2021, Vol. 38
黄林川, 李天祥, 杨家敏, 王肖丽, 欧健, 朱静. 三元体系KH2PO4-CO(NH2)2-H2O在283.15 K的固液相平衡测定与关联[J]. 化学工业与工程, 2021, 38(3): 64-69. 
Huang Linchuan, Li Tianxiang, Yang Jiamin, Wang Xiaoli, Ou Jian, Zhu Jing. Determination and Correlation of Solid-liquid Equilibrium of Ternary System KH2PO4-CO(NH2)2-H2O at 283.15 K[J]. Chemical Industry and Engineering, 2021, 38(3): 64-69.
三元体系KH2PO4-CO(NH2)2-H2O在283.15 K的固液相平衡测定与关联
贵州大学化学与化工学院, 贵阳 550025
摘要：采用等温溶解平衡法研究了KH2PO4-CO（NH2）2-H2O在283.15 K下的固液相平衡，根据实验结果绘制了相应的稳定相图，采用湿渣法和X射线衍射法相结合的方法鉴定了平衡固相的组成与结构。结果表明，相图中有1个共饱和点，2条单变量曲线和3个结晶区。该体系为简单共饱和型，无复盐和加和物形成。采用Wilson方程和NRTL方程关联计算了三元系KH2PO4-CO（NH2）2-H2O的溶解度数据，计算值与实验值吻合度较好。其中Wilson方程计算值与实验值的相对平均方差（Relative Average Deviation，RAD）和均方根差（Root Mean Square Deviation，RMSD）分别为0.575%和0.159%；NRTL方程计算值与实验值的RAD和RMSD分别为1.58%和0.136%。
关键词：固液相平衡 溶解度 Wilson方程 NRTL方程
Determination and Correlation of Solid-liquid Equilibrium of Ternary System KH2PO4-CO(NH2)2-H2O at 283.15 K
College of Chemistry and Chemical Engineering, Guizhou University, Guiyang 550025, China
Abstract: The solid-liquid phase equilibrium of KH2PO4-CO(NH2)2-H2O at 283.15 K was studied by isothermal dissolution equilibrium method. The corresponding stable phase diagram was drawn according to the experimental results, and the composition and structure of the equilibrium solid phase were identified by wet slag method and X-ray diffraction method. The results show that there are a invariant point, two univariate curves and three crystalline regions in the phase diagram, and the system is a simple co-saturation type, no double salts or adducts were formed. Wilson equation and NRTL equation were used to calculate the solubility of ternary KH2PO4-CO(NH2)2-H2O, and the calculated values were in good agreement with the experimental values. The relative average deviation (RAD) and root mean square deviation (RMSD) of the calculated values of Wilson equation and experimental values are 0.575% and 0.159%, respectively; the RAD and RMSD of the calculated of NRTL equation and experimental values are 1.58% and 0.136%, respectively.
Keywords:
solid-liquid phase equilibrium solubility Wilson equation NRTL equation
