液相法合成三聚氰酸体系热力学分析

doi:10.11949/0438-1157.20231318

摘要/Abstract

摘要：

以二元醇为循环剂液相法合成三聚氰酸是一个由醇解、消去和环加成反应构成的连串反应体系。采用基团贡献法计算了该反应体系中各组分热力学数据以及各步反应的焓变、Gibbs自由能变和平衡常数，依据热力学计算结果并结合已有文献实验数据分析反应路径的可行性及难易程度。结果表明，醇解和消去反应为吸热反应，升温有利于反应，但反应平衡常数小；环加成反应为放热反应且进行较为完全，适当强化条件下三步连串反应可顺利进行。计算及分析结果可为该体系的工业放大工艺过程开发提供理论指导。

关键词: 三聚氰酸, 尿素, 醇, 双氨基甲酸酯, 热解, 热力学, 基团贡献法

Abstract:

The synthesis of cyanuric acid (CA) via urea and diol (recirculating agent) is a consecutive reaction system composed of alcoholysis, elimination and cycloaddition. The thermophysical properties of components, enthalpy changes, Gibbs free energy changes and equilibrium constant of this reaction system were carried out by group contribution method. Then feasibility and difficulty of the reactions were analyzed on the basis of thermodynamic calculation combined with available experimental data. The results show that alcoholysis and elimination are both endothermic process and the equilibrium constants of the two reactions are small,which can be promoted forward by improving temperature. Cycloaddition reaction is exothermic and can be fully proceeded. The consecutive reaction can proceed under the appropriate conditions. The outcome from thermodynamic calculation and analysis can provide theoretical guidance for the development of the industrial scale-up process of the reaction.

Key words: cyanuric acid, urea, alcohol, dicarbamate, pyrolysis, thermodynamics, group contribution method

中图分类号:

TQ 013.1

晁惠雨, 白振敏, 侯汉青, 田立志, 李洪, 房晓权, 石晓华. 液相法合成三聚氰酸体系热力学分析[J]. 化工学报, DOI: 10.11949/0438-1157.20231318.

Huiyu CHAO, Zhenmin BAI, Hanqing HOU, Lizhi TIAN, Hong LI, Xiaoquan FANG, Xiaohua SHI. Thermodynamics analysis on liquid-phase synthesis of cyanuric acid[J]. CIESC Journal, DOI: 10.11949/0438-1157.20231318.

图/表 13

表1 不同点群对应外对称数［29-30］

Table 1 Symmetry number of various point groups［29-30］

C₁, C_i, C_s

C₂, C_2ν, C_2h

C₃, C_3ν, C_3h

C₄, C_4ν, C_4h

C₆, C_6ν, C_6h

D₂, D_2d, D_2h

D₃, D_3d, D_3h

D₄, D_4d, D_4h

D₆, D_6d, D_6h

S₆

C_∞ν

D_∞ν

T, T_d

O_h

表2 Benson法基团贡献值（298.15 K）及各组分的对称数［20］

Table 2 Group contributions and symmetry number of components （Benson method， 298.15 K）［20］

Group	n_i				∆H $f, 298.15, i Θ$ /(kJ·mol^-1)	S $298.15, i Θ$ /(J·mol^-1·K^-1)
Group	Urea	MPO	MPDC	HIBC	∆H $f, 298.15, i Θ$ /(kJ·mol^-1)	S $298.15, i Θ$ /(J·mol^-1·K^-1)
CO—(N)₂^*	1	0	0	0	-137.30	67.80
N—(CO)(H)₂	2	0	2	1	-62.40	103.37
C—(C)₃(H)	0	1	1	1	-7.95	-50.53
C—(C)(H)₃	0	1	1	1	-42.20	127.32
C—(O)(C)(H)₂	0	2	0	2	-30.14	-46.05
O—(C)(H)	0	2	2	1	-158.68	121.71
O—(CO)(C)	0	0	2	1	-185.68	35.13
CO—(N)(O)^*	0	0	2	1	-137.30	67.80
σ	8	3	3	3	—	—

表2 Benson法基团贡献值（298.15 K）及各组分的对称数［20］

Table 2 Group contributions and symmetry number of components （Benson method， 298.15 K）［20］

Group	n_i				∆H $f, 298.15, i Θ$ /(kJ·mol^-1)	S $298.15, i Θ$ /(J·mol^-1·K^-1)
Group	Urea	MPO	MPDC	HIBC	∆H $f, 298.15, i Θ$ /(kJ·mol^-1)	S $298.15, i Θ$ /(J·mol^-1·K^-1)
CO—(N)₂^*	1	0	0	0	-137.30	67.80
N—(CO)(H)₂	2	0	2	1	-62.40	103.37
C—(C)₃(H)	0	1	1	1	-7.95	-50.53
C—(C)(H)₃	0	1	1	1	-42.20	127.32
C—(O)(C)(H)₂	0	2	0	2	-30.14	-46.05
O—(C)(H)	0	2	2	1	-158.68	121.71
O—(CO)(C)	0	0	2	1	-185.68	35.13
CO—(N)(O)^*	0	0	2	1	-137.30	67.80
σ	8	3	3	3	—	—

