Kinetics for Dimethyl Toluene-2,4-dicarbamate Synthesis from 2,4

Article pubs.acs.org/IECR

Kinetics for Dimethyl Toluene-2,4-dicarbamate Synthesis from 2,4-Diaminotoluene, Urea, and Methanol Shuai Sun, Ning Liang, Hualiang An, Xinqiang Zhao,* Guirong Wang, and Yanji Wang Hebei Provincial Key Lab of Green Chemical Technology and Efficient Energy Saving, Hebei University of Technology, Tianjin 300130, China ABSTRACT: Dimethyl toluene-2,4-dicarbamate (TDC) is an important intermediate for the nonphosgene manufacture of toluenediisocyanate. The synthesis of TDC from 2,4-diaminotoluene (TDA), urea, and methanol is a green route with a good industrialization prospect. So, the study on its reaction kinetics is of great significance. First, the reaction network was structured and simplified on the basis of experimental result analyses. Second, the experimental data for kinetics were measured on an autoclave. Last, the reaction kinetics model was established by means of parametric estimation. Model test results showed that the prediction values of the reaction kinetics model agreed well with the experimental data. Therefore, the reaction kinetics model can be used in the process analyses and scale-up of the reaction of TDA, urea, and methanol to TDC.

1. INTRODUCTION As one of the important feedstocks for the manufacture of polyurethanes, toluenediisocyanate (TDI) is now produced industrially by a phosgenation route. Because one of the major feedstock phosgenes is severely toxic and the byproduct hydrogen chloride is strongly corrosive, the phosgenation route is not environmentally friendly. So, it is extremely urgent to develop nonphosgene routes to TDI synthesis. As a crucial intermediate of the nonphosgene routes, dimethyl toluene2,4-dicarbamate (TDC) can be synthesized by reductive carbonylation of nitro derivatives,1 oxidative carbonylation of amines,2 methoxycarbonylation of amines,3−5 and a urea route.6 However, there are some problems, such as the use of poisonous CO and the explosive mixture of CO and O2, low utilization of CO, and deactivation of noble-metal catalysts in the reductive carbonylation of nitro derivatives and the oxidative carbonylation of amines. As one of the feedstocks, dimethyl carbonate (DMC) is expensive and difficult to separate from the byproduct methanol in methoxycarbonylation of amines. In contrast, the urea route has distinct advantages, such as the availability of feedstock, moderate reaction conditions, use of non-noble-metal catalysts, ease of product separation (no azeotrope such as DMC−methanol), recycle of the byproduct ammonia to a urea synthesis unit, etc. So, it is a prospective route with a “zero emission” process from the viewpoint of green chemistry. Reaction kinetics is very important and necessary for process simulation and scale-up. The synthesis of TDC from 2,4diaminotoluene (TDA), urea, and methanol is a complex reaction system. To the best of our knowledge, the kinetics for this reaction has not been published yet. Wang7 studied a single reaction of this complex system, the reaction of TDA with urea to toluenebiurea (TBU), and established its reaction kinetics model when urea was very excessive with respect to TDA and obtained a pseudo-first-order reaction with the 5 reaction rate constant of k′ = 1.681 × 1028e−2.209 × 10 /RT. The kinetics about other single reactions in this complex system © 2013 American Chemical Society

has not been reported up to now. In the present work, the reaction network for the synthesis of TDC from TDA, urea, and methanol was constructed, and then the kinetics model was established.

