The Effects of NaI, KBr, and KI Salts on the Vapor-Liquid Equilibrium of the H2O+CH3OH System

The vapor–liquid equilibrium (VLE) in chemical engineering is indispensable for the design of equilibrium separation processes such as distillation, absorption, extraction, and crystallization. VLE data were measured for H2O+CH3OH+NaI, H2O+CH3OH+KBr, and H2O+CH3OH+KI systems. By analyzing and summarizing the results of H2O+Methanol+Alkali metal halide systems, the salt effects of NaI, KBr, and KI on the vapor–liquid equilibrium were obtained. Simultaneously, a model based on the NRTL equation (non-random two liquid) was proposed to correlate and calculate the VLE for the systems. In addition, the assumption of solvation based on hydration was introduced in this model. The proposed model can be successfully used to calculate the VLE for H2O+Methanol+Alkali metal halide systems.


INTRODUCTION
Vapor-liquid equilibrium (VLE), solid-liquid equilibrium (SLE), and liquid-liquid equilibrium (LLE) are important in industry, natural processes, chemistry, and other fields. The VLE for electrolyte systems and, more specifically, for mixed solvent electrolyte mixtures (such methanol-water-salt systems) are of considerable importance to a variety of fields, such as the extractive distillation of salt-containing liquids (Iliuta et al., 2000). There has been an increase in the amount of research into the phase equilibrium of electrolyte and non-electrolyte solutions.
Phase equilibrium and the thermodynamics of electrolyte solutions have been studied for decades, including activity coefficient, phase equilibrium data, and activity coefficient models. The Wilson model (Aebischer et al., 2018), NRTL model (Farajnezhad et al., 2016), and UNIQUAC model (Pereira et al., 2019) can be used to accurately calculate thermodynamic properties of non-electrolyte solutions. The Lu-Maurer model (Qian et al., 2011;Kontogeorgis et al., 2018), homsen's model (Pitzer, 2018), Pitzer's model (Hossain et al., 2016), ElecNRTL model (Puentes et al., 2018;Das et al., 2019), OLI model (Xu et al., 2016), and Xu's model (Yuan et al., 2019) have been successfully used to calculate the thermodynamic properties and the phase equilibrium for electrolyte solutions. In recent years, many researchers have begun to study the VLE of mixed-solvent electrolytes, and the VLE is important in the design of separation processes. Yang and Lee (1998) studied the VLE of H 2 O+CH 3 OH+NaCl, H 2 O+CH 3 OH+NaBr, and H 2 O+CH 3 OH+KCl through an experiment. The LIQUAC model (Li et al., 2010;Mohs and Gmehling, 2013) has been proposed to calculate the phase equilibria of mixed-solvent electrolyte solutions. In this model, Yan et al. treated the solutes as non-electrolyte solution interactions. Zhong et al. (2017) combined the UNIFAC model with the LIQUAC model and then developed the LIFAC model. Chen and Song (2004) proposed a modified model based the electrolyte NRTL model; it can be used to calculate the ionic activity coefficients of mixed-solvent electrolyte systems. These studies reported some experimental data and modified models. Experimental data were relatively abundant for single or mixed electrolyte aqueous systems (Yang and Lee, 1998), but the phase equilibrium data of the methanol-water-salt system with a wide range of pressures and temperatures were still rare. Such systems may be of practical importance or of interest to the development of a general electrolyte solution model. The models combine local composition activity coefficient models with either Debye-Hückel's law or the modifications of Debye-Hückel's law. Researchers have expanded the range of applications. The models can be used to calculate binary, multi-component electrolyte solutions at high temperatures and high concentrations. In general, there are great challenges in the research of mixed-solvent electrolytes, such as unavailable experimental data, unobtained salt-salt interaction parameters, and limited predictive capability.
In this work, we measured the VLE data of H 2 O+CH 3 OH+NaI, H 2 O+CH 3 OH+KBr, and H 2 O+CH 3 OH+KI systems. Then, a modified model was proposed to correlate the VLE of mixed solvent electrolyte systems.

