# Solid-Liquid Phase Equilibria of the Quaternary System NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O at 283.15 and 313.15 K

Authors: Shuangshuang Gu; Haoran Li; Kangrui Sun; Yafei Guo; Tianlong Deng; Lingzong Meng
Journal: Journal of Chemistry
 (2023)

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## Abstract

The solid-liquid phase equilibria for the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K were studied with the isothermal solution method. There are four crystallization regions corresponding to NaCl, NH4Cl, NaHCO3, and NH4HCO3, five univariant solubility curves, and two invariant points saturated with the three coexisting minerals in the phase diagrams at the two temperatures. A comparison of the phase diagrams at 283.15 and 313.15 K shows that the areas of regions for NaCl, NaHCO3, and NH4Cl increase obviously. In contrast, the area of NH4HCO3 region decreases significantly as the temperature rises. The density and refractive index in the quaternary system change regularly with the concentration changing. The calculated densities and refractive indices in the quaternary system at the two temperatures with the empirical equations agree well with the experimental values.


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## Body

## 1. Introduction

Sodium carbonate is an important raw material for chemical production and is widely used in industry and daily life [1, 2]. Currently, the ammonia-alkali method and the combined alkali method are the two most representative methods for producing sodium carbonate in industry. Sodium bicarbonate crystallization and ammonium chloride solution were produced by the carbonate reaction [3]. The ammonia-alkali method, also known as the Solvoir method, uses ammonia and carbon dioxide as raw materials to prepare sodium carbonate, but the utilization coefficient of raw materials is low [4]. The combined alkali production method combines an ammonia plant with an alkali plant to produce sodium carbonate and by-product ammonium chloride, which fully uses sodium chloride and reduces some processes and equipment [5, 6]. The main components of the solution in the process of production of sodium bicarbonate by the combined alkali method and ammonia-alkali method can be represented with the system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) [7]. With the difference in solubilities for different salts in the above system, the sodium bicarbonate can be crystallized from the solution. In the process of phase transformation of sodium bicarbonate crystallization, the phase equilibrium of the system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) is necessary and meaningful for the production of sodium bicarbonate.The phase equilibrium data of this quaternary system at 273.15 K, 288.15 K, 308.15 K, and 323.15 K were reported in the literature [8–11]. In the production of sodium bicarbonate, the temperature for the carbonating reaction is about 313.15 K, and the crystallizing temperature for sodium bicarbonate is about 283.15 K. However, the solubility data for the quaternary system at 283.15 K and 313.15 K were not complete. The solubility data in its subsystems at 283.15 K and 313.15 K can be found in the literature[12–14]. No double salts and solid solutions form in the subsystems. The solubility of sodium bicarbonate, which is smaller than sodium carbonate, sodium chloride and sodium bicarbonate, increases as temperature increases [12–14]. With this information, the sodium bicarbonate can be crystallized with the ammonia-alkali method. In this study, the solubilities, refractive indices, and densities in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 K and 313.15 K were presented. The phase diagram and physicochemical property diagrams were plotted.


## 2. Experimental Section

### 2.1. Reagents and Instruments

The chemicals NaCl, NH4Cl, NaHCO3, and NH4HCO3 used in the experiments were all of the analytical grade, as shown in Table 1. All the water used in the experiment was double deionized water (DDW, pH = 6.60, conductivity = 1 × 10−4 S·m−1, at 298.15 K). The precision electronic balance (0.01 mg, Mettler Toledo, Swiss New Classic M) with an uncertainty of 0.2 mg was used for weighing. A magnetic stirring thermostatic water bath (HXC-500-6A, Beijing Fortune Joy Science Technology Co. Ltd., China) was used for the solid and liquid phase equilibrium [15–17]. The density was measured by DMA 4500 M high-precision vibrating tube densimeter (Anton Parr, Austria). The densimeter was calibrated at 293.15 K and atmospheric pressure with dry air and fresh deionized de-gas water. The precision of the densimeter (DMA 4500, Austria) is 1.0 × 10−5 g·cm−3 and the uncertainty is ±1.4 mg·cm−3. The density of deionized distilled de-gas water was in good agreement with the literature value. The Abbe refractometer was calibrated with double-deionized water at 293.15 K and atmospheric pressure was used for refractive index measurement with an uncertainty less than ±0.0001. An X-ray powder diffractometer (XRD, MSAL XD-3, Beijing Purkinje General Instrument Co., Ltd, China) was used to identify the solid equilibrium phase.Table 1
Reagents used in this work.
Chemical nameCAS reg. noGradeInitial mass fraction purityPurification methodFinal mass fraction purityAnalysis methodNaCl7647-14-5A.R0.99Recrystallization0.992Titration for Cl−NH4Cl12125-02-9A.R0.99Recrystallization0.992Titration for and NH4+NaHCO3144-55-8A.R0.99Recrystallization0.992Titration for HCO3−NH4HCO31066-33-7A.R0.99Recrystallization0.992Titration for HCO3− and NH4+


### 2.2. Experimental Methods

The isothermal solution equilibrium method was adopted for the solid and liquid phase equilibrium experiments, which was described in our previous work [15–17]. The reagents NaCl, NH4Cl, NaHCO3, NH4HCO3,and DDW were mixed in a different ratio in a series of sealed hard polyethylene bottles, and then the bottles were placed in a magnetic stirring constant temperature water bath at a stirring speed of 120 r/min to accelerate the solid and liquid equilibrium. After stirring for a period of time, the supernatant of the liquid phase in each bottle was taken out no less than twice for chemical analysis. About 5 mL liquid phases were filtered from the polyethylene bottles, weighed, and diluted into a 250 mL volumetric flask. If the relative error of two measurements is less than 0.003, it is considered that the solid and liquid equilibrium has reached. The result shows that the equilibrium state for this quaternary system can be attained in 30 d at 283.15 K and in 20 d at 313.15 K. The average concentrations were considered to be the solubilities of the salts. The equilibrium liquid phase was also taken out for physicochemical property measurement. Meanwhile, about 5.0 mL sample of the clarified solution was also taken out from the liquid phase through a filter pipet rapidly. