96 -5.76
1.10 1.21 1.44 1.80 2.15 2.24 2.38 2.45 2.52
-2.88 -3.56 -3.88 -4.10 -3.94 -3.90 -3.66 -3.51 -3.24
-3.97 -4.57 -5.73 -6.10 -6.19 -5.46 -5.34 -4.12 0
1.10 1.00 0.81 0.52 0.25 0.18 0.08 0.04 0
-2.88 -3.57 -4.91 -5.58 -5.94 -5.28 -5.25 -4.08 0
a
Mole fraction of the first component of the alcoholic mixture.
Figure 1. Gibbs energies of transfer (kJ mol-1) for the heterolysis of t-BuCl in methanol + ethanol, methanol + 2-methoxyethanol, and ethanol + 2-methoxyethanol mixtures as function of the mole fraction, x1, of the first component.
Figure 2. Gibbs energies of transfer (kJ mol-1) for the heterolysis of t-BuCl in 2-methoxyethanol + ethane-1,2-diol, ethanol + ethane1,2-diol, and methanol + ethane-1,2-diol mixtures as function of the mole fraction, x1, of the first component.
is very similar. This clearly shows that the intermolecular processes occurring in the solvolytic reaction of
t-BuCl are dominant for the contribution of the transition state interaction terms.
3762 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
Intermolecular affinities in this kind of reaction can be viewed in two complementary ways: (i) because there is a large number of H-bonding (donor and acceptor) sites in the alcohols, a H-bonding network is formed, between similar and nonsimilar molecules, that can be disrupted with the introduction of the substrate molecules into the solvent (initial state); (ii) substrate and solvent molecules are able to participate in dipoledipole interactions, particularly in the transition state, since the activated complex is expected to be a highpolarity species. This also implies an “order effect”, i.e., a stronger alcohol/alcohol interaction at least into the cybotatic region of the substrate. The behavior of the different Gibbs energies of transfer of tert-butyl chloride from the six target solvent mixtures to ethanol (Figures 1 and 2) leads us to conclude that it is most likely the result of the second effect. Another interesting feature of the results shown in Figure 1 is the systematic broad minimum that occurs at x1 = 0.75. This might arise from preferential solvation in the mixed solvent media, thereby indicating that the solvent structural changes play an important role in controlling the energetics of the interaction processes. Based on this assumption, the position of the minima correspond to regions of structure promotion. Conclusions The Gibbs energies of transfer, which can be obtained through cooperative experimental kinetic work, to obtain rate constant values, and the theoretical calculation from the UNIFAC group contribution method, to obtain the activity coefficients values, provide a useful quantitative means of describing dominant substratesolvent interactions during reaction paths. Application to binary alcohol/alcohol mixtures (or other solvent composition) also yields valuable information on selective interactions. If both solvents of each alcoholic mixture have the same solvating ability, the variation in the Gibbs energies of transfer with the mole fraction should be a straight line going from the value of one pure solvent to that of the other pure solvent. Our plots of δGi show only a slight curvature, but, conversely, δ∆qG and δGt show a large deviation from linearity. This provides an obvious marker for significant preferential solvation during the activation process and for the transition state in binary alcoholic mixtures. In fact, in the systems studied, the variation in the transfer Gibbs energies of activation with the solvent composition is markedly dependent on the interactions that took place in the transition state of tert-butyl chloride heterolysis. Furthermore, the mixtures methanol/ethanol, methanol/2-methoxyethanol, and ethanol/ 2-methoxyethanol show evidence of particular interactions between molecules of different types. This information is very useful when selecting more suitable solvent compositions for many industrial chemical processes occurring in liquid media. Acknowledgment
