Determination and Calculation of Phase Equilibrium for Aqueous Ternary System (NH2)2CO+KCl+H2O at 283.15K

The solid-liquid phase equilibrium for ternary system (NH2)2CO+KCl+H2O was determined by isothermal saturation method at 283.15K under atmosphere pressure. The isothermal phase diagrams was drawn in according to the measured solubility data. There are one co-saturated point and two pure solids occurred in this ternary system. The solid phases were confirmed by Schreinemaker’s wet residue method and X-ray powder diffraction. Two thermodynamic models, Wilson model and NRTL model, were used to calculate the solubility data. The value of root mean-square deviation in Wilson model and NRTL model for this ternary system was 0.22 and 0.66 respectively, and the value of relative average deviation was 0.61% and 2.33% respectively, which indicated that the calculated data and the experimental results are nearly consistent.


Introduction
Nitrogen and potassium are the two main nutrients necessary for plant growth. Nitrogen is the greatest demand for plant growth and development [1]. Potassium can enhance the tolerance of crops to various harsh environments and the stress resistance of crops, meanwhile promote the absorption and utilization of nitrogen by plants [2]. Humans apply a large amount of chemical fertilizers containing nitrogen and potassium elements to provide a large amount of nitrogen and potassium elements needed in the process of plant growth, and to achieve the purpose of improving crop yield and quality.
As a new type of chemical fertilizer, water-soluble fertilizer has high utilization rate of effective ingredients, less environmental pollution, and can save water resources. So it is widely used on the large areas of farmland by the way of spraying, sprinkling and drip irrigation [3]. Water-soluble fertilizer obtained by chemical synthesis has better solubility and stability. Water-soluble fertilizer with stable ingredients and properties has been produced by co-crystallization technology. Therefore, the phase equilibrium data of water-soluble fertilizer has important guiding significance for the study of its production process.
Co-crystallization is the process of precipitating or crystallizing of different materials simultaneously. Usually, they had the corporate form of crystal, namely multi-component crystal, produced from vapor, solution or molten material [4]. Co-crystal is actually a mixture in the level of molecules and atoms [5]. The co-crystallization technology not only solves the problem of poor dispersibility and uniformity when the solid product is compounded, but also improves the crystal shape, fluidity, hygroscopicity and stability of the product [6]. Co-crystallization technology has been widely used in the preparation of pharmaceutical co-crystals [7][8][9][10], food additives [11], materials industry [12], energy and environment [13] and catalyst manufacturing [14].
Solid-liquid phase equilibrium is considered as fundamental content in chemical thermodynamics. Thermodynamics may be applied in the unit operations such as distillation, crystallization, extraction and purification in the chemical industry [15][16]. Multi-component solid-liquid phase equilibrium data and phase diagrams are the theoretical basis of crystallization process, so it has been a hot topic in recent years.
(NH 2 ) 2 CO and KCl are often used to produce mixed water-soluble fertilizers, and their multi-system solid-liquid phase equilibrium is the basis of their crystallization process. In this work, the solid-liquid phase equilibrium of ternary system (NH 2 ) 2 CO+KCl+H 2 O at 283.15K were determined and its isothermal phase diagrams were plotted accordingly. Wilson model and NRTL model were used to calculate the solubility data.

Experimental procedure
The solid-liquid equilibrium for ternary system (NH 2 ) 2 CO+KCl+H 2 O was obtained by isothermal saturation method [17][18]. The experimental procedure for phase equilibrium determination have been described by the author in the author's published article [19].

Analysis
The content of KCl in equilibrium liquid phase and that of wet solid were determined by NH 4 Fe(SO 4 ) 2 ꞏ12H 2 O indicator method. The content of urea was determined with UV spectrophotometry [20][21]. Solid phase were confirmed by Schreinemaker's method and X-ray powder diffraction [22][23][24].