表3 Cp 的基团贡献值［19］

Table 3 Group contributions of Cp［19］

Group	∆a/ (J·mol^-1·K^-1)	∆b/ (J·mol^-1·K^-1)	∆c/ (J·mol^-1·K^-1)	∆d/ (J·mol^-1·K^-1)
—NH₂	26.90	-4.12×10^-2	1.64×10^-4	-9.76×10^-8
	6.45	6.70×10^-2	-3.57×10^-5	2.86×10^-9
—CH₃	19.50	-8.08×10^-3	1.53×10^-4	-9.67×10^-8
—CH₂—	-9.09×10^-1	9.50×10^-2	-5.44×10^-5	1.19×10^-8
	-2.03×10^-1	2.04×10^-1	-2.65×10^-4	1.20×10^-7
—COO—(ester)	24.50	4.02×10^-2	4.02×10^-5	-4.02×10^-8
—OH(alcohol)	25.70	-6.91×10^-2	1.77×10^-4	-9.88×10^-8

表4 三聚氰酸固体热容拟合计算值与实验值对比

Table 4 Experimental and calculated values of CA（s）

T/K	C_p_,exp/(J·mol^-1·K^-1)	C_p_,cal/(J·mol^-1·K^-1)	Relative deviation/%
300.477	142.2681	142.6466	0.2660
320.477	149.7612	151.3982	1.0931
340.477	157.4001	158.8823	0.9416
360.477	162.3271	165.3906	1.8872
380.477	169.1645	171.2149	1.2121
400.477	176.0664	176.6472	0.3298
420.477	182.4120	181.9793	0.2372
440.477	188.7937	187.5029	0.6837
460.477	195.7330	193.5100	1.1357
480.477	200.8936	200.2924	0.2993
500.477	206.2091	208.1418	0.9372
520.477	210.7179	217.3503	3.1475
540.477	223.7279	228.2095	1.0031

表5 各物质基本热力学数据（298.15 K）

Table 5 Thermodynamic data of components（298.15 K）

Component	∆H $f, 298.15 Θ$ /(kJ·mol^-1)	S $298.15 Θ$ /(J·mol^-1·K^-1)	C_p /(J·mol^-1·K^-1)
Urea(g)	-262.10	257.25	1.366×10^-8T³-9.87×10^-5T²+0.1946T+22.32
MPO(g)	-435.33	393.14	5.55×10^-8T³-2.58×10^-4T²+0.4577T+30.95
MPDC(g)	-937.87	723.68	-2.55×10^-8T³-2.03×10^-4T²+0.5939T+82.35
HIBC(g)	-561.83	483.49	1.68×10^-8T³-2.31×10^-4T²+0.5258T+56.65
CA(s)	-703.50	142.20	6.08×10^-6T³-7.43×10^-3T²+3.2924T-340.76
NH₃(g)	-46.19	192.51	6.69×10^-8T³+9.90×10^-5T²+0.0260T+27.55
HNCO(g)	-101.67	238.22	4.49×10^-8T³-1.13×10^-4T²+0.11756T+18.86

表5 各物质基本热力学数据（298.15 K）

Table 5 Thermodynamic data of components（298.15 K）

Component	∆H $f, 298.15 Θ$ /(kJ·mol^-1)	S $298.15 Θ$ /(J·mol^-1·K^-1)	C_p /(J·mol^-1·K^-1)
Urea(g)	-262.10	257.25	1.366×10^-8T³-9.87×10^-5T²+0.1946T+22.32
MPO(g)	-435.33	393.14	5.55×10^-8T³-2.58×10^-4T²+0.4577T+30.95
MPDC(g)	-937.87	723.68	-2.55×10^-8T³-2.03×10^-4T²+0.5939T+82.35
HIBC(g)	-561.83	483.49	1.68×10^-8T³-2.31×10^-4T²+0.5258T+56.65
CA(s)	-703.50	142.20	6.08×10^-6T³-7.43×10^-3T²+3.2924T-340.76
NH₃(g)	-46.19	192.51	6.69×10^-8T³+9.90×10^-5T²+0.0260T+27.55
HNCO(g)	-101.67	238.22	4.49×10^-8T³-1.13×10^-4T²+0.11756T+18.86