Apparatus and Procedures
We used a circulation glass ebulliometer to measure the VLE, and the capacity of the ebulliometer was 40 cm 3 , as shown in Figure 1 . The main experimental instruments included a vacuum pump in the ebulliometer (40 cm 3 , Tianjin Wuqing Beiyang Chemical Factory), a pressure controller (Ruska Series 7000, Ruska Instrument Corp., Houston), a heating mantle, and a temperature controller (Model SRS13A, SHIMADEN, Japan).
During the experiments, the sample was placed into the glass ebulliometer, and the sample was added to the height of mark 2, as shown in Figure 1. The sample was then heated by the heating mantle controlled by the temperature controller. The operation pressure was controlled by the vacuum pump, the pressure sensor, and control valve. The vapor sample was condensed in a spherical condenser (length 40 cm) and then returned to the mixing chamber for recirculation. The time was 0.5-1 h in the first equilibrium, and the following equilibrium time was 10-20 min. The judging standard of the VLE is an important factor. The condensate reflux of the ebulliometer was controlled at 2-3 drops per second and was stably refluxed for approximately 15 min to establish an equilibrium state. After the VLE was reached, we recorded the temperature and pressure. At last, the component results of the vapor sample were tested through the gas chromatography with a TCD detector and a FFAP capillary chromatogram column.
The reliability of measurement has been verified in literature (Xu et al., 2018 (i.e., H 2 O+CaCl 2 and H 2 O+C 2 H 5 OH). The experimental VLE data for three ternary systems (i.e., H 2 O+CH 3 OH+NaI, H 2 O+CH 3 OH+KBr, and H 2 O+CH 3 OH+KI) were listed in Tables 1-3. In the tables, x and y are the components in the liquid phase and in the vapor phase, respectively.

Modification of Xu's Model for Mixed Solvent Electrolyte Systems
Xu's model (Yuan et al., 2019) can be employed to correlate and predict the VLE for electrolyte solution systems. In this work, a modified Xu's model was proposed to be used to calculate the VLE for mixed solvent electrolyte systems. The model for the excess Gibbs energy was expressed by the NRTL term. For mixed solvent electrolyte system, we added the solvent-salt terms and the solvent-solvent terms in the proposed model (Xu et al., 2016). Then, the activity coefficients were calculated by the excess Gibbs energy of the solvent-salt term and solvent-solvent term. For example, in a solvent 1-solvent 2-salt system n t G RT = n 1 n 3 τ 1,3 G 1,3 n 3 + n 1 G 1,3 + τ 3,1 G 3,1 n 1 + n 3 G 3,1 +n 2 n 3 τ 2,3 G 2,3 n 3 + n 2 G 2,3 + τ 3,2 G 3,2 n 2 + n 3 G 3,2   +n 1 n 2 τ 1,2 G 1,2 n 2 + n 1 G 1,2 + τ 2,1 G 2,1 n 1 + n 2 G 2,1 (1) This approach has been used to calculate activity coefficient between 298 and 355 K. For correlating data at different temperatures, a temperature dependence of the parameters τ i,j and τ i,j was used in which where subscript 1, 2, and 3 are solvent 1, solvent 2, and salt, respectively; nt is the molar of solute; and solvent mx is the total molality of solute, α = 0.3. The reference state of the activity coefficients in the excess Gibbs energy model is γi→ 1 as x i (=n i /n t )→ 1. In Equation 10, the solvation of solvent based on the hydration of Xu's model was introduced: where n 1 , n 2 , and n 3 are active contents; n 0 1 , n 0 2 , and n 0 3 are actual contents; and Z 1 and Z 2 are solvation parameters.

RESULTS AND DISCUSSION
The experimental data for three ternary systems (i.e., H 2 O+CH 3 OH+NaI, H 2 O+CH 3 OH+KBr, and H 2 O+CH 3 OH+KI) at different molality are listed in Tables 1-3. Meanwhile, we analyzed and summarized the results of H 2 O+CH 3 OH+NaCl (Yang and Lee, 1998),  H 2 O+CH 3 OH+NaBr (Xu et al., 2018), H 2 O+CH 3 OH+NaI, H 2 O+CH 3 OH+KCl (Xu et al., 2018), H 2 O+CH 3 OH+KBr, and H 2 O+CH 3 OH+KI shown in Figures 2, 3, and we obtained the possible relationship between the solubility of salt and the VLE.
From the Tables and Figures, we can see that the VLE are similar in the alkali metal systems. For the H 2 O+CH 3 OH+NaCl, H 2 O+CH 3 OH+NaBr, and H 2 O+CH 3 OH+NaI systems, as the salt concentration x 3 increased under the condition (x 2 = 0.08 and T = 316 K), P 1 of water decreased, and P 2 of methanol rose regularly. As the salt concentration x 3 increased under the condition (x 2 = 0.46 and T = 341K), P 1 of water decreased first and then rose, and P 2 of methanol rose regularly. For the H 2 O+CH 3 OH+KCl, H 2 O+CH 3 OH+KBr, and H 2 O+CH 3 OH+KI systems, as the salt concentration x 3 increased under the condition (x 2 = 0.45 and T = 315K), P 1 of water decreased, and P 2 of methanol rose regularly. As the salt concentration x 3 increased under the condition (x 2 = 0.22 and T = 335K), P 1 of water decreased, and P 2 of methanol rose. Through the above analysis, we found that the solubility of salt is an important factor affecting the VLE.