2. EXPERIMENTAL SECTION 2.1. Chemical Reagents. The chemical reagents including TDA, urea, methanol, and TDI (80:20) were all commercial products with analytical grade. TDA was recrystallized before use, and others were used as received. A TDC standard sample was prepared by the reaction of TDI with methanol at room temperature. 2.2. Reaction Procedure. The kinetics experiments were conducted on an autoclave with a sampling system and an ammonia-release system. A typical operation with an initial concentration of TDA = 0.1 mol/L and at a reaction temperature of 140 °C was described as follows: 3.054 g of TDA, 15.015 g of urea, and 250 mL of methanol were charged into the autoclave. After purged with nitrogen to remove the air inside, the autoclave was pressured to 1.1 MPa with nitrogen and heated to 140 °C with stirring. During the reaction process, the flow of nitrogen was steadily controlled to facilitate the removal of ammonia released. The first sample was withdrawn when the reaction temperature reached 140 °C, and the succeeding samples were taken out at time intervals of 30 min until the ninth sample was withdrawn at 240 min. Then the autoclave was cooled to room temperature, and the reaction solution was taken out. The sample amount for analysis was too small to affect the reaction process. 2.3. Product Analysis. The samples were quantitatively analyzed on a Waters high-performance liquid chromatograph equipped with Waters 515 pumps, a Waters 2487 Received: Revised: Accepted: Published: 7684

February 15, 2013 April 30, 2013 May 12, 2013 May 13, 2013 dx.doi.org/10.1021/ie4005095 | Ind. Eng. Chem. Res. 2013, 52, 7684−7689

Industrial & Engineering Chemistry Research

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UV detector operated at 232 nm, and a Turner C18 column (⌀ 4.6 mm × 150 mm). The flow rate of the mobile phase with a volumetric ratio of methanol/water of 4:6 was 0.4 mL/min. Methyl carbamate (MC) and DMC were quantitatively analyzed on a SP 2100 gas chromatograph equipped with a PEG 20 M column and a flame ionization detector. The column temperature was program-controlled as follows: first starting from 80 °C and holding for 1 min, then ramping to 150 °C at a rate of 6 °C/min and holding for another 1 min, and last increasing to 220 °C at a rate of 10 °C/min and holding for 5 min. The products were qualitatively analyzed on a LCQ Deca XP MAX model highperformance liquid chromatograph−mass spectrometer (HPLC−MS) equipped with a Turner C18 column (⌀ 4.6 mm × 150 mm), and the mass spectra were obtained in the range of 50−600 amu.

We conducted a lead-catalyzed reaction of TBU with methanol under the conditions of a reaction temperature of 120 °C, a reaction pressure of 0.7 MPa, and a reaction time of 3 h. The results showed that TBU conversion was 84%, TDC yield was 15.4%, TMC yield was 8.4%, and TDA yield was 33.8%, suggesting that methanolysis of TBU not only produced TMC but also yielded TDA as follows:

3. RESULTS AND DISCUSSION 3.1. Reaction Network Construction. The results from HPLC−MS analysis showed that the following intermediates were in the reaction system of TDA, urea, and methanol to TDC: 3-amino-4-methylphenylurea (TU1), 2-methyl-5-aminophenylurea (TU2), 2,4-toluenebiurea (TBU), methyl 3-ureido-4methylphenylcarbamate (TUC1), methyl 2-methyl-5-ureidophenylcarbamate (TUC2), methyl 3-amino-4-methylphenylcarbamate (TMC1), methyl 2-methyl-5-aminophenylcarbamate (TMC2), methyl carbamate (MC), and dimethyl carbonate (DMC).6 Both TU1 and TU2 were called TU for convenience. Simlarly, both TUC1 and TUC2 were called TUC, while both TMC1 and TMC2 were called TMC. According to our previous report,6 there were three plausible reaction paths in this system:

Additionally, the reaction for conversion of TMC to TDC was studied under the conditions of a molar ratio of TMC2: urea:methanol = 1:5:110, a reaction temperature of 140 °C, and a reaction time of 6 h. It was found that the yield of TDC was 11.0%, while TDA yield attained 2.9%, suggesting that TMC could react with methanol to TDA. When the reaction temperature increased to 190 °C, the yield of TDC decreased to only 4.7%, while TDA yield increased to 36.4%, suggesting that a higher temperature favored methanolysis of TMC to TDA as follows:

In order to confirm methanolysis of TDC, the following experiment was conducted using TDC prepared from TDI (80:20) as a reactant: 3 g of TDC and 200 mL of methanol were charged into the autoclave and heated to 190 °C after being purged by nitrogen. The reaction lasted for 6 h at a pressure of 3.0 MPa, and then the reaction solution was analyzed by HPLC. It was found from Table 1 that the peak percentage of TDC

If all three plausible paths existed simultaneously in this reaction system, the reaction network for the formation of TDC from TDA, urea, and methanol was constructed as Figure 1.

Table 1. HPLC Analysis Results of the TDC Methanolysis Reaction before reaction after reaction

component

retention time (min)

peak percentage (%)

2,6- TDC 2,4-TDC TDA TMC1 2,6- TDC TMC2 2,4-TDC

12.21 22.40 6.768 10.33 12.22 12.58 21.84

12.7 85.5 2.1 8.8 12.7 7.0 63.4

decreased from 85.5% to 63.4%, while TMC and TDA were generated simultaneously, indicating that TDC indeed methanolyzed to TMC and TDA. Therefore, reaction network 1 was modified to reaction network 2, as illustrated in Figure 2, according to the above experimental results. We studied the change of the concentration of all reaction components with the reaction time for investigation on the reaction paths to TDC.6 The result shown in Figure 3 provided useful information for understanding the complicated reaction

Figure 1. Reaction network 1.

Then some experiments were carried out to improve the reaction network 1. Our previous paper8 studied the reaction of TBU with methanol to TDC and found that TMC became the major product at a temperature above 160 °C, suggesting that high temperature favored methanolysis of TBU to TU and then to TMC as follows: 7685

dx.doi.org/10.1021/ie4005095 | Ind. Eng. Chem. Res. 2013, 52, 7684−7689


Article


Therefore, reaction network 2 was simplified to reaction network 3, as in Figure 4. Because the reaction order, preexponential factor, and activation energy in every single reaction must be estimated, the reaction network has to be further simplified because too many parameters not only interfere with the convergence of the computation program but also affect the accuracy of the parameter estimation. Reaction 2 in Figure 4 can proceed in theory but, in fact, with difficulty. Under the conditions of a reaction temperature of 140 °C, a reaction pressure of 1.1 MPa, a molar ratio of TDA:MC:methanol = 1:5:110, and a reaction time of 6 h, TMC yield was only 3.55%, suggesting that it is difficult for TDA to react with MC to TMC under the experimental conditions investigated. So, reaction 2 is neglected. Additionally, the effect of the reaction conditions on TDC synthesis from TMC, urea, and methanol in the absence of catalyst showed that TMC converted to TDC at a lower temperature, while TMC methanolyzed to TDA at a higher temperature. Hence, reactions 4 and 7 in Figure 4 should be taken into account. Although reaction 6 in Figure 4 was able to proceed according to the result of TDC methanolysis, it should be ignored because it is not a major side reaction. Above all, reaction network 3 is simplified to reaction network 4, as in Figure 5. The reaction components including TDA, urea, MC,


Figure 3. Content of the components versus reaction time.6 Reaction conditions: nTDA:nZnCl2:n(urea):n(methanol) = 1:0.07:5:80, 170 °C, 24 h, 2.0 MPa.

mechanism and simplifying the reaction network further. What can be seen from Figure 3 is the following: 1. TDA concentration declined while the TDC concentration increased monotonically with the reaction time. 2. The concentration of both TMC1 and TMC2 increased first to their maxima and then decreased gradually with the reaction time, exhibiting the characteristics of an intermediate in a consecutive reaction. 3. The concentration of TU was high at the beginning of the reaction and then decreased slowly with the reaction time, indicating that the formation rate of TU was less than its consumption rate. Because there was no TU present in the feed, it must be formed during the heat-up process. TU was determined to be an intermediate for it was consumed rapidly. In order to lessen the optimized parameters and simplify the reaction network further, methanolysis of TU was ignored because the TDA concentration kept decreasing. 4. The concentrations of TBU and TUC were small and almost did not change during the whole reaction process, suggesting that their formation and consumption attained a dynamic equilibrium. Thus, the reactions related to TBU and TUC including reactions 2−4, 7, and 12 in reaction network 2 were neglected and simplified to the following reaction:


TU, TMC, and TDC need a quantitative measurement for kinetics study. 3.2. Establishment and Solution of Reaction Kinetics. The single-reaction equations in reaction network 4 and their rate expressions which apply to the reactions in a constantvolume batch reactor are as follows: Reaction 1:

Reaction 2:

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dCTU = r1 − r2 − r3 dt

Reaction 3:

α3 α1 α2 = k 01e−E1/ RT CTDA − k 02e−E2 / RT CTU − k 03e−E3 / RT CTU

dCTMC = r3 − r4 − r5 dt

Reaction 4:

α3 α4 α5 = k 03e−E3 / RT CTU − k 04 e−E4 / RT CTMC − k 05e−E5 / RT CTMC

dCTDC α5 α2 = r2 + r5 = k 02e−E2 / RT CTU + k 05e−E5 / RT CTMC dt

Although the heat-up of the autoclave was relatively fast, a period of time was still needed to heat the mixture from room temperature to the required reaction temperature. If the time point at the required reaction temperature is defined as t = 0, the concentrations of every component at this moment have to be analyzed because the reactions have already occurred during the heat-up process. The initial conditions for the rate equations are as follows:

Reaction 5:

t = 0,

Methanol is very much in excess in the feed compared with the stoichiometric ratio because it acts not only as a reactant but also as a solvent. So, the methanol concentration can be treated as a constant in the solution of the reaction rate equations. In addition, because it is difficult to analyze urea quantitatively, the concentration of urea is arranged to be 10 times more than that of TDA. So, the concentration of urea can be treated as a constant also. Similarly, the MC concentration is considered a constant because urea reacts with methanol easily to form MC.9−11 Thus, the reaction rate expressions are simplified as follows: α1 r1 = k′1CTDA

β1 k′1 = k1Curea

α2 r2 = k′2 CTU

β2 2 k′2 = k 2Curea CMeOH

α3 r3 = k′3 CTU

3 k′3 = k 3CMeOH

CTDA = CTDA ‐ 0 , CTU = CTU ‐ 0 , CTMC = CTMC ‐ 0 , CTDC = CTDC ‐ 0

The concentrations of every component were analyzed at 30 min intervals from t = 0 and were used as the experimental data. The solution of the rate equations is an initial-value problem of a set of first-order ordinary differential equations. If the initial values of the parameters k01, E1, α1, k02, E2, α2, k03, E3, α3, k04, E4, α4, k05, E5, and α5 are given, the concentrations of every component at t = 30 min, CTDA‑30‑cal, CTU‑30‑cal, CTMC‑30‑cal, and CTDC‑30‑cal, can be obtained by integrating the set of first-order ordinary differential equations using a fourth-order Runge− Kutta method at the time interval of [0, 30]. Similarly, the concentrations of every component at t = i, CTDA‑i‑cal, CTU‑i‑cal, CTMC‑i‑cal, and CTDC‑i‑cal, can be attained at the time interval of [0, i]. These obtained concentrations were used as the prediction values of the reaction kinetics model, while the experimental data at t = i, CTDA‑i‑exp, CTU‑i‑exp, CTMC‑i‑exp, and CTDC‑i‑exp, were obtained by HPLC analysis of the concentrations of every component. Then the objective function for parameter estimation is expressed as follows:

γ

β

β

α4 r4 = k′4 CTMC

4 k′4 = k4CMeOH

α5 r5 = k′5 CTMC

5 k′5 = k5CMC

β

When each of the rate constants k is replaced with the Arrhenius equation k = k0e−E/RT, the above reaction rate expressions become the following forms:

f=

0 T CTDA

i

+ (CTU ‐ i ‐ exp − CTU ‐ i ‐ cal)2 + (CTMC ‐ i ‐ exp − CTMC ‐ i ‐ cal)2

α1 r1 = k 01e−E1/ RT CTDA

+ (CTDC ‐ i ‐ exp − CTDC ‐ i ‐ cal)2 ]

α2 r2 = k 02e−E2 / RT CTU

where T represents different reaction temperatures, C0TDA represents different initial concentrations of TDA, and i is the number of samples analyzed. The parameters of k01, E1, α1, k02, E2, α2, k03, E3, α3, k04, E4, α4, k05, E5, and α5 can be estimated by minimizing this function and then solved using the improved simplex method. 3.3. Determination of Kinetics Parameters. 3.3.1. Arrangement for Kinetics Experiment. Our previous paper6 studied the influence of reaction conditions on the synthesis of TDC from TDA, urea, and methanol and obtained the following suitable reaction conditions: molar ratio of TDA:ZnCl2 catalyst:urea:methanol = 1:0.07:5:80 (where the initial concentration of TDA was 0.3 mol/L), a reaction temperature of 190 °C, and a reaction time of 9 h. Under the above reaction conditions, the conversion of TDA, TDC yield, and selectivity were 98.8%, 41.1%, and

α3 r3 = k 03e−E3 / RT CTU α4 r4 = k 04 e−E4 / RT CTMC

α5 r5 = k 05e−E5 / RT CTMC

According to reaction network 4, the change of the concentration of the component with the reaction time is expressed as follows: −

∑ ∑ ∑ [(CTDA ‐ i‐ exp − CTDA ‐ i‐ cal)2

dCTDA α4 α1 = r1 − r4 = k 01e−E1/ RT CTDA − k 04 e−E4 / RT CTMC dt 7687



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dCTU = r1 − r2 − r3 dt

41.6%, respectively. Because the urea concentration must be 10 times higher than that of TDA in the kinetics study, the TDA initial concentrations were selected as 0.1, 0.2, 0.3, and 0.4 mol/L to avoid affecting the reaction (blockage of the ammonia-release pipe) because of too high of a urea concentration. The reaction temperature was determined as 140, 150, 160, 170, 180, and 190 °C to cover the reaction temperature range in nonkinetics studies. Because the reaction can take place rather easily, the kinetics experiment was conducted in the absence of a catalyst. During the experimental process, sampling and analysis were done at 30 min intervals from t = 0 to t = 240 min. 3.3.2. Determination of the Kinetics Parameters and Model Test. a. Determination of the Kinetics Parameters. The kinetics parameters in every reaction rate expression were obtained by using MATLAB software and are listed in Table 2.

⎛ 7.55 × 104 ⎞ 1.12 = 6.58 × 105 exp⎜ − ⎟CTDA RT ⎝ ⎠ ⎛ 1.21 × 105 ⎞ 0.43 − 6.45 × 105 exp⎜ − ⎟CTU RT ⎝ ⎠ ⎛ 3.76 × 104 ⎞ 1.00 − 2.43 × 102 exp⎜ − ⎟CTU RT ⎝ ⎠

dCTMC = r3 − r4 − r5 dt ⎛ 3.76 × 104 ⎞ 1.00 = 2.43 × 102 exp⎜ − ⎟CTU RT ⎝ ⎠

Table 2. Estimation of the Kinetic Parameters reaction

k0

E (J/mol)

