I n d . Eng. Chem. Res. 1987, 26, 1725-1735
1725
Kinetic Modeling of the Toluene Chloromethylation M. I. Ortiz Uribe, A. Romero Salvador,+and A. Irabien Gulias* Departamento de Quimica T&nica, Facultad de Ciencias, Universidad del Pais Vasco, Bilbao, Apdo. 644-48080, Spain
T h e kinetic analysis and modeling of the chloromethylation of toluene in a homogeneous liquid phase containing toluene, paraformaldehyde, hydrochloric acid, acetic acid, and zinc chloride has been carried out. From the initial reaction rates, a hyperbolic kinetic expression describing the influence of toluene, paraformaldehyde, and acids on the formation of chloromethyltoluene, methyl tolueneacetate, and ditolylmethane has been obtained. T h e Himmelblau e t al. method has been applied to discriminate between different reaction schemes, leading to five significant reactions that are able to describe the main products. Kinetic parameters have been evaluated, and the influence of the temperature has been fitted by the Arrhenius law. A simulation for the reaction involving five reagents a n d three main products leads t o less than 10% error with the experimental results. Chloromethylation is a specific and the most important example of halogenoalkylation. It consists of the direct substitution of a hydrogen atom by the chloromethyl group (CH2C1). This reaction has been applied to manufacture different products, as Ionescu (1977) and Belen'kii et al. (1977) report, but only scarce results are given for a kinetic interpretation. Dvorak (1962), Dalmonte et al. (1963), Pesin et al. (1964), and Ripple (1980) give some results of the yield of the reaction. Mironov et al. (1970) use a power law to fit the formaldehyde consumption rate to a kinetic model. Irabien et al. (1983) fit the trioxane consumption rate to a semiempirical hyperbolic model, and general reviews are found in Fuson and McKeever (1942), Olah (1963), and Belen'kii et al. (1977). The reactivity of reagents and products leads to the formation, besides the monochloromethylated product, of other products and byproducts such as diarylmethanes, polychloromethylated compounds, bis(chloromethy1) ethers, and condensation byproducts, as it has been suggested in the literature by Szmant and Dudek (1949), Nazarov and Semenovskii (1956), Kontsova and Yukel'son (1970) and Brown and Nelson (1953). For the chloromethylation of toluene in a homogeneous liquid phase, the following additives have been used in this work: hydrochloric acid and paraformaldehyde as chloromethylating agent; zinc chloride as catalyst and acetic acid to avoid the organic phase segregation. The acetic acid leads to the formation and stabilization of hydroxymethyl derivatives and acetic esters together with the byproducts described above, as Ogata and Okano (1956) point out in the chloromethylation of mesitylene. The kinetic analysis and modeling of this complex reaction has four major points: stoichiometric analysis, scheme of reactions, development and evaluation of a kinetic model, and evaluation of the kinetic parameters. From the stoichiometric point of view, much work has been directed toward solving complex reaction systems (Uphadye, 1983, and others). However, we have not been able to determine quantitatively all byproducts; a mass balance has been applied, obtaining a significant amount of nonidentified byproducts. The purpose of this work is the development of a kinetic model which will enable us to describe the rate of formation of the main products (chloromethyltoluene, methyl
* Author to whom correspondence should be-addressed. t Present address: Departamento de Ingenieria Quimica, Fa-
cultad de Quimicas, Universidad Complutense, Madrid, Spain.
0888-5885/87/2626-1725$01.50/0
tolueneacetate, and ditolylmethane) as a function of the initial conditions of the reaction. In modeling the reactions, the Himmelblau et al. (1967) integration method has been used to discriminate between alternative potential models. An initial reaction rates study was necessary to find the kinetic expression to describe the reaction rates. Only two consecutive reactions of the products have shown a significant influence in the kinetic model. The influence of the acids has been taken into account through the Hammett acidity function, which has been correlated in the investigated range of variables by a semiempirical expression (Cox and Yates, 1981). Six kinetic parameters have been evaluated: one corresponds to the hyperbolic model and five to the description of the formation of the products (three) and of the consecutive reactions (two). The kinetic parameters have been evaluated following the integral method of Himmelblau et al. (1967) and the temperature influence has been taken into account, fitting the kinetic parameters to the Arrhenius law. The kinetic model and the evaluated parameters enable us to describe the yield of chloromethyltoluene, methyl tolueneacetate, and ditolylmethane in the investigated range of variables with an error of less than 10% as it has been shown in the simulation.
Experimental Section The chloromethylation reaction has been carried out in a homogeneous liquid phase in a stirred reactor provided with a reflux condenser under isothermal conditions. Reagents were hydrochloric acid, acetic acid, paraformaldehyde, toluene, and zinc chloride as catalyst. These compounds were the purest grade products available commercially. In the kinetic analysis, the initial concentrations of toluene and paraformaldehyde and the temperature have been taken as variables. Hydrochloric acid concentration, acetic amount, and zinc chloride concentration have been taken at constant values: 3.0 M, 40%, and lo%, respectively. The influence of the acids in the kinetic model has been earlier studied through the Hammett acidity function (Rey et al., 1987); experiments at different concentrations of acids have been used to fit the kinetic parameters. The central point, E-0, has been taken in the experimental design, (CTo= 0.075 M, CF0= 2.5 M, CHcl = 3.0 M, CHAc= 40%, CZnClz = l o % , and Te = 70 "C), and each variable has been studied at an upper level and a lower level (0.05 M < CTo< 0.1 M, 0.5 M 6 CFo6 4.5 M, 2.0 M 0 1987 American Chemical Society
1726 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987
6 CHC~6 4.0 M, 30% < C H A6~ 5070,5% 6 Cznc12< 1570, and 50 "C < Te < 90 "C), keeping the other variables at the central point. Experiments E-1 and E-2 allow us to study the influence of the toluene in the kinetic model at CT, = 0.1 and 0.05 M, respectively, experiments E-3 and E-4 show the influence of the paraformaldehyde at CF, = 0.5 and 4.5 M, respectively, and experiments E-5 and E-6 show the influence of the temperature at T" = 50 and 90 "C, respectively. Experiments E-7-E-12, which have earlier been used to determine the influence of the acidity function in the reaction rate at the central point, and different concentrations of the acids = 2 M, CHCl= 4 M, CHAc= 30%, CHAc = 50%, CZnC12 = 570, and CZnC12 = 1570, respectively) have been also fitted to the kinetic model. At selected times under each condition, the reaction is stopped in an ice bath. After the reaction cools, a known amount of acetic acid is poured into the reactor to avoid the organic phase separation which could lead to experimental errors. The difficulty in analyzing acetic acid solutions makes it necessary to perform the extraction and neutralization of organic substances in one step to avoid the interference of acetic acid in the analysis. The neutralization was performed with Na2C03,and simultaneously an extraction with dichloromethane takes place (Courtier, 1966). A relation of 1to 4 between solution and dichloromethane has been used for a complete extraction. The extraction yield was tested with synthetic samples of acetic acid, zinc chloride, and water and weighted amounts of toluene and chloromethyltoluene.
Analytical Methods After the operations described above, samples were ready for the chromatographic analysis. Qualitative Analysis. The identification of the products was carried out by capillary gas chromatography/mass spectrometry in a compact Hewlett-Packard 5992B GC/MS model. The qualitative analysis conditions were as follows: column, Hewlett-Packard, 25 m long; di, 0.2 mm; 0.33 pm particle size; 5% phenylmethylsilicone over fused silica cross-linked; injection temperature, 250 "C; detection temperature, 280 "C; carrier gas, helium, 21 psia; elution time for the solvent, 2 min; oven programmed at initial temperature, 70 "C, initial time, 1 min, heating rate, 5 "C/min, final temperature, 250 "C, final time, 0 min. The mass spectrometry results for the identified products expressed as m/e (% 0 ,were as follows: CMT, 51.05 (16.21, 77.1 (17.1), 105.15 (loo), 140.1 (23.9); DTM, 104.15 (74.9), 165.05 (45.4), 181.2 (loo), 196.1 (85.5);AMT, 43.15 (77.7), 104.15 (79.2), 105.15 (93), 122.1 (100); DTM-C, 152.05 (52.2), 195.1 (57.7), 209.15 (72.5), 244.2 (100); HMT, 104.05 (35.7), 105.05 (56.5), 107.05 (47), 122.1 (100);DCMT, 115.05 (26.3), 117.1 (38.8), 153.15 (loo), 155.05 (33.4); BCME(l), 73.2 (31.6), 281.35 (loo), 282.35 (52.1), 283.35 (40.2); BCME(2), 73.2 (82.9), 341.35 (loo), 342.35 (56.6), 343.35 (46.1). Taking into account a semiquantitative evaluation, the following classification was undertaken: (minor products) bis(chloromethy1) ethers with 8 and 10 atoms of carbon BCME(1) and BCME(2), hydroxymethyltoluene (HMT), and dichloromethyltoluene (DCMT); (major products) chloromethyltoluene (CMT), methyl tolueneacetate (AMT), ditolylmethane (DTM), and chloromethylated ditolylmethane (DTM-C). Quantitative Analysis. For the quantitative analysis, a Perkin-Elmer Sigma 3B gas chromatograph coupled with a Sigma 10B data station with flame ionization detector has been used.