x ) mole fraction γ∞ ) infinite dilution activity coefficient ∆qG ) Gibbs energy of activation δ∆qG ) transfer Gibbs energy of activation δGi ) transfer Gibbs energy of the reactants δGt ) transfer Gibbs energy of the activated complex
Literature Cited Abraham, M. H. Solvent Effects on Reaction Rates. Pure Appl. Chem. 1985, 57, 1055-1064. Abraham, M. H.; Grellier, P. L.; Abboud, J.-L. M.; Doherty, R. M.; Taft, R. W. Solvent Effects in Organic Chemistry-Recent Developments. Can. J. Chem. 1988, 66, 2673-2686. Bastos, J. C. Modelagem de Processos de Destilac¸ a˜o Extractiva: Selecc¸ a˜o de Solventes, Simulac¸ a˜o e Integrac¸ a˜o Energe´tica. Ph.D. Thesis, University of Porto, Porto, Portugal, 1987. Bastos, J. C.; Soares, M. E.; Medina, A. G. Infinite Dilution Activity Coefficients Predicted by UNIFAC Group Contribution. Ind. Eng. Chem. Res. 1988, 27, 1269-1277. Fredenslund, Aa.; Jones, R. L.; Prausnitz, J. M. Group-Contribution Estimation of Activity Coefficients in Non Ideal Liquid Mixtures. AIChE J. 1975, 21, 1086-1099. Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria using UNIFAC; Elsevier: Amsterdam, 1977; Chapter 4. Gmehling, J.; Rasmussen, P.; Fredenslund, Aa. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension 2. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 118127. Gonc¸ alves, R. M. C.; Simo˜es, A. M. N.; Albuquerque, L. M. P. C.; Macedo, E. A. Study of Initial and Transition-State Solvation in the Solvolysis of tert-Butyl Halides in Alcohols from Infinite Dilution Activity Coefficients. J. Phys. Org. Chem. 1993a, 6, 133-138. Gonc¸ alves, R. M. C.; Calado, A. R. T.; Pinheiro, L. M. V.; Albuquerque, L. M. P. C.; Macedo, E. A. Study of Initial and Transition-State Solvation in the Menschutkin Reaction of Triethylamine with Ethyl Iodide in Alcohols from Infinite Dilution Activity Coefficients. J. Phys. Org. Chem. 1993b, 6, 595-599. Gonc¸ alves, R. M. C.; Simo˜es, A. M. N.; Albuquerque, L. M. P. C. Linear-Solvation Energy Relationships: Solvolytic Reactions of t-Butyl Bromide and t-Butyl Iodide in Hydroxylic Solvents. J. Chem. Soc., Perkin Trans. 2 1990, 1379-1383. Hansen, H. K.; Rasmussen, P.; Fredenslund, Aa.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension 5. Ind. Eng. Chem. Res. 1991, 30, 2352-2355. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, Aa. On the Combinatorial Part of the UNIFAC and UNIQUAC Models. Can. J. Chem. Eng. 1980, 58, 253-258. Macedo, E. A.; Gonc¸ alves, R. C.; Simo˜es, A. N.; Ventura, C. M.; Albuquerque, L. C. Infinite Dilution Activity Coefficients from UNIFAC Model for 2-Chloro-2-methylpropane in Binary Mixtures of Alcohols. Application to the Mechanistic Study of Solvolytic Reactions. Ind. Eng. Chem. Res. 1995, 34, 1910-1913. Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria by UNIFAC Group Contribution. Revision and Extension 3. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 676678. Skjold-Jorgensen, S.; Kolbe, B.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Ind Eng. Chem. Process Des. Dev. 1979, 18, 714-722. Swinbourne, E. S. Analysis of Kinetic Data; Appleton Century Crofts: New York, 1971. Tiegs, D.; Gmehling, J.; Rasmussen, P.; Fredenslund, Aa. VaporLiquid Equilibria by UNIFAC Group Contribution. Revision and Extension 4. Ind. Eng. Chem. Res. 1987, 26, 159-161.
This work was supported by JNICT (Portugal). Nomenclature aij ) UNIFAC interaction parameter between groups i and j k ) rate constant Q ) group area parameter R ) group volume parameter
Received for review January 26, 1996 Accepted May 23, 1996X IE960052Q
X Abstract published in Advance ACS Abstracts, July 15, 1996.