Results and discussion
The solubility data in mass fraction and the phase diagram for the ternary system of (NH 2 ) 2 CO+KCl+H 2 O are shown in Table1 and Figure1.
Table1. Mass fraction solubility for the ternary system of (NH2)2CO(1)+KCl (2) In Figure1, the points A 1 , B 1 and C 1 stands for the pure water, potassium chloride and urea respectively. a 1 and b 1 represent the mass fraction solubility of urea and potassium chloride in water at 283.15K respectively. e 1 is invariant point, at which urea and potassium chloride were saturate with a liquid phase. a 1 e 1 and b 1 e 1 are crystalline curves of pure urea and potassium chloride, respectively. The phase diagram is divided into four regions by two crystalline curves: A 1 a 1 e 1 b 1 is an unsaturated region, C 1 a 1 e 1 is the crystallization zone of urea, B 1 b 1 e 1 is the crystallization zone of Potassium chloride, C 1 e 1 B 1 is the crystallization region of mixture solids of urea and Potassium chloride.
The solid of invariant point was collected and analyzed by X-ray diffraction from 10° to 90° at a scan speed of 8°ꞏmin −1 . The pattern of XRD diagram is shown in Figure2, it can be determined that the solid phase at the invariant point is mixture solid of urea and Potassium chloride.

Solid-liquid phase equilibrium correlation and calculation
In this paper, Wilson model [25] and NRTL model [26] were used to correlate the solid-liquid phase equilibrium data of the ternary system (NH 2 ) 2 CO+KCl+H 2 O at 283.15K.
Wilson model was showed in Equation (1).
where, Λ ij are the Wilson parameters, which is related to the molar volume of pure substance and interaction energy of molecules, can be expressed as Equation (2).
v i and v j are the molar volume of pure substances i and j respectively, which can be calculated from the molar mass and density. Δg ij is the adjustable interaction energy parameter (Jꞏmol -1 ), which is less affected by temperature and can be regarded as a constant in a not too wide temperature range.
NRTL model and the computational formula of relative parameters was showed in Equation α is a nonrandom parameter and usually varies in the range from 0.2 to 0.47. In this paper, it is taken as 0.3.
The relative average deviation (RAD) and root mean-square deviation (RMSD) was used to evaluate the applicability and accuracy of the two models( Equation (7) and (8) During the regression process, the density of urea, the melting temperature T m and fusion enthalpy Δ fus H, the density and melting temperature of potassium chloride, the fusion enthalpy Δ fus H for potassium chloride were cited from in the References [27][28][29][30]. The interaction energy parameter Δg ij for binary systems of (NH 2 ) 2 CO+H 2 O, KCl+H 2 O were obtained on the basis of the solubility data by the nonlinear regression method through 1stopt software [31][32]. For the two binary systems, the root mean-square deviation were no more than 0.3% in the Wilson model, and that were no more than 0.4% in the NRTL model. Based on the interaction energy parameters of binary system of (NH 2 ) 2 CO+H 2 O and KCl+H 2 O, the binary interaction energy parameters of (NH 2 ) 2 CO+KCl was acquired and shown in Table2.
Table2. The regressed binary interaction energy parameter of (NH 2 ) 2 CO(1)+KCl (2) The solubility were calculated based on the obtained interaction energy parameters, and the calculated results were presented in Table 1. The value of RMSD and RAD of Wilson model and NRTL model for the ternary system (NH 2 ) 2 CO+KCl+H 2 O are listed in Table 1. The value of root mean-square deviation in Wilson model and NRTL model for this ternary system was 0.22 and 0.66 respectively, and the value of relative average deviation was 0.61% and 2.33% respectively, which indicated that the calculated data and the experimental results are nearly consistent.

Conclusion
The solid-liquid equilibrium for ternary system (NH 2 ) 2 CO+KCl+H 2 O was determined by isothermal saturation method at 283.15 K under atmosphere pressure and their isothermal dissolution phase diagrams were constructed. This ternary system belongs to a simple eutectic type with an invariant point and neither solid solutions nor double salts are found.
The solid-liquid phase equilibrium data were correlated by using the Wilson model and NRTL model. The largest value of RMSD for the ternary system (NH 2 ) 2 CO+KCl+H 2 O were 0.66, and that of RAD were E3S Web of Conferences 185, 04045 (2020) ICEEB 2020 http://doi.org/10.1051/e3sconf/202018504045 2.33%. So the calculated solubility via the two models provided good agreement with the experimental values. Furthermore, the Wilson model provided a better correlation results than NRTL model for this system