The difficulty in analyzing quantitatively aromatic chloromethyl derivatives by gas chromatography has been shown by Handrick (1966) and Olah et al. (1976), but it is possible for the chloromethyl derivatives of toluene in a packed column with the following characteristics: 4.5 m long, d, 1/8 in., 5% Bentone-34 + 1% DC-200 over Chromosorb W (a.w.), 60-80 mesh (Olah et al., 1976). For the selection of the optimum conditions of the analysis, synthetic samples were prepared with dichloromethane, toluene, p-chloromethyltoluene (Merck), and benzyl chloride (Merck) as internal patron. This was selected for its similarity with the product. The analysis of the samples must be able to determine toluene, chloromethyltoluene, methyl tolueneacetate, ditolylmethane, and chloromethylated ditolylmethane concentrations. These species have been taken as reagent and main products. Three different conditions have been selected for the quantitative analysis because a high sensitivity is needed in the investigated range of variables; see supplementary material. Toluene was determined under mild conditions of temperature and carrier gas flow, chloromethyltoluene with the internal patron used as reference under moderate conditions, and methyl tolueneacetate, ditolylmethane, and chloromethylated ditolylmethane under severe conditions. Quantitative Analysis of Toluene. The conditions for the separation of dichloromethane and toluene were as follows: carrier gas, nitrogen; flow, 30 cm3/min; injection temperature, 300 "C; detection temperature, 350 "C; oven temperature, 90 "C; initial time, 7 min; temperature slope, 20 "C/min; final temperature, 200 "C; final time, 6 min; injection volume, 1 FL. The quantitative evaluation was performed after Calibration with synthetic samples in the range of concentrations to be evaluated. The retention times were as follows: dichloromethane, 0.80 f 0.20 min; toluene, 2.0 f 0.2 min. The error of this analysis determined by statistical methods was less than f10% in the investigated range of variables. Quantitative Analysis of Chloromethyltoluene. The response of this product was greatly influenced by the carrier gas flow and oven temperature, so that an internal standard (benzyl chloride), as explained above, has been used in the quantitative evaluation. The optimum conditions of the analysis were as follows: carrier gas, nitrogen; flow, 60 cm3/min; oven program at initial temperature, 140 "C,initial time, 0 min; temperature slope, 15 "C/min, final temperature, 200 " C ; final time, 6 min, injection temperature, 400 "C; detection temperature, 400 "C; injection volume, 1 p L . The retention times were as follows: dichloromethane, 0.35 f 0.05 min; benzyl chloride, 1.17 f 0.05 min; chloromethyltoluene, 1.72 f 0.05 min. Synthetic samples were also prepared with o-chloromethyltoluene and m-chloromethyltoluene (Aldrich) and dichloromethane, toluene, benzyl chloride, and p-chloromethyltoluene (Merck). From these results, it was possible to conclude that the three isomers have the same retention time following these conditions and a quantitative Calibration with synthetic samples does not show any difference between them. The quantitative evaluation of the chloromethyltoluene (three isomers together) under these conditions shows good reproducibility and the error of the analysis determined by statistical methods was less than A570, Quantitative Analysis of Methyl Tolueneacetate, Ditolylmethane, and Chloromethylated Ditolylmethane. The reproducibility of the analysis of these
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1727
5 10 15 20 t(hrs) Figure 1. Kinetic results for the experiment E-0; ( 0 )toluene, (0) chloromethyltoluene, (0) methyl tolueneacetate, (A)ditolylmethane. (A)chloromethylated ditolylmethane.