水溶性肥料是一种可以完全溶于水的多元复合型肥料，能迅速地溶解于水中，相比于传统化肥它有肥效利用率更高，施用更方便经济，养分可以自由搭配等众多优点[1-2]。它的生产工艺有物理混配和化学合成2种，采用化学合成法将多组分原料溶解，反应，最终通过结晶分离得到全水溶的产品，所得产品的外观、均匀性和纯度都要优于简单的物理混配法[3-4]。而在化学合成法生产水溶肥的工艺过程中结晶分离部分尤为重要[5]，因为固-液相平衡是结晶分离过程研究的理论基础[6-8]，所以要研究一个多组分体系的结晶过程，就必须要有多组分体系在不同温度下的相平衡数据。
本研究采用等温溶解平衡法研究了三元体系KH2PO4-CO(NH2)2-H2O在283.15 K时的固液相平衡, 测定了该体系的相平衡溶解度数据，采用湿渣法与X射线衍射法相结合的方法鉴定了平衡固相的组成与结构，为其在生产水溶肥的结晶分离工艺中的应用提供了理论基础。
1 实验部分 1.1 试剂及仪器
表 1 实验仪器与药品
Table 1 Experimental equipment and chemical reagents
| 名称 | 型号 | 厂家 |
| 低温恒温槽 | DC-4006 | 上海衡平仪器仪表厂 |
| 电子天平 | HX-T(100Z) | 浙江省慈溪市天东衡器厂 |
| 磁力搅拌器 | S10-3 | 上海司乐仪器有限公司 |
| 紫外可见分光光度计 | UV-6100S | 上海美普达仪器有限公司 |
| 电热鼓风干燥箱 | GZX-9146MBE | 上海博讯实验有限公司医疗设备厂 |
| X射线粉末衍射仪 | D8 Advance | 北京布鲁克科技有限公司 |
| 实验室超纯水器 | Moletom1820s | 重庆摩尔水处理设备有限公司 |
| 温度计 | 0~50 ℃(刻度0.1 ℃) | 河北省冀县耀华玻璃仪器制品厂 |
| 夹套容器 | 250 mL | 自制 |
| 磷酸二氢钾(分析纯) | 500 g | 成都金山化学试剂有限公司 |
| 尿素(分析纯) | 500 g | 天津市科密欧化学试剂有限公司 |
| 注：实验中所用的水均为电阻率为18.25 MΩ ·cm的去离子水。 | ||
本实验采用等温溶解平衡法，在三元体系的相平衡实验中，从其二元子体系饱和点开始逐渐加入另一种物质，实验装置见文献[9]。实验过程将低温恒温槽温度控制在283.15(±0.1) K范围内，分别取上层清液和湿固相分析，得到液相和湿渣组成。当液相组成不变时，确定系统达到平衡，根据前期试验测试，得到本研究的三元体系KH2PO4-CO(NH2)2-H2O的平衡时间为8 h。
1.3 分析方法采用钼锑抗分光光度法测定KH2PO4的含量[10-11]；采用对二甲氨基苯甲醛(p-dimethylaminobenzaldehyde，PDAB)比色法测定CO(NH2)2的含量[12-13]；采用差减法测定H2O的含量；采用湿渣法[14-15]结合X射线粉末衍射法[16]测定固相组成。
2 结果与讨论表 2为283.15 K时KH2PO4-CO(NH2)2-H2O三元体系溶解度数据。由表 2中的数据绘制了三元体系KH2PO4-CO(NH2)2-H2O在283.15 K时的等温溶解相图，如图 1所示。图 1中的3个顶点A表示水、B表示尿素、C表示磷酸二氢钾。由表 2和图 1可看出三元体系KH2PO4-CO(NH2)2-H2O是1个简单共饱和型体系，有1个共饱和点，其组成的质量分数为：KH2PO4 7.50%，CO(NH2)2 36.85%，H2O 55.65%。图 1中共有4个区域，Aaeb为不饱和区域，Bae为尿素结晶区域，Ceb为磷酸二氢钾结晶区域，BeC为尿素和磷酸二氢钾的共饱和结晶区域。由于在该温度下尿素在水中的溶解度比磷酸二氢钾的大，在图 1中体现为磷酸二氢钾的结晶区面积大于尿素的结晶区面积。
表 2 KH2PO4-CO(NH2)2-H2O在283.15 K的相平衡溶解度数据
Table 2 Solubility data of phase equilibrium of KH2PO4-CO(NH2)2-H2O at 283.15 K
| 序号 | w液相组成/% | w湿渣组成/% | 平衡固相 | |||||
| KH2PO4 | CO(NH2)2 | H2O | KH2PO4 | CO(NH2)2 | H2O | |||
| 1, a | 0 | 45.65 | 54.35 | CO(NH2)2 | ||||
| 2 | 1.04 | 43.09 | 55.88 | 0.01 | 57.70 | 42.29 | CO(NH2)2 | |
| 3 | 3.95 | 40.31 | 55.74 | 0.94 | 80.64 | 18.42 | CO(NH2)2 | |
| 4 | 5.01 | 38.68 | 56.31 | 1.85 | 61.67 | 36.48 | CO(NH2)2 | |
| 5 | 6.86 | 36.77 | 56.38 | 2.37 | 75.28 | 22.35 | CO(NH2)2 | |
| 6 | 7.02 | 36.53 | 56.45 | 5.13 | 60.69 | 34.18 | CO(NH2)2 | |
| 7, e | 7.50 | 36.85 | 55.65 | 15.59 | 57.18 | 27.23 | KH2PO4+CO(NH2)2 | |
