Znd. Eng. Chem. Res. 1995,34, 1910-1913
1910
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 Eugbnia A. Macedo* LSRE-Laboratbrio de Processos de Separaqtio e Reacqtio, Faculdade de Engenharia do Porto, Rua dos Bragas, 4099 Porto Codex, Portugal
Raquel C. Gonqalves, Ana N. Simbes, Cristina M. Ventura, and Lidia C. Albuquerque* GERQ-Grupo de Estrutura e Reactividade Quimica, Faculdade de Cihcias da Universidade de Lisboa, Calqada Bento da Rocha Cabral, 14, 1200 Lisboa, Portugal
In this work infinite dilution activity coefficients ( y m ) of 2-chloro-2-methylpropane(tert-BuC1) in solvent mixtures of methanoVethane-l,2-diol, ethanoVethane-l,2-diol, and 2-methoxyethanoV ethane-1,2-diol have been calculated using the UNIFAC group-contribution model. For each system nine different compositions of the solvent mixtures were considered. The modification of the Flory-Huggins term in the combinatorial equation and the group-contribution parameters from the vapor-liquid equilibrium parameter table were used. These values together with the Gibbs energies of activation (A'G), obtained from the new experimental rate constant values of the solvolytic reactions of the same substrate in the binary alcoholic mixtures, allow the analysis of the solvent effect during the activation process, by means of the contributions of the initial state and the transition state.
Introduction The past decade has seen a nearly explosive development in the application of group-contribution activity coefficient models in areas such as design of chemical separation processes, flash point calculations, and many others. Infinite dilution activity coefficient values can also give an important contribution in the establishment of reaction mechanisms through the development of thermodynamic functions of transfer, accurate correlations, and prediction methods. From this kinetic point of view its knowledge is a powerful means for influencing reaction rates and industrial selectivity of solvents in order t o obtain the best profits. Many different models have been proposed in the literature, but due to the availability of large groupinteraction parameter tables, UNIFAC (Fredenslund et al., 1975) is the one which has the widest practical interest. There are several types of tables, with group-interaction parameters estimated from different data bases. The VLE (vapor-liquid equilibrium) parameter table is the most extensive one, containing interaction parameters for 50 commonly applicable groups (Fredenslund et al., 1977; Skjold-Jgrgensen et al., 1979; Gmehling et al., 1982; Macedo et al., 1983;Tiegs et al., 1987; Hansen et al., 1991). An UNIFAC parameter table specially suited for the prediction of infinite dilution activity coefficients was proposed by Bastos et al. (1988) with the aim of improving the accuracy and range of applicability of the UNIFAC method, as far as the calculation of infinite dilution activity coefficients is concerned. In this work infinite dilution activity coefficients ( y m ) of 2-chloro-2-methylpropane(tert-BuC1) in the binary mixtures methanol/ethane-1,2-diol, ethanollethane-1,2diol, and 2-methoxyethanol/ethane-1,2-diol were calcu-
* Authors
to whom correspondence should be addressed.
lated using the UNIFAC group-contributionmodel. The combinatorial activity coefficients were calculated using the modified Flory-Huggins term proposed by Kikic et al. (1980). The group-interaction parameters from the VLE parameter table were used in the calculations carried out in this work. The y" values were then used to calculate the transfer Gibbs energy of the reactants (dG,)-eq l-which are related to the transfer Gibbs energy of the activated complex (6Gt) through eq 2, as follows (Abraham et al., 1985; Gonqalves et al., 1993a,b):
dG, = RT ln(yj"/y,")
(1)
+ ~ A * G= d ~+,A*G~- A*G,
(2)
d ~ =, d~~
A'Gj refers to the Gibbs energy of activation in the solventj and A'G, refers to that in the reference solvent r. To perform this analysis, new experimental values of the rate constants were determined for the solvolytic reaction of tert-BuC1 in the binary alcoholic mixtures methanoyethane- 1,2-diol, ethanoyethane-1,2-diol, and 2-methoxyethanollethane-1,2-diol, at 25 "C. The reference solvent was the pure alcohol ethane-1,2-diol. Our attention is focused on solvent effects arising from the change of molar fraction in each mixture and from the change of one solvent to another in the studied binary mixtures. The reactions of tert-BuC1 with the specified alcohols were chosen for this kinetic study because, assuming the mechanism of the displacement reactions to be simple, attention could be focused on the role of the solvent. A particular interest of this kind of reactions is the fact that preferential solvation phenomena occur in monoalcoholldiol mixtures which plays an important role in many chemical reactions. Furthermore, diols can
0888-588519512634-1910$09.00/00 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1911 Table 1. Infinite Dilution Activity Coefficients for tert-BuC1 in AlcohoYAlcohol Mixtures, at 25 "C
15.00
Y" Xa
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
methanol/ ethane-1,Z-diol 15.6 15.7 15.9 15.9 15.3 15.0 14.4 14.0 13.6
ethanol/ ethane-1,Z-diol 15.6 ' 14.4 12.2 9.30 6.88 6.38 5.59 5.26 4.94
2-methoxyethanov ethane-1,Z-diol 15.6 10.6' 14.6 9.77c 12.8 8.38" 10.7 6.52' 4.96' 9.02 4.6ZC 8.67 4.1W 8.13 3.88' 7.90 3.6BC 7.68
Mole fraction; x = 0 corresponds to pure ethane-1,Z-diol. Values calculated from UNIFAC-VLE parameter table, unless noted otherwise. ' Values calculated from UNIFAC y" parameter table.