Figure 3. Kinetic results for the experiment E-2.
C(molll1
8.10-2
\
6.10-' \ *
4.1 0-'
2.10-'
''
6
t ( t i r5 )
lE
Figure 4. Kinetic results for the experiment E-3.
0 2
4
6
8
t(hrs)
Figure 2. Kinetic results for the experiment E-1.
products forced severe conditions: carrier gas, nitrogen; flow, 60 cm3/min; oven programmed at isothermal, 190 "C; injection temperature, 400 "C; detection temperature, 400 "C; injection volume, 1 pL. The retention times were as follows: methyl tolueneacetate, 1.85 f 0.05 min; ditolylmethane, 2.75 f 0.05 min; chloromethylated ditolylmethane, 4.0 f 0.15 min. It was possible to separate the different isomers of each product under different conditions, but the reproducibility of the analysis was not acceptable when the time of analysis was longer than 5 min. For the quantitative evaluation of the products, methyl tolueneacetate, ditolylmethane, and chloromethylated ditolylmethane, a calibration was performed with synthetic samples of dichloromethane, methyl toluenebenzoate (Merck), biphenyl (Merck), and fluorene (Merck), respectively. It was not possible to calibrate the products with the same commercial compounds, but the dilution of the products and calibration compounds showed similar behavior. Chromatograms and calibration curves are included as supplementary material (S-1). Kinetic Results
Experimental results are shown in Figures 1-7 as concentration (mol/L) against reaction time (h) for toluene, chloromethyltoluene, methyl tolueneacetate, ditolylmethane, and chloromethylated ditolylmethane, which
Cholll) 6.1 0-'
i
2 L 6 8 Figure 5. Kinetic results for the experiment E-4.
t(hrs)
C(mol/l) 6
\
2 40-21
10
30
Figure 6. Kinetic results for the experiment E-5.
50
t(hrs)
1728 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987
2
1
3
4
t(hrs)
Figure 7. Kinetic results for the experiment E-6. Table I. Reactions Considered i n t h e Complex Scheme T+F+HCl-CCMT+HzO
-
(1) (2)
+
T + F H A C - +AMT + HzO 2T + F DTM + H,O
+
+
----
CMT T DTM HC1 AMT + T DTM + HAC DTM + T + F C1+ HgO DTM-C + T C1 + HCI CMT + DTM C1+ HC1 2CMT DTM-C + HCl C7 + HC1 CMT + AMT CMT AMT DTM-C + HC1 nCMT Cz + (n- 1)HCl DTM F HCl DTM-C HC1 DTM + AMT C1 + HAC AMT + DTM-C C6 HC1 C, HCl AMT + DTM-C C3 + HCI DTM + DTM-C DTM-C CMT C b + HC1 C4 + HC1 nDTM-C +
+ + +
--
+
+
+
+
+
+ +
+
+
(3) (4) (5)
09
(6) (7)
1.2 t(hrs)
Figure 8. Initial reaction rates for experiment E-1; ( 0 )CMT, (A) AMT, and (0) DTM.