| 8 | 8.06 | 34.42 | 57.52 | 72.34 | 9.46 | 18.20 | KH2PO4 | |
| 9 | 8.98 | 33.01 | 58.01 | 78.03 | 6.74 | 15.23 | KH2PO4 | |
| 10 | 9.02 | 27.90 | 63.08 | 80.17 | 7.47 | 12.37 | KH2PO4 | |
| 11 | 10.40 | 23.92 | 65.68 | 75.33 | 7.47 | 17.21 | KH2PO4 | |
| 12 | 10.55 | 20.74 | 68.71 | 70.17 | 4.05 | 25.78 | KH2PO4 | |
| 13 | 11.44 | 16.65 | 71.91 | 88.45 | 0.52 | 11.03 | KH2PO4 | |
| 14 | 11.86 | 14.10 | 74.04 | 78.91 | 2.22 | 18.87 | KH2PO4 | |
| 15 | 12.48 | 10.44 | 77.08 | 79.68 | 1.30 | 19.03 | KH2PO4 | |
| 16 | 12.00 | 7.96 | 80.04 | 73.21 | 1.25 | 25.54 | KH2PO4 | |
| 17 | 13.79 | 3.84 | 82.37 | 76.20 | 1.51 | 22.30 | KH2PO4 | |
| 18, b | 15.47 | 0 | 84.53 | KH2PO4 | ||||
|
| 图 1 KH2PO4-CO(NH2)2-H2O体系在283.15 K的三元等温相图 Fig.1 Isothermal phase diagram of ternary system KH2PO4-CO(NH2)2-H2O at 283.15 K |
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图 2为三元体系KH2PO4-CO(NH2)2-H2O共饱和点e的固相的X射线衍射谱图。由图 2可知共饱和点e处与液相平衡的固相为CO(NH2)2晶体和KH2PO4晶体的混合物，没有固溶体或加和物。
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| 图 2 KH2PO4-CO(NH2)2-H2O体系在283.15 K的共饱和结晶点e的X射线衍射图 Fig.2 X-ray diffraction pattern of the co-saturated crystal point e of KH2PO4-CO(NH2)2-H2O at 283.15 K |
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采用Wilson和NRTL 2种模型对KH2PO4-CO(NH2)2-H2O三元体系在283.15 K的溶解度数据进行关联。
关联过程中设定目标函数值为F，F是实验中所测定所得的溶解度数据与用Wilson或NRTL模型计算溶解度数据的差值，其表达式为：
| $ F=\sum\limits_{i=1}^{N}\left(w_{i}^{\mathrm{e}}-w_{i}^{\mathrm{cal}}\right)^{2} $ | (1) |
式(1)中：N为实验点的个数，wie为组分i的质量分数测量值，wical为组分i的质量分数计算值。
运用最小二乘法，并使用1stpot优化分析计算软件拟合，当目标函数值F达到最小值时拟合结束，以相对平均方差(Relative Average Deviation，RAD)和均方根差(Root Mean Square Deviation，RMSD)来判断模型的可行性，其表达式为：
| $ \mathrm{R} \mathrm{AD}=\frac{1}{N} \sum\limits_{i=1}^{N}\left(\frac{w_{i}^{\mathrm{e}}-w_{i}^{\mathrm{cal}}}{w_{i}^{\mathrm{e}}}\right) $ | (2) |
| $ \mathrm{RMSD}=\left[\frac{1}{N} \sum\limits_{j=1}^{N}\left(w_{j}^{\mathrm{e}}-w_{j}^{\mathrm{cal}}\right)^{2}\right]^{1 / 2} $ | (3) |
Wilson方程和NRTL方程都是摩尔分数与活度系数的关系式，所得出的活度系数最终都需要带入下列的固-液相平衡方程中[17]：
| $ \begin{array}{c} \ln \left(x_{i} \gamma_{i}\right)=\frac{\Delta H_{\mathrm{tp}}}{R}\left(\frac{1}{T_{\mathrm{tp}}}-\frac{1}{T}\right)- \\ \frac{\Delta C_{p}}{R}\left(\ln \frac{T_{\mathrm{tp}}}{R}-\frac{T_{\mathrm{tp}}}{R}-1\right)-\frac{\Delta V}{R T}\left(P-P_{\mathrm{tp}}\right) \end{array} $ | (4) |