α

1 2 3 4 5

6.58 × 105 6.45 × 105 2.43 × 102 9.08 × 104 5.46 × 105

7.55 × 104 1.21 × 105 3.76 × 104 3.19 × 105 8.14 × 104

1.12 0.43 1.00 1.64 0.56

⎛ 3.19 × 105 ⎞ 1.64 − 9.08 × 104 exp⎜ − ⎟CTMC RT ⎠ ⎝ ⎛ 8.14 × 104 ⎞ 0.56 − 5.46 × 105 exp⎜ − ⎟CTMC RT ⎝ ⎠ dCTDC = r2 + r5 dt ⎛ 1.21 × 105 ⎞ 0.43 = 6.45 × 105 exp⎜ − ⎟CTU RT ⎠ ⎝ ⎛ 8.14 × 104 ⎞ 0.56 + 5.46 × 105 exp⎜ − ⎟CTMC RT ⎠ ⎝

b. Test of the Kinetics Model. Figure 6 shows a comparison between the prediction values of the kinetics model and the experimental data. What can be seen is that the points scatter on both sides of the diagonal line, indicating the absence of systematic errors in the data fitting, and that the prediction values accord well with the experimental data. The results of variation analysis and the F-test on the kinetics model are listed in Table 3. As we know from variation analysis theory, the larger the correlation coefficient and F-test absolute value F, the better the regression model; the model is considered to be suitable to α level if the correlation coefficient is larger than 0.9 and F is larger than 10Fα.12,13 In this work, the kinetics model is significant to the α = 0.05 level and thus is able to describe the reaction process for synthesis of TDC from TDA, urea, and methanol.

Figure 6. Prediction of the concentration (Cpre) versus the experimental data (Cexp) for TDA, TU, TMC, and TDC: TDA initial concentrations = 0.1, 0.2, 0.3, and 0.4 mol/L and at temperatures of 140, 150, 160, 170, 180, and 190 °C.

Then the kinetics equations were described as follows:

4. CONCLUSIONS The reaction network for TDC synthesis from TDA, urea, and methanol was structured and simplified according to the experimental results. Then the kinetics experiment was conducted on an autoclave to collect the experimental data, and finally the reaction kinetics model was established. (1) Because the reaction of TDA, urea, and methanol is a complicated system, the reaction network is simplified as follows:

dC − TDA = r1 − r4 dt ⎛ 7.55 × 104 ⎞ 1.12 = 6.58 × 105 exp⎜ − ⎟CTDA − 9.08 RT ⎝ ⎠ ⎛ 3.19 × 105 ⎞ 1.64 × 104exp⎜ − ⎟CTMC RT ⎝ ⎠

Table 3. Model Statistics experiment points

free variation number

regression square sum

residual error square sum

correlation coefficient

F

F0.05(14,177)

192

15

0.9817

0.081

0.939

86.62

1.75

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Grants 20976035 and 21076059), the Natural Science Foundation of Hebei Province (Grant B2010000019), the Natural Science Foundation of Tianjin City (Grant 12JCYBJC12800), and the Key Basic Program of Applied Basic Research Plan of Hebei Province (Grant 12965642D). We are appreciative of their contributions.