Table 2. Rate Constants (6-l) for the Solvolysis of tert-BuC1 in AlcohoYAlcohol Mixtures, at 25 "C
2-Methoxyethanol
12.00
/ Ethane-
1,2-diol
9.00
6.00
3.00
0.00
-3.00
j
15.00
1
106k xQ
methanol/ ethane-1.2-diol
ethanol/ ethane-1.2-diol
2-methoxyethanoV ethane-1.2-diol
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
24.55 23.44 19.06 10.96 4.786 3.548 2.239 1.349 0.871
24.55 22.91 13.49 5.754 1.072 0.759 0.501 0.209 0.0851
24.55 17.44 7.218 2.484 1.160 0.802 0.647 0.482 0.423
a
6.00
Mole fraction; x = 0 corresponds to pure ethane-1,2-diol.
Table 3. Gibbs Energies of Activation (kJ mol-') for the Solvolysis of tert-BuC1 in AlcohoYAlcohol Mixtures, at 25 "C
xa
methanol/ ethane-1,Z-diol
A*G ethanol/ ethane-1,Z-diol
2-methoxyethanol/ ethane-1,Z-diol
0.000 0.086 0.250 0.500 0.750 0.810 0.910 0.955 1.000
99.33 99.45 99.97 101.34 103.39 104.13 105.28 106.53 107.62
99.33 99.51 100.82 102.94 107.10 107.96 108.98 111.15 113.37
99.33 100.20 103.36 105.05 106.93 107.84 108.36 109.10 109.39
3.00
0.00
-3.00
15.00 Methanol
Mole fraction; x = 0 corresponds to pure ethane-1,Z-diol.
replace water in biological processes and it seems of fundamental importance to analyze the behavior of our mixtures.
9.00
/ Ethane- 1,2-dioI
i
6.00
Results and Discussion Experimental Section. The description of the kinetic procedure has been presented previously (GonGalves et al., 1990, 1991). The conductimetric results were analyzed in terms of the Kezdy-Swinbourne method for first-order equation. Good straight lines were obtained. The experimental errors in the rate constants, k, are less than 2%. The alcohols were from BDH and Merck. They were dried over molecular sieves, and their purity was established by gas chromatography and infrared spectrometry. The water content was kept lower than 0.02%. The substrate (tert-BuC1)was used as supplied by BDH.
3.00
0.00
Figure 1. Gibbs energies of transfer for the solvolytic reaction of tert-BuC1 in binary mixtures of alcohols as function of mole fraction, x , of the monoalcohol: (*) 6A*G (A)6Gi; (0)dGt.
Application of UNIFAC Method. In the present work, for the combinatorial term the modified Flory-
1912 Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 Table 4. Gibbs Energies of Transfer (kJ mol-') from Ethane-l,a-diolto Other Solvents of tert-BuC1in AlcohoYAlcohol Mixtures, at 25 "C methanoVethane-l,2-diol ethanoYethane-1,2-diol 2-methoxyethanoVethane-1,2-diol 6 A'G 6Gi 6Gt 6G,b 6Gtb 6G, 6Gt 6A*G 6A*G XO 0.000 0.086
0 0.02
0 0.12
0
0
0.14
0.18
0.250
0.64
0.05
0.69
1.49
0.500
2.01
0.05
2.06
3.60
0.750
4.06
-0.05
4.01
7.77
0.810
4.80
-0.09
4.71
8.63
0.910
5.94
-0.20
5.75
9.66
0.955
7.20
-0.26
6.94
11.8
1.000
8.29
-0.33
7.96
14.0
a
Mole fraction;x
=
0
0
-0.20 (-0.19) -0.61 (-0.57) -1.28 (- 1.19) -2.02 (-1.87) -2.21 (-2.05) -2.54 (-2.34) -2.69 (-2.48) -2.85 (-2.61)
0
-0.02
0
0
0.86
-0.17
0.70
3.03
-0.48
2.56
5.72
-0.93
4.79
7.60
-1.35
6.25
8.51
-1.45
7.06
9.03
-1.61
7.42
9.77
--1.68
8.09
-1.75
8.30
(-0.01)
0.88 (0.92) 2.33 (2.41) 5.75 (5.90) 6.42 (6.58) 7.12 (7.32) 9.13 (9.32) 11.2 (11.4)
10.1
0 corresponds to pure ethane-1,2-diol.Values in parentheses from y" in the fourth column of Table 1.