(8)
(9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)
can be combined to study the complex scheme shown in Table I. An order of 0 or 1has been taken for the influence of the initial concentrations in the reaction rates. As it is shown in the matrix of compounds against reactions, Table 11, the maximum number of parameters required for the description of chloromethyltoluene is eight, corresponding to reactions 1 , 4 , 8-12, and 18; similarly seven parameters are the maximum number required for methyl tolueneacetate, eight for ditolylmethane, and nine for chloromethylated ditolylmethane. By use of the integral variables (see Nomenclature section), a multiple linear regression has been carried out from the models containing the maximum number of parameters for each product to the models containing only two parameters, the minimum number of parameters which can explain the maximum in the concentration of the products. These expressions have been unable to fit the experimental results adequately, leading to negative kinetic constants or very poor fits. Taking into account this, it is not possible to describe the reaction rates by using potential laws, although if a complex scheme of reactions is considered new kinetic data have been obtained at small conversions to determine in-
have been quantitatively evaluated. A mass balance for the results has shown a residual amount of byproducts depending on the time and conditions, which must be explained by reactions leading to known products, which have not been analyzed by gas chromatography. For the explanation of results of the experimental curves which show a maximum for the main products, it is necessary to develop a complex scheme of reactions. Previous Screening of the Kinetic Model. Taking into account different possibilities for the reactions taking place in the system after chemical considerations, 19 reactions were selected, as is shown in Table I. For discrimination, the Himmelblau et al. integral method has been used, defining 21 integral variables which
Table 11. Matrix of Compounds-Reactions for t h e General Scheme of Reactions
i j
T F HCI HAC CMT AMT DTM DTM-C
c, c2 c3 c4 c5 cs c;
H,O
3 4 5 6 7 - 1 - 1 - 2 - 1 - 1 - 1 - 1 0 1
2
- 1 - 1 - 1 0 -1 0
0 0 - 1 0
+1
0
0
0
+ 1 0
0
0 0
0 0
0
0 0
0
0
0
0
0 0 0 + 1
0 0
0 +
+1 0 0 0 0 0 0 0 0 1 + 1
- 1 0 0 0 +I + 1 0 0 0 0 0 - 1 0 0 +1 -1 0 0 0 -1 0 + 1 + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + l o 0
+I
0 -1 0 +1 0 0
0 0 0 0 0 0 0
8
9 0
10 0
11 12 13 14 0 0 0 0 0 0 0 0 0 - 1 0 +1 +1 +1 0 n-1 -1 0 0 0 0 + 1 0 0 + 1 -1 -2 -1 -1 -n 0 0 0 0 - 1 - 1 0 0 - 1 -1 0 0 0 0 -1 -1 0 +1 0 +1 0 +1 0 1 + 1 0 0 0 0 0 + 1 0 0 0 0 + 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 + l o 0 0 0 0 0 0 0 0 + 1 0
15 0 0 0 + 1 0 - 1 0 -1 0 0 0 0 + 1 0 0 0
16 17 18 0 0 0 0 0 0 +1 +1 +1 0 0 0 0 0 +1 - 1 0 0 0 -1 0 -1 -1 -1 0 0 0 0 0 0 0 + 1 0 0 0 + 0 0 + 1 + I O 0 0 0 0 0 0 0
19 0 0 0 0 0 0 0 -n 0 0 0 1 0 0 0 0
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1729
Figure 11. Initial reaction rates for E-4.
0.3
0.6
0.3
1.1
t(hrs)
Figure 9. Initial reaction rates for E-2.
I
/
/o-
I
Figure 12. Initial reaction rates for E-5. Table 111. Initial Reaction Rates of Chloromethyltoluene, Methyl Tolueneacetate, and Ditolylmethane
I (his:
Figure 10. Initial reaction rates for E-3.
expt E-i
E-o E-2
~ C M T ~
~ A M T ~
~ D T M ~
5.05 x 10-3 4.68 x 10-3 3.98 X
9.33 x 10-3 8.52 x 10-3 6.19 X
5.14 x 10-3 3.98 x 10-3 3.73 X
ArCH20H + H C 1 2 ArCH2C1+ H 2 0
The influence of the acid compounds on the reaction rate has been fitted to the Hammett acidity function in a previous work (Rey et al., 1987),and a specific influence of hydrochloric acid, acetic acid, or zinc chloride has not been found in the researched range of variables so that the second mechanism seems to be suitable to describe our kinetic results. Considering elementary reactions d[CH20H+] dt K+,h[CH20] - K-,[CH20H+] - K2[HAr][CH,OH+l d[ArCH,OH] dt K2[HAr][CH20H+]- K3[ArCH20H][HC1]
two different hypotheses can be considered in the reaction mechanism.