表6 ∆vHb的基团贡献值［19］

Table 6 Group contributions of ∆vHb［19］

Group	∆ $i 0$ / (kJ·mol^-1)	∆ $i l$ / (kJ·mol^-1)	∆ _i / (kJ·mol^-1)	∆T_b_i /K	∆T_c_i /K
—CH₃	-17.520	70.037	2.373	23.58	0.0141
—CH₂—	190.833	-27.338	2.226	22.88	0.0189
	194.137	118.629	1.691	21.74	0.0164
—NH₂	286.164	410.002	10.788	73.23	0.0243
	644.875	-428.108	—	76.75	0.0380
—COO—	363.706	1315.350	9.633	81.10	0.0481
—OH	—	—	16.826	92.88	0.0741

表6 ∆vHb的基团贡献值［19］

Table 6 Group contributions of ∆vHb［19］

Group	∆ $i 0$ / (kJ·mol^-1)	∆ $i l$ / (kJ·mol^-1)	∆ _i / (kJ·mol^-1)	∆T_b_i /K	∆T_c_i /K
—CH₃	-17.520	70.037	2.373	23.58	0.0141
—CH₂—	190.833	-27.338	2.226	22.88	0.0189
	194.137	118.629	1.691	21.74	0.0164
—NH₂	286.164	410.002	10.788	73.23	0.0243
	644.875	-428.108	—	76.75	0.0380
—COO—	363.706	1315.350	9.633	81.10	0.0481
—OH	—	—	16.826	92.88	0.0741

表7 各组分的Tb、Tc、∆vHb值及∆vH表达式

Table 7 Tb， Tc， ∆vHb and ∆vH of components

Component	T_b/K	T_c/K	∆_vH_b/(kJ·mol^-1)	∆_vH/(kJ·mol^-1)
Urea	421.21	638.13	42.19	64.61×(1－T/638.13)^0.395
MPO	474.84	636.47	57.47	102.76×(1－T/636.47)^0.424
MPDC	597.74	803.17	53.75	90.37×(1－T/803.17)^0.381
HIBC	536.29	719.71	61.06	107.54×(1－T/721.06)^0.414

表8 部分热力学数据的估算值和文献值［22，26］对比

Table 8 Comparison of calculation with literature［22，26］

Component	Parameter	Calculation	Literature	Relative deviation/%
Urea(g)	∆H $f, 298.15 Θ$ /(kJ·mol^-1)	-262.10	-262.10	0
	S $298.15 Θ$ /(J·mol^-1·K^-1)	257.25	257.25	0
	∆_vH_b/(kJ·mol^-1)	42.19	42.19	0
	T_b/K	421.21	421.21	0
	T_c/K	638.13	638.13	0
HNCO(g)	C_p (298.15 K)/(J·mol^-1·K^-1)	45.043	45.056	0.028
	C_p (400 K)/(J·mol^-1·K^-1)	50.729	50.678	0.101
	C_p (500 K)/(J·mol^-1·K^-1)	55.007	55.003	0.008
	C_p (600 K)/(J·mol^-1·K^-1)	58.410	58.414	0.007
	C_p (700 K)/(J·mol^-1·K^-1)	61.228	61.183	0.074

表8 部分热力学数据的估算值和文献值［22，26］对比

Table 8 Comparison of calculation with literature［22，26］

Component	Parameter	Calculation	Literature	Relative deviation/%
Urea(g)	∆H $f, 298.15 Θ$ /(kJ·mol^-1)	-262.10	-262.10	0
	S $298.15 Θ$ /(J·mol^-1·K^-1)	257.25	257.25	0
	∆_vH_b/(kJ·mol^-1)	42.19	42.19	0
	T_b/K	421.21	421.21	0
	T_c/K	638.13	638.13	0
HNCO(g)	C_p (298.15 K)/(J·mol^-1·K^-1)	45.043	45.056	0.028
	C_p (400 K)/(J·mol^-1·K^-1)	50.729	50.678	0.101
	C_p (500 K)/(J·mol^-1·K^-1)	55.007	55.003	0.008
	C_p (600 K)/(J·mol^-1·K^-1)	58.410	58.414	0.007
	C_p (700 K)/(J·mol^-1·K^-1)	61.228	61.183	0.074

表9 不同温度下各组分相应状态的∆fHmΘ（T）、SmΘ（T）

Table 9 ∆fHmΘ（T）， SmΘ（T） of the corresponding states of components at different temperatures

