Thermodynamic Analysis and Kinetic Study on the Sucrose-6-acetate Chlorination Process
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摘要: 蔗糖-6-乙酸酯（S-6-A）氯化制备三氯蔗糖-6-乙酸酯（TGS-6-A）是合成三氯蔗糖（TGS）的关键步骤。首先采用基团贡献法对氯化反应进行了热力学计算，结果表明，在372~389 K的温度范围内，该反应为放热且不可逆反应。同时对目标产物TGS-6-A的水解反应进行了热力学计算，获得了不同温度下的平衡常数计算值，与平衡常数实验值的对比进一步验证了该计算方法的可靠性。通过间歇实验研究了温度对反应速率的影响，建立了氯化连串反应动力学模型。在研究温度范围内其主反应依次生成二氯蔗糖-6-乙酸酯和目标产物TGS-6-A的活化能分别为103.87 kJ/mol、153.87 kJ/mol，副反应生成四氯蔗糖-6-乙酸酯的活化能为87.09 kJ/mol；动力学实验结果表明主反应受温度的影响更大，升高温度并且控制反应时间能有效地提高目标产物TGS-6-A的收率。Abstract: The chlorination of sucrose-6-acetates (S-6-A) to produce sucralose-6-acetate (TGS-6-A) is a key step in the synthesis of sucralose. In this work, the thermodynamic calculation of the chlorination reaction was carried out using the group contribution method. The results show that the reaction is exothermic and irreversible in the temperature range of 372 K to 389 K. The thermodynamic calculations were performed on the hydrolysis reaction of TGS-6-A and the equilibrium constants at different temperatures were obtained, which agree well with the experimental value, confirming the reliability of the calculation methods used in this work. Then the effect of temperature on reaction rate was studied by batch experiments and a chain reaction kinetic model of chlorination reaction was established. The activation energy of the main reactions was calculated as 103.87 kJ·mol−1 and 153.87 kJ·mol−1, respectively, and the activation energy of the side reaction was 87.09 kJ·mol−1. The kinetic experiment results show that the main reaction is more affected by reaction temperature, increasing the temperature and controlling the reaction time can effectively increase the yield of the target product TGS-6-A.
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图 3 不同温度下氯化反应各组分浓度拟合图。其中点表示实验值，线为模型计算值
Figure 3. Concentration curve of components in chlorination reaction under different temperatures. Symbols: experimental data; Line: calculated values by kinetic model
图 4 不同温度下氯化反应各组分浓度实验值和计算值的比较
Figure 4. Comparison between experimental and calculated concentration values of components in chlorination reaction under different temperatures
表 1 各组分的热力学基团贡献值（Benson）
Table 1. Thermodynamic data of group contribution of each component (Benson method)
Group S-6-A TGS-6-A TGS $ {\Delta }_{\mathrm{f}}{H}_{298,i}^{\mathrm{\Theta }} $/
(kJ·mol−1)$ {S}_{298,i}^{\mathrm{\Theta }} $/
(J·mol−1·k−1)$ {C}_{p,i}^{\mathrm{\Theta }}\left(T\right) $ /(J·mol−1·K−1) 300 K 400 K 500 K 600 K 800 K 1000 K C−(CO)(H)3 1 1 0 −42.29 127.32 25.69 32.24 39.36 45.18 54.51 61.84 CO−(O)(C) 1 1 0 −146.86 20.01 25.00 28.05 30.98 33.58 37.14 39.19 O−(CO)(C) 1 1 0 −185.48 35.13 16.33 15.11 17.54 19.34 20.89 20.18 C−(O)(C)(H)2 3 1 1 −33.91 41.03 20.89 28.68 34.75 39.48 46.52 51.62 C−(O)(C)2(H) 7 6 6 −30.14 −46.05 20.10 27.80 33.91 36.55 41.07 43.54 C−(Cl)(H)(C)2 0 1 1 −62.00 73.70 38.90 41.40 44.00 46.90 58.20 61.10 