and steady-state conditions for the intermediates [CH20H+]*and [ArCH,OH]*
itial reactions rates, Figures 8-12. From the mechanistic studies of Olah and Yu (1975) ZnCl + 2HC1 d (C1CH20H2)+ZnC13C1CH2ArH+ (C1CH20H)2+ZnC13-+ HAr
CHzO
F=
C1CH2ArH++ ClCH2Ar + H+ and Ogata and Okano (1956) CHzO + H+-
K+1
x-CH20H+
-
HAr t CH20H+
Kz
ArCH20H + H+
1730 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987
[CH,OH+]* = [ArCH,OH]* =
K+1h[CHzOI K-, + K2[HAr]
K2[HAr][CH20H+]
-
K3[HC11 K+,K,h[HArl [CH201 K3[HC1]{K-, + K,[HAr]l
rCMT= K3[ArCH20H]*[HCl] rCMT
rCMT
=
K+1K2K3h[HC1][HAr] [CH20] = K3[HC1](K_,+ K,[HAr]]
K+,K,h[HArI [CH201 - K1,1h[CH@I [HArl K-, + K,[HAr] 1 + K[HAr]
where K2 K+&2 KlJ = - and K = K-1 K-1 h1,2h(F)(T) rAMT = 1 + K(T) and rDTM
h&(F)(T12 + K(T)
Table IV. Fitting of the Expression C,, Droduct In K“, , CMT -5.7 -5.23 AMT DTM -5.74
in rLo = In K”,,, n
0.515 0.528 0.517
+ n In
r2 0.99 0.99 0.98
The description of ditolylmethane initial reaction rates does not show good correlation coefficients, and this product will be fitted taking into account two hyperbolic expressions: K‘1,3CT
~ D T M=
l+KCT
+ l K’&T~ +KCT
Influence of t h e Initial Concentration of Paraformaldehyde. Results for the initial reaction rates in the conditions of experiments E-0, E-3, and E-4 (CFo= 2.5, 4.5, and 0.5 M, respectively) under constant concentrations of toluene (0.075 M), acetic acid (40%), hydrochloric acid (3 M), and zinc chloride (10%) and constant temperature (70 OC) were evaluated from Figures 8, 11, and 12. Considering constant conditions of K and CTo,initial reaction rates can be related to the initial concentration of paraformaldehyde following the hyperbolic kinetic expression for the three main products ~ C M T=~K”i,iC~on
= 1
These expressions have been applied to the description of the initial reaction rates of chloromethyltoluene, methyl tolueneacetate, and ditolylmethane formation. Influence of the Initial Concentration of Toluene. Results for the initial reaction rates in the conditions of experiments E-0, E-1, and E-2 (CTo= 0,075, 0.10, and 0.05 M, respectively) under constant concentrations of paraformaldehyde (CFo= 2.5 M), acetic acid (Cmc = 40%), zinc chloride (CZnC12 = lo%), and hydrochloric acid (CHCI = 3 M) and constant temperature (70 OC) are given in Table I11 for the three main products, evaluated from Figures 8-10. Considering constant conditions of h and CFo,initial reaction rates can be expressed as
rAMTo
=
K”l,2CFon
In r, = In K”,,, + n In CF, Results of the logarithmic linear fitting are shown in Table IV, for the three main products. These results allow the consideration of the kinetic expressions Kl,lappCF~’52CTo
~ C M T , ,=
1 + 28CT0 Kl,2appCF:’5PCTo
~ A M T ,=
+ 28C~, - K1,3appCF:’52CTo + KlappCF:’5PCT~ ~ D T M-~ 1 + 28CT, 1+ 28C~,
leading te the results l/K’l,l = 5.05
K/K’,,, = 156.4
r2 = 0.98
l/K’l,z = 3.26
K/Krl,, = 78.4
r2 = 0.99
1
for the description of the initial reaction rates of the three main products formation. The 0.52-order referring to paraformaldehyde can be explained taking into account the paraformaldehyde depolymerization equilibrium (CH,O),, * n’CH,O taking
and parameters
K’, = 2.27 ( M / ( L min))-l K’,,, = 1.98 X 10-1 min-’ K = 30.97 (M/L)-’
K = 26.8 (M/L)-’ r2 = 0.96 K’1,2= 3.27
X
and assuming that 1 >>
cy
lo-’ min-l
K = 24.05 (M/L)-’
The nearly constant value of K for the hyperbolic expression of the main products allows the consideration of a mean value parameter, K = 28.0 (M/L)-’, in the kinetic model.