式(4)中：xi为组分i在液相中的摩尔分数，可由实验中测得的质量分数w转换而来；γ为组分i在液相中的活度系数；ΔHtp为该温度下的摩尔熔化焓；R为气体常数，8.314 J·mol-1·K-1；T为温度；Ttp为三相点的温度，ΔCp与ΔV分别为固相和液相间溶质i的摩尔热熔差(J·mol-1·K-1)和摩尔体积差(L·mol-1)。
根据Wilson模型通式[18-19]得到三元体系KH2PO4-CO(NH2)2-H2O计算活度系数γ的的展开式为：
| $ \begin{array}{c} \ln \gamma_{1}=1-\ln \left({\mathit{\Lambda}}_{12} x_{2}+x_{1}+{\mathit{\Lambda}}_{13} x_{3}\right)- \\ \frac{x_{1}}{x_{1}+x_{2} {\mathit{\Lambda}}_{12}+x_{3} {\mathit{\Lambda}}_{12}}-\frac{x_{2} {\mathit{\Lambda}}_{21}}{x_{1} {\mathit{\Lambda}}_{21}+x_{2}+x_{3} {\mathit{\Lambda}}_{23}}- \\ \frac{x_{3} {\mathit{\Lambda}}_{31}}{x_{1} {\mathit{\Lambda}}_{31}+x_{2} {\mathit{\Lambda}}_{32}+x_{3}} \end{array} $ | (5) |
| $ \begin{array}{c} \ln \gamma_{2}=1-\ln \left({\mathit{\Lambda}}_{21} x_{1}+x_{2}+{\mathit{\Lambda}}_{23} x_{3}\right)- \\ \frac{x_{1} {\mathit{\Lambda}}_{12}}{x_{1}+x_{2} {\mathit{\Lambda}}_{12}+x_{3} {\mathit{\Lambda}}_{13}}-\frac{x_{2}}{x_{1} {\mathit{\Lambda}}_{21}+x_{2}+x_{3} {\mathit{\Lambda}}_{31}}- \\ \frac{x_{3} {\mathit{\Lambda}}_{32}}{x_{1} {\mathit{\Lambda}}_{31}+x_{2} {\mathit{\Lambda}}_{32}+x_{3}} \end{array} $ | (6) |
| $ \begin{array}{c} \ln \gamma_{3}=1-\ln \left({\mathit{\Lambda}}_{31} x_{1}+{\mathit{\Lambda}}_{32} x_{2}+x_{3}\right)- \\ \frac{{\mathit{\Lambda}}_{13} x_{1}}{x_{1}+{\mathit{\Lambda}}_{12} x_{2}+{\mathit{\Lambda}}_{13} x_{3}}-\frac{{\mathit{\Lambda}}_{23} x_{2}+}{{\mathit{\Lambda}}_{21} x_{1}+x_{2}+{\mathit{\Lambda}}_{23} x_{3}}- \\ \frac{x_{3}}{{\mathit{\Lambda}}_{31} x_{1}+{\mathit{\Lambda}}_{32} x_{2}+x_{3}} \end{array} $ | (7) |
式(5)~式(7)中：下标的1、2和3分别表示KH2PO4、CO(NH2)2、H2O，Λij为Wilson参数，与纯组分分子间的相互作用能和摩尔体积相关，关系式为：
| $ {\mathit{\Lambda}}_{i j}=\frac{V_{j}}{V_{i}} \exp \left[\frac{-\left(g_{i j}-g_{i i}\right)}{R T}\right]=\frac{V_{j}}{V_{i}} \exp \left(\frac{-\Delta g_{i j}}{R T}\right) $ | (8) |
式(8)中Vi、Vj分别为组分i、j的摩尔体积；Δgij为二元作用能量参数。
使用1stpot软件将Wilson模型计算所得实验数据拟合[20-21]，得到磷酸二氢钾-水和尿素-水2个二元交互作用能量参数，然后采用非线性回归方法结合式(1)~式(8)拟合实验数据得到尿素-磷酸二氢钾的二元交互作用能量参数Δgij，结果列于表 3。
表 3 三元系KH2PO4-CO(NH2)2-H2O在Wilson与NRTL 2种模型中的二元交互作用参数
Table 3 Binary interaction parameters of ternary system KH2PO4-CO(NH2)2-H2O in the two models of Wilson and NRTL
| i-j | Wilson模型 | NRTL模型 | |||