Results of the New Model
Parameters, τ 0 2,1 , τ 0 3,1 , τ 0 2,3 , τ 0 3,2 , τ 1 2,1 , τ 1 3,1 , τ 1 2,3 , τ 1 3,2 , Z 1, and Z 2 were obtained from the correlation of the experimental and literature data, as listed in Table 4. The results of correlation for 11 mixed solvent electrolyte systems were listed in Table 5 in the form of mean deviation between literature and calculated value. It can be seen from Table 5 that dY ≤ 0.24 kPa, and the mean value of dY = 0.11 kPa; dP ≤ 3.79%, and the mean value of dP = 2.38%. dY and dP were calculated via equations: where N is the data point number, and P exp and P cal are experimental vapor pressure and calculated vapor pressure, respectively. Seven salts (i.e., NaCl, NaBr, NaI, KCl, KBr, KI, and CaCl 2 ) in water, methanol, ethanol, and normal propyl solvent systems were chosen to correlate the proposed new model, as shown in Table 5 and

Comparison With Other Methods
We selected eight systems for comparing Yang's model (Yang and Lee, 1998), Iliuta's model (Kumagae et al., 1992), Kumagae's model (Robinson and Stokes, 2012), and Xu's model (Xu et al., 2018) with the proposed model in this work. Comparison results are shown in Tables 6, 7.
For water-methanol-salt systems (Table 6), the dY maximum value (dY = 0.03 kPa) of the proposed model in this work was   Table 7, the maximum value dP p and dP x of the proposed model were 3.79 and 1.67%, respectively. The maximum value dP p and dP x of Kumagae's model were 6.12 and 1.87%, respectively, and the maximum value dP p and dP x of Xu's model were 6.47 and 2.00%, respectively. The mean value dP p and dP x of the proposed model were 2.97 and FIGURE 5 | Correlation of VLE data of H2O(1)+ CH3OH(2)+NaCl(3) system. Filled symbols ( x2 = 0.45, T = 315 K; •x2 = 0.22, T = 335 K) indicate Literature data (Yang and Lee, 1998). Curves indicate correlation of the model.  (Xu et al., 2018); curves indicate correlation of the model.
1.03%, respectively. The mean value dP p and dP x of Kumagae's model were 3.64 and 1.14%, respectively, and the mean value dP p and dP x of Xu's model were 3.48 and 1.62%, respectively. In this section, dP p and dP x were calculated via two equations: From the results in

CONCLUSIONS
In this paper, the VLE data for H 2 O+CH 3 OH+NaI, H 2 O+CH 3 OH+KBr, and H2O+CH3OH+KI systems were reported. The reliability of measurements was verified by comparing our experimental data in two binary systems (i.e., H 2 O+CaCl 2 and H 2 O+C 2 H 5 OH).  Through the analysis, it has been shown that the solubility of salt is an important factor affecting the VLE.
Contemporaneously, a modified model was developed for calculating the VLE of mixed solvent electrolyte systems. The proposed model introduced a new excess Gibbs energy equation that is based on the NRTL model and Xu's model. We obtained the new model's parameters by correlating the experimental and literature data. The calculation results were compared to Yang's model, Iliuta's model, Kumagae's model, and Xu's model. In general, the model in this work can be used to successfully calculate VLE data for mixed solvent electrolyte systems.

DATA AVAILABILITY STATEMENT
All datasets generated for this study are included in the article/supplementary material.

AUTHOR CONTRIBUTIONS
XX and ZW: overall planning of the article and modeling. NZ: experimental design and data processing. YZ: experimental design and experimental equipment assembly. YW: experimental operation and data processing.

FUNDING
This work was supported by the National Natural Science Foundation of China (no. 21703115).