Huggins equation in the Staverman-Guggenheim expression (Kikic et al., 1980) was used. For the residual term group-interaction parameters from the UNIFACVLE parameter table (Fredenslund et al., 1977; SkjoldJ~rgensenet 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 that only for the solvent mixture ethanol/ethane-1,2-diol, UNIFAC yw parameters (Bastos et al., 1988) are available. In order to use the same model parameters in all calculations, the VLE parameter table was chosen. Regarding the solvent ethane-1,2-diol,it is worthwhile noting that we used the interaction parameters from the alcohol group (OH), instead of considering this solvent as a single group, as is usually advised (Skjold-J~rgensenet al., 1979;Macedo et al., 1983), because relevant parameters for the diol group are not available. We also note that 2-methoxyethanol is considered to be built by the following groups: 2 CH2, 1 OH, 1 CH30. The y m values of tertBuCl in pure methanol, ethanol, and ethane-1,2-diol are different from those published before (Gonqalves et al., 1993a). This is because the values from Gonqalves et al. (1993a) were obtained from the yw parameter table (Bastos et al., 1988). Table 1gives the infinite dilution activity coefficients of tert-BuC1in alcohoYalcoho1mixtures for nine different mole fractions, x (x = 0 corresponds to pure ethane-1,2diol), at 25 "C. The UNIFAC group-contributionmethod (Fredenslund et al., 1975,1977) was used. Also in this table y m values predicted from the Bastos et al. (1988) TJNIFAC parameter table are presented for the solvent mixture ethanol/ethane-l,2-diol, for comparative purposes. Calculation of Transfer Functions. The experimental rate constant values, K , are presented in Table 2. According to the transition state theory, A*G = -RT ln(hk/k,T)
(3)
the Gibbs energies of activation, A*G, were calculated. In eq 3, h and kg are, respectively, the Planck and the Boltzmann constants. Table 3 gives the calculated values of A*G. If we use eqs 1 and 2, we obtain the energies of transfer for the activated process, 6A*G,the initial state, 6Gi, and the transition state, 6Gt. The results are collected in Table 4. This table also shows 6Gi and 6Gt
for the mixture ethanol/ethane-l,2-diol using y m calculated from Bastos et al. (1988). It is important to mention that, although y- values from both sources differ considerably (Table l),the transfer energies for the initial state and transition state are very similar, leading t o a common interpretation. Interpretation. Figure 1 (6G vs x ) compares the behavior of the three systems under study. All the transfer thermodynamic functions show monotonous changes with the mole fraction, x , of the solvents. This behavior may be explained in terms of entropy-enthalpy compensations. Another general conclusion we may draw from Figure 1 is that the gradient in 6Gt is much larger (and of opposite sign) than that in 6Gi. Variations in 6Gt with x exhibit trends similar to those of 6A*G. This means that solvent effects on 6A*G are highly dependent on solvent effects on 6Gt which leads to the conclusion that the structural configuration of the activated complex may show a high degree of charge separation. This is, no doubt, influenced by the electrostatic interactions between solvent and activated complex. Conversely, the different behavior of 6Gi and 6A*G suggests that the solute-solvent interaction mechanisms acting in the initial state have a minor influence on the properties examined here. The same kind of conclusions are consistent with previous views of Abraham et al. (1988) and Gonqalves et al. (1993a) with respect to pure hydroxylic solvents. It is also instructive to compare the values of the transfer functions for the three systems. The deviation of 6Gt (and 6A*G)from a linear function of mole fraction is negative when methanol or ethanol participates in the binary solvent mixture and positive when 2-methoxyethanol is present. This may be explained by changes in solvent liquid structure, which occur particularly in mixed solvents, or by preferential solvation phenomena. Assuming that the major reason is the preferential solvation effect, for the mixtures methanol/ethane-1,2the monoalcohol appears diol or ethanol/ethane-1,2-diol, to solvate preferentially to the dialcohol; the reverse is true for 2-methoxyethanoYethane-l,2-diol.
Acknowledgment We recognize with thanks the financial support of JNICT (Portugal).
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1913
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