| Δgij | Δgji | Δλij | Δλji | ||
| 磷酸二氢钾-尿素 | 69 408.20 | -3 765.02 | -12 658.14 | -5 959.19 | |
| 尿素-水 | -2 111.43 | 1 045.29 | -4 223.09 | 7 634.08 | |
| 磷酸二氢钾-水 | 9 211.76 | 21 604.64 | -16 485.70 | 8 747.16 | |
根据NRTL模型通式[22-24]得到三元体系KH2PO4-CO(NH2)2-H2O计算活度系数γ的的展开式为：
| $ \begin{aligned} \ln \gamma_{1}=& \frac{\left(G_{21} x_{2}+G_{31} x_{3}\right)\left(\tau_{21} x_{2} G_{21}+\tau_{31} x_{3} G_{31}\right)}{\left(x_{1}+G_{21} x_{2}+x_{3} G_{31}\right)^{2}} \\ & \frac{\left(\tau_{12}-\tau_{32}\right) x_{3} x_{2} G_{32} G_{12}+\tau_{12} x_{2}^{2} G_{12}}{\left(x_{2}+G_{12} x_{1}+x_{3} G_{32}\right)^{2}}+\\ & \frac{\left(\tau_{13}-\tau_{23}\right) x_{3} x_{2} G_{13} G_{23}+\tau_{13} x_{3}^{2} G_{13}}{\left(x_{3}+G_{13} x_{1}+x_{2} G_{23}\right)^{2}} \end{aligned} $ | (9) |
| $ \begin{aligned} \ln \gamma_{2}=& \frac{\left(G_{32} x_{3}+G_{12} x_{1}\right)\left(\tau_{12} x_{1} G_{21}+\tau_{32} x_{3} G_{32}\right)}{\left(x_{2}+G_{32} x_{3}+x_{1} G_{12}\right)^{2}}+\\ & \frac{\left(\tau_{23}-\tau_{13}\right) x_{3} x_{1} G_{23} G_{13}+\tau_{23} x_{3}^{2} G_{23}}{\left(x_{3}+G_{13} x_{1}+x_{2} G_{23}\right)^{2}}+\\ & \frac{\left(\tau_{21}-\tau_{31}\right) x_{3} x_{1} G_{21} G_{31}+\tau_{21} x_{1}^{2} G_{21}}{\left(x_{1}+G_{31} x_{3}+x_{2} G_{21}\right)^{2}} \end{aligned} $ | (10) |
| $ \begin{aligned} \ln \gamma_{3}=& \frac{\left(G_{13} x_{1}+G_{23} x_{2}\right)\left(\tau_{13} x_{1} G_{13}+\tau_{23} x_{2} G_{23}\right)}{\left(x_{2}+G_{32} x_{3}+x_{1} G_{12}\right)^{2}}+\\ & \frac{\left(\tau_{31}-\tau_{21}\right) x_{1} x_{2} G_{21} G_{31}+\tau_{21} x_{1}^{2} G_{31}}{\left(x_{1}+G_{31} x_{3}+x_{2} G_{21}\right)^{2}}+\\ & \frac{\left(\tau_{32}-\tau_{12}\right) x_{1} x_{2} G_{12} G_{32}+\tau_{32} x_{2}^{2} G_{32}}{\left(x_{2}+G_{32} x_{3}+x_{1} G_{12}\right)^{2}} \end{aligned} $ | (11) |
式(9)~式(11)中：1、2、3分别表示KH2PO4、CO(NH2)2、H2O；
| $ G_{i j}=\exp \left(-\alpha_{i j} \tau_{i j}\right) $ | (12) |
| $ \tau_{i j}=\frac{\lambda_{i j}-\lambda_{j i}}{R T}=\frac{\Delta \lambda_{i j}}{R T} $ | (13) |
| $ \alpha_{i j}=\alpha_{j i} $ | (14) |
α是一个经验参数，取值范围一般在0.20~0.47之间，本实验中取α=0.30；Δλij为二元交互作用能量参数。同理，结合式(1)~式(3)、式(9)~式(14)式可得二元交互作用能量参数Δλij，结果列于表 3。
最后计算出的Wilson模型的均方差RMSD=0.159%，相对平均方差RAD=0.575%。NRTL模型的均方差RMSD=0.136%，相对平均方差RAD=1.58%。将Wilson模型与NRTL模型在283.15 K下的溶解度计算值与实验值列于表 4。