Parameter	T/K	Component
Parameter	T/K	Urea(l)	MPO(l)	MPDC(l)	HIBC(l)	CA(s)	NH₃(g)	HNCO(g)
∆_fH $m Θ$ (T)/ (kJ·mol^-1)	483.15	-283.55	-459.50	-899.95	-687.75	-671.47	-35.59	-92.41
	493.15	-281.63	-455.92	-895.98	-683.95	-669.44	-34.87	-91.87
	503.15	-279.66	-452.25	-891.95	-680.09	-667.37	-34.14	-91.32
	513.25	-277.64	-448.49	-887.87	-676.16	-665.25	-33.39	-90.76
	523.15	-275.56	-444.62	-883.74	-672.17	-663.09	-32.62	-90.21
S $m Θ$ (T)/ (J·mol^-1·K^-1)	483.15	297.21	477.36	696.40	591.76	224.69	219.70	262.20
	493.15	299.17	481.45	702.98	597.09	228.85	221.17	263.32
	503.15	301.11	485.51	709.50	602.38	233.01	222.64	264.43
	513.25	303.03	489.53	715.97	607.63	237.18	224.12	265.51
	523.15	304.94	493.5 2	722.38	612.84	241.25	225.60	266.58

表9 不同温度下各组分相应状态的∆fHmΘ（T）、SmΘ（T）

Table 9 ∆fHmΘ（T）， SmΘ（T） of the corresponding states of components at different temperatures

Parameter	T/K	Component
Parameter	T/K	Urea(l)	MPO(l)	MPDC(l)	HIBC(l)	CA(s)	NH₃(g)	HNCO(g)
∆_fH $m Θ$ (T)/ (kJ·mol^-1)	483.15	-283.55	-459.50	-899.95	-687.75	-671.47	-35.59	-92.41
	493.15	-281.63	-455.92	-895.98	-683.95	-669.44	-34.87	-91.87
	503.15	-279.66	-452.25	-891.95	-680.09	-667.37	-34.14	-91.32
	513.25	-277.64	-448.49	-887.87	-676.16	-665.25	-33.39	-90.76
	523.15	-275.56	-444.62	-883.74	-672.17	-663.09	-32.62	-90.21
S $m Θ$ (T)/ (J·mol^-1·K^-1)	483.15	297.21	477.36	696.40	591.76	224.69	219.70	262.20
	493.15	299.17	481.45	702.98	597.09	228.85	221.17	263.32
	503.15	301.11	485.51	709.50	602.38	233.01	222.64	264.43
	513.25	303.03	489.53	715.97	607.63	237.18	224.12	265.51
	523.15	304.94	493.5 2	722.38	612.84	241.25	225.60	266.58

表10 各反应不同温度下∆rH、∆rS、∆rG及KΘ值

Table 10 ∆rH， ∆rS， ∆rGand KΘ of reactions at different temperatures

T/K	Reaction(1)
T/K	∆_rH/(kJ·mol^-1)	∆_rS/(J·mol^-1·K^-1)	∆_rG/(kJ·mol^-1)	lnK^Θ	K^Θ
483.15	55.46	64.02	24.53	-6.11	2.23×10^-3
493.15	53.46	65.52	21.14	-5.16	5.76×10^-3
503.15	51.35	67.06	17.61	-4.21	1.48×10^-2
513.25	49.12	68.61	13.92	-3.26	3.83×10^-2
523.15	46.75	70.19	10.04	-2.31	9.95×10^-2
T/K	Reaction(2)
T/K	∆_rH/(kJ·mol^-1)	∆_rS/(J·mol^-1·K^-1)	∆_rG/(kJ·mol^-1)	lnK^Θ	K^Θ
483.15	119.79	157.55	43.67	-10.87	1.90×10^-5
493.15	120.16	157.42	42.53	-10.37	3.13×10^-5
503.15	120.55	157.30	41.40	-9.90	5.03×10^-5
513.25	120.95	157.17	40.30	-9.44	7.91×10^-5
523.15	121.36	157.03	39.21	-9.01	1.22×10^-4
T/K	Reaction(3)
T/K	∆_rH/(kJ·mol^-1)	∆_rS/(J·mol^-1·K^-1)	∆_rG/(kJ·mol^-1)	lnK^Θ	K^Θ
483.15	-394.23	-561.90	-122.75	30.46	1.87×10¹³
493.15	-393.84	-561.09	-117.14	28.48	2.56×10¹²
503.15	-393.41	-560.24	-111.53	26.58	3.79×10¹¹
513.25	-392.96	-559.34	-105.93	24.75	6.07×10¹⁰
523.15	-392.47	-558.39	-100.34	23.00	1.05×10¹⁰

图1 不同温度下反应(1)的∆rH、∆rG及KΘ

Fig.1 ∆rH, ∆rG and KΘ of reaction(1) at different temperatures

图2 不同温度下反应(2)的∆rH、∆rG及KΘ

Fig.2 ∆rH, ∆rG and KΘ of reaction(2) at different temperatures

图3 不同温度下反应(3)的∆rH、∆rG及KΘ

Fig.3 ∆rH, ∆rG and KΘ of reaction(3) at different temperatures

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