C−(O)2(C)(H) 1 1 1 −68.24 −48.56 21.19 30.48 37.81 39.40 43.17 45.01 O−(C)2 3 3 3 −99.23 36.34 14.24 15.49 15.49 15.91 18.42 19.26 O−(C)(H) 7 4 5 −158.68 121.71 18.13 18.63 18.63 21.90 25.20 27.67 C−(O)2(C)2 1 1 1 −77.87 −149.85 6.66 16.54 16.54 30.94 31.90 35.50 C−(Cl)(H)2(C) 0 2 2 −69.10 158.30 37.30 44.80 51.50 56.10 64.10 69.90 四氢呋喃 1 1 1 24.70 105.90 −17.80 −19.01 −19.01 −14.86 −12.94 −10.92 四氢吡喃 1 1 1 2.09 78.69 −17.92 −12.73 −12.73 −5.99 −1.21 0.33 氧醚歪曲作用 2 2 2 1.30 − −0.42 −3.73 −3.73 −3.06 −2.51 −0.96 
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表 2 各组分的热力学数据
Table 2. Thermodynamic data for each component
Component $ {\Delta }_{\mathrm{f}}{H}_{298}^{\mathrm{\Theta }} $/
(kJ·mol−1)$ {S}_{298}^{\mathrm{\Theta }} $/
(J·mol−1·k−1)$ {C}_{p}^{\mathrm{\Theta }} $=C+DT+ET 2+FT 3+JT 4/(J·mol−1·k−1) $ {r}^{2} $ Data sources C D 105 E 107 F 1010 J S-6-A −2212.51 921.24 64.27 1.08 113.21 −25.73 11.95 0.999 calculated TGS-6-A −1838.71 910.39 31.68 1.45 22.33 8.63 4.73 0.999 calculated TGS −1622.76 858.78 −58.78 1.89 166.11 7.24 −1.25 0.999 calculated
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表 3 各组分的
$ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{{\rm{b}}} $ ，$ {T}_{{\rm{b}}} $ ，$ {T}_{{\rm{c}}} $ 和$ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{T} $ 的值Table 3.
$ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{{\rm{b}}} $ ,$ {T}_{{\rm{b}}} $ ,$ {T}_{{\rm{c}}} $ and$ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{T} $ of each componentComponent $ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{{\rm{b}}} $/(kJ·mol−1) $ {T}_{{\rm{b}}} $/K $ {T}_{{\rm{c}}} $/K $ {\mathrm{\Delta }}_{\mathrm{V}}{H}_{T} $/(kJ·mol−1) Data sources S-6-A 99.94 863.18 1181.18 177.01(1−T/1181.18)0.38 calculated TGS-6-A 93.83 830.98 1030.61 190.88(1−T/1030.61)0.38 calculated TGS 98.03 825.05 1026.55 181.10(1−T/1026.55)0.38 calculated
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表 4 乙酸热力学数据的计算值和文献值的对比
Table 4. Comparison of calculation value and literature value of acetic acid
Parameter Calculation
valueLiterature
valueRelative
deviation %${\Delta }_{{\rm{f}}}{H}_{298}^{\mathrm{\Theta } }$/(kJ·mol−1) −432.40 −432.54 0.03 $ {S}_{298}^{\mathrm{\Theta }} $/(J·mol−1·K−1) 282.69 (ABWY法) 283.47 0.27 ${\mathrm{\Delta } }_{\mathrm{V} }{H}_{{\rm{b}}}$/(kJ·mol−1) 23.70 23.70 0.00 ${T}_{{\rm{b}}}$/K 390.01 391.05 0.26 ${T}_{{\rm{c}}}$/K 586.26 590.7 0.75 $ {C}_{p} $(298 K)/(J·mol−1·K−1) 66.91 63.62 5.15 $ {C}_{p} $ (400 K)/(J·mol−1·K−1) 81.14 79.06 2.63 $ {C}_{p} $ (500 K)/(J·mol−1·K−1) 94.62 93.85 0.82 $ {C}_{p} $ (600 K)/(J·mol−1·K−1) 105.3 106.75 1.36 $ {C}_{p} $ (800 K)/(J·mol−1·K−1) 121.75 125.34 2.86 $ {C}_{p} $ (1000 K)/(J·mol−1·K−1) 133.48 138.74 3.79
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表 5 氯化反应不同温度下的
$ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $ ,$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ 和$ {K}^{\mathrm{\Theta }} $ Table 5.
$ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $ ,$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ and$ {K}^{\mathrm{\Theta }} $ of chlorination reaction at different temperaturesT/K $ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $/
(kJ·mol−1)$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $/
(J·mol−1·K−1)$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $/
(kJ·mol−1)$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ $ {K}^{\mathrm{\Theta }} $ 298 −67.31 665.86 −265.73 107.26 3.80×1046 310 −67.08 650.42 −268.70 104.26 1.89×1045 320 −66.89 637.53 −270.90 101.82 1.67×1044 330 −66.72 624.65 −272.85 99.45 1.55×1043 340 −66.55 611.76 −274.55 97.12 1.52×1042 350 −66.39 598.89 −276.00 94.85 1.56×1041 360 −66.24 586.03 −277.21 92.62 1.67×1040 370 −66.09 573.20 −278.18 90.43 1.87×1039 380 −65.96 560.39 −278.90 88.28 2.18×1038 390 −65.83 547.60 −279.39 86.17 2.64×1037 400 −65.71 534.86 −279.65 84.09 3.31×1036
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表 6 水解反应不同温度下的
$ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $ ,$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ 和$ {K}^{\mathrm{\Theta }} $ Table 6.
$ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $ ,$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $ ,$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ and$ {K}^{\mathrm{\Theta }} $ of hydrolysis reaction at different temperaturesT/K $ {\mathrm{\Delta }}_{{\rm{r}}}{H}^{\mathrm{\Theta }} $/
(kJ·mol−1)$ {\mathrm{\Delta }}_{{\rm{r}}}{S}^{\mathrm{\Theta }} $/
(J·mol−1·K−1)$ {\mathrm{\Delta }}_{{\rm{r}}}{G}^{\mathrm{\Theta }} $
(kJ·mol−1)$ \mathrm{l}\mathrm{n}{K}^{\mathrm{\Theta }} $ $ {K}^{\mathrm{\Theta }} $ 298 12.22 48.45 −2.22 0.89 2.45 308 13.44 51.68 −2.47 0.97 2.63 318 14.68 54.85 −2.76 1.04 2.84 328 15.94 57.95 −3.07 1.13 3.08 338 17.21 61.00 −3.41 1.21 3.36 348 18.49 63.98 −3.77 1.30 3.68 358 19.79 66.91 −4.16 1.40 4.05 368 21.11 69.79 −4.57 1.49 4.46 378 22.44 72.61 −5.01 1.59 4.92 388 23.79 75.39 −5.46 1.69 5.44
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表 7 反应速率常数和置信度为95%时对应的置信区间
Table 7. Estimated reaction rate constants and corresponding confidence intervals with the confidence level of 95%
T/K $ {k}_{1} $ $ {k}_{2} $ $ {k}_{3} $ 372 0.1677±0.0318 0.1142±0.0136 0.0323±0.0233 379 0.3128±0.0649 0.3560±0.0295 0.0548±0.0251 386 0.5357±0.0787 0.8342±0.0465 0.0814±0.0174 389 0.7257±0.1528 0.9259±0.0727 0.1165±0.0315
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表 8 Arrhenius拟合各反应过程的指前因子和活化能
Table 8. Arrhenius fitting of the pre-factor and activation energy for each reaction
Reaction number $ \mathrm{l}\mathrm{n}{k}_{0} $ $E_\mathrm{a}$ (kJ·mol−1) $ {r}^{2} $ 1 31.78 103.87 0.997 $ 2 $ 47.65 153.87 0.980 $ 3 $ 24.70 87.09 0.987
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符号说明 $ {\rm{A,B,P,S}} $ ——各反应组分 $ {C},{D},{E},{F},{J} $ ——定压比热容多项式参数 $ {C}_{p} $ ——定压比热容 $ E_\mathrm{a} $ ——活化能，kJ/mol $ \Delta G $ ——Gibbs自由能变，kJ/mol $ \Delta H $ ——焓变，kJ/mol $ K $ ——反应平衡常数 $ {k}_{0} $ ——反应速率指前因子，h−1 $ k $ ——反应速率常数，h−1 $ R $ ——摩尔气体常数 $ {r}^{2} $ ——相关系数 $ \Delta S $ ——熵变，J/（mol·K） $ T $ ——温度，K $ \sigma $ ——总对称数 $ \eta $ ——光学异构体数 上角标 $ \mathrm{\Theta } $ ——标准态 下角标 ${\rm{ b}} $ ——常压沸点 $ {\rm{c}} $ ——临界点 $ {\rm{f}} $ ——生成态 $ \mathrm{g} $ ——气态 $ i $ ——组分 $ {\rm{l }}$ ——液态 $ {{p}} $ ——压力 $ {\rm{r}} $ ——反应态 $ \mathrm{V} $ ——蒸发态
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