表 4 三元体系KH2PO4-CO(NH2)2-H2O在283.15 K的溶解度实验值与计算值
Table 4 Experimental and calculated values of solubilities of ternary system KH2PO4-CO(NH2)2-H2O at 283.15 K
| 序号 | w实验值/% | wWilson计算值/% | 相对误差Wilson模型/% | wNRTL计算值/% | 相对误差NRTL模型/% | 平衡固相 | |||||||||
| KH2PO4 | CO(NH2)2 | KH2PO4 | CO(NH2)2 | KH2PO4 | CO(NH2)2 | KH2PO4 | CO(NH2)2 | KH2PO4 | CO(NH2)2 | ||||||
| 1 | 0 | 45.65 | 45.18 | 0.010 | 45.02 | 0.014 | CO(NH2)2 | ||||||||
| 2 | 1.04 | 43.09 | 43.94 | 0.020 | 42.39 | 0.016 | CO(NH2)2 | ||||||||
| 3 | 3.95 | 40.31 | 39.73 | 0.014 | 39.68 | 0.016 | CO(NH2)2 | ||||||||
| 4 | 5.01 | 38.68 | 38.65 | 0.001 | 38.16 | 0.013 | CO(NH2)2 | ||||||||
| 5 | 6.86 | 36.77 | 36.82 | 0.001 | 36.70 | 0.002 | CO(NH2)2 | ||||||||
| 6 | 7.02 | 36.53 | 36.69 | 0.004 | 38.94 | 0.066 | CO(NH2)2 | ||||||||
| 7 | 7.50 | 36.85 | 7.56 | 0.008 | 7.57 | 0.009 | KH2PO4+CO(NH2)2 | ||||||||
| 8 | 8.06 | 34.42 | 8.11 | 0.006 | 8.08 | 0.002 | KH2PO4 | ||||||||
| 9 | 8.98 | 33.01 | 8.99 | 0.001 | 8.76 | 0.024 | KH2PO4 | ||||||||
| 10 | 9.02 | 27.90 | 9.06 | 0.004 | 9.14 | 0.013 | KH2PO4 | ||||||||
| 11 | 10.40 | 23.92 | 10.40 | 0.000 | 10.30 | 0.010 | KH2PO4 | ||||||||
| 12 | 10.55 | 20.74 | 10.56 | 0.001 | 10.61 | 0.006 | KH2PO4 | ||||||||
| 13 | 11.44 | 16.65 | 11.43 | 0.001 | 11.45 | 0.001 | KH2PO4 | ||||||||
| 14 | 11.86 | 14.10 | 11.85 | 0.001 | 11.89 | 0.003 | KH2PO4 | ||||||||
| 15 | 12.48 | 10.44 | 12.46 | 0.002 | 12.52 | 0.003 | KH2PO4 | ||||||||
| 16 | 12.00 | 7.96 | 12.03 | 0.002 | 12.32 | 0.027 | KH2PO4 | ||||||||
| 17 | 13.79 | 3.84 | 13.76 | 0.002 | 13.78 | 0.001 | KH2PO4 | ||||||||
| 18 | 15.47 | 0 | 15.38 | 0.006 | 15.19 | 0.018 | KH2PO4 | ||||||||
采用等温溶解平衡法研究了三元体系KH2PO4-CO(NH2)2-H2O在283.15 K下的相平衡，根据所测的溶解度数据绘制出三元相图，相图中有1个共饱和点，其液相组成质量分数为：w(KH2PO4)=7.50%；w[CO(NH2)2]=36.85%；w(H2O)=55.65%。有2条单变量曲线，2条单变量曲线ae、be，以及共饱和点e和平衡的2个固相点B和C分别的连线将相图分为4个区域：不饱和区、CO(NH2)2结晶区、KH2PO4结晶区、KH2PO4和CO(NH2)2的共饱和结晶区。并采用湿渣法和X射线衍射法相结合的方法鉴定了平衡固相的组成与结构，结果表明该体系为简单共饱和型体系，平衡固相为KH2PO4与CO(NH2)2的混合物，无固溶体或加成物生成。
用Wilson、NRTL 2种模型关联计算该体系的溶解度数据，得到了KH2PO4-CO(NH2)2的二元交互作用能量参数。其中Wilson模型关联值的RAD=0.575%，RMSD=0.159%；NRTL模型关联值的RAD=1.58%，RMSD=0.136%，2种模型的关联值与计算值基本吻合。
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