(2) The reaction kinetics model was obtained as follows: −

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dCTDA = r1 − r4 dt

REFERENCES

(1) Toochinda, P.; Chuang, S. S. C. Carbamate synthesis on Pd/C catalysts: gas-solid versus slurry processes. Ind. Eng. Chem. Res. 2004, 43, 1192. (2) Shi, F.; Deng, Y.; Sima, T.; Yang, H. A novel PdCl2/ZrO2-SO42− catalyst for synthesis of carbamates by oxidative carbonylation of amines. J. Catal. 2001, 203, 525. (3) Heitkamper, P.; Schieb, T.; Wershofen, S. Process for the preparation of bis (ethoxycarbonylamino) toluols and their use in the preparation of diisocyanato toluos. Eur. Patent 0520273, 1992. (4) Wang, Y.; Zhao, X.; Li, F.; Wang, S.; Zhang, J. Catalytic synthesis of toluene-2,4-diisocyanate from dimethyl carbonate. J. Chem. Technol. Biotechnol. 2001, 76, 857. (5) Baba, T.; Kobayashi, A.; Kawanami, Y.; Inazu, K.; Ishikawa, A.; Echizenn, T.; Murai, K.; Aso, S.; Inomata, M. Characteristics of methoxycarbonylation of aromatic diamine with dimethyl carbonate to dicarbamate using a zinc acetate catalyst. Green Chem. 2005, 7, 159. (6) Zhao, X.; Wang, N.; Geng, Y.; An, H.; Wang, Y. Direct synthesis of dimethyl toluene-2,4-dicarbamate from 2,4-toluenediamine, urea, and methanol. Ind. Eng. Chem. Res. 2011, 50, 13636. (7) Wang N. Synthesis of toluene dicarbamate by urea route based on toluene bisurea. M.S. Thesis, Hebei University of Technology, Tianjin, China, 2011. (8) Geng, Y.; Wang, N.; An, H.; Zhao, X.; Wang, Y. Synthesis of dimethyl toluene-2,4-dicarbamate by urea route via 1-methyl-2,4-phenyl bisurea intermediate. J. Chem. Eng. Chinese Univ. 2012, 26, 840. (9) Li, P.; Xia, D.; Qi, Z.; Bo, X. Study on the synthesis of methyl carbamate through alcoholysis of urea. Ind. Catal. (in Chinese) 2006, 14, 47. (10) Zhao, X.; Wang, Y.; Shen, Q.; Yang, H.; Zhang, J. Synthesis of dimethyl carbonate from urea and methanol over metal oxide catalysts. Acta Petrolei Sinica (Petroleum Processing Section, in Chinese) 2002, 18, 47. (11) Wang, M.; Wang, H.; Zhao, N.; Wei, W.; Sun, Y. Synthesis of dimethyl carbonate from urea and methanol over solid base catalysts. Catal. Commun. 2006, 7, 6. (12) Wang, G.; Wang, F.; Xin, F.; Liao, H. The kinetics of vapor phase benzene hydrogenation reaction on Ni/Al3O3 catalyst. J. Hebei Univ. Technol. 2000, 29, 81. (13) Liu, Z.; Huang, R.; Tian, A. Experiment Design and Data Processing; Chemical Industry Press: Beijing, 2005.

⎛ 7.55 × 104 ⎞ 1.12 = 6.58 × 105 exp⎜ − ⎟CTDA RT ⎝ ⎠ ⎛ 3.19 × 105 ⎞ 1.64 − 9.08 × 104 exp⎜ − ⎟CTMC RT ⎠ ⎝

dCTU = r1 − r2 − r3 dt ⎛ 7.55 × 104 ⎞ 1.12 = 6.58 × 105 exp⎜ − ⎟CTDA RT ⎝ ⎠ ⎛ 1.21 × 105 ⎞ 0.43 − 6.45 × 105 exp⎜ − ⎟CTU RT ⎠ ⎝ ⎛ 3.76 × 104 ⎞ 1.00 − 2.43 × 102 exp⎜ − ⎟CTU RT ⎝ ⎠

dCTMC = r3 − r4 − r5 dt ⎛ 3.76 × 104 ⎞ 1.00 = 2.43 × 102 exp⎜ − ⎟CTU RT ⎝ ⎠ ⎛ 3.19 × 105 ⎞ 1.64 − 9.08 × 104 exp⎜ − ⎟CTMC RT ⎝ ⎠ ⎛ 8.14 × 104 ⎞ 0.56 − 5.46 × 105 exp⎜ − ⎟CTMC RT ⎝ ⎠ dCTDC = r2 + r5 dt ⎛ 1.21 × 105 ⎞ 0.43 = 6.45 × 105 exp⎜ − ⎟CTU RT ⎝ ⎠ ⎛ 8.14 × 104 ⎞ 0.56 + 5.46 × 105 exp⎜ − ⎟CTMC RT ⎝ ⎠

The variation analysis and F-test results showed that there is a good agreement of the model with the experimental data, indicating that the model is able to describe the reaction of TDA, urea, and methanol to TDC.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-22-60202427. Fax: +86-22-60204294. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 7689


Kinetics for Dimethyl Toluene-2,4-dicarbamate Synthesis from 2,4

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