Influence of t h e Acidic Reagents. The influence of the acids in the reaction rate taking toluene as reference has been fitted by a potential expression to the Hammett acidity function in an earlier work (Rey et al., 1987), leading to the conclusion that the influence of the acids
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1731 Table V. Kinetic Parameters at Different Temperatures T, " C al a, al 8.99 x 10-2 50 4.78 X 3.74 x 10-2 1.22 x 10-1 70 2.26 X lo-' 2.0 x 10-1 7.36 X lo-' 2.58 X lo-' 90 1.95
can be modeled in the range of variables 30% < CHAc < 50%, 5% < CZnC12 < 1570,and 2 M < CHcl < 4 M, taking
2alR 5.81 x 10-4 1.69 x 10-3 1.41 x
a2
5.24 6.60 2.38
X X
lo-' lo-'
a17 7.73 1.85 X 10' 8.67 X 10' CMl
X18iX22
ro 0: h" where m = 1.25 and h = 10-H~. After these considerations, a general kinetic model can be considered for the three main products, as Kl,;hmCFnCTq =
1
+ KCT
where m, n, and K take the values 1.25, 0.52, and 28.0 (M/L)-' for the three main products and q takes the value 1 for chloromethyltoluene and methyl tolueneacetate and 1 and 2 for ditolylmethane.
Kinetic Modeling with Hyperbolic Expressions The new kinetic expressions must be proved in the general scheme of reactions. Following the Himmelblau et al. integral method, variables X22 and X24 are defined 100
'0
X16iX22
Figure 13. Linear representation of the integral variables (X18/X22 vs. X16/X22) for chloromethyltoluene; ( X ) E-0, (0)E-1, (A)E-2, (v) E-3, (0) E-4, ( 0 )E-7, ( 0 )E-8, ( 0 )E-9, (+) E-10, ( 0 )E-11, (e) E-12.
and
where $ = h/hR, @ = C,/CF , and r = CTo/CToR.$, @, and 7 factors are defined as non8mensional variables referring to the central point conditions of the experimental design, and hence hR = 19.95 (obtained from the Hammett acidity function measurement of a mixture comDosition at the conditions of the central point), CFoR= 2.5 M, and CToR= 0.075 M. A new discrimination of the scheme of reactions, taking into account hyperbolic kinetic expressions, shows, according to the sign criteria, that only five reactions are needed to describe the evolution of the products:
T
f
F
5
CMT
:A DTM
-
Ci
>-
Table VI. Arrhenius Parameters for the Kinetic Constants A;, m i d E , / R ,K A;, min-' E,IR, K al,l 7.36 X lo-' 10.6 X lo3 a 2 3.79 X lo5 4.33 X lo3 2.47 X 1O'O 8.79 X lo3 a I 2 1.91 X 10" 6.87 X l o 3 a1,3 8.32 X 10' 3.01 X lo3 aI6 2.19 X lo8 9.8 X lo3
These expressions have been plotted in linear form for chloromethyltoluene and methyl tolueneacetate in Figures 13 and 14, respectively. The apparent kinetic parameters in the model take the following values: for chloromethyltoluene, q 1= 2.26 X 10-1 h-l
This has been applied to the main products, so that
h-l
for methyl tolueneacetate, a1,2 = 2.0 X
c2
a16 = 1.69 X
lo-'
h-'
a12 = 1.85 X 10 h-l
for ditolylmethane, ~ 1 ,= 3
1.02 X 10-l h-l
a2 = 0.66 h-'
a12 = 1.72 X 10 h-' and for toluene, a, = 5.35 X 10-1 h-'
2a2 = 1.13 h-'
Showing that the difference between a, and q 1+ q 2+ is less than l o % , the same order as the differences between a2 coming from toluene and ditolylmethane and a12coming from methyl tolueneacetate and ditolylmethane.
Temperature Influence Kinetic data at 50 "C (E-6) and 90 "C (E-7) have been fitted to the kinetic model (results are shown in Table V), and the kinetic constants have been fitted by the Arrhenius law as shown in Figures 15-17.
1732 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987
'"a12
!n
4.0
2.0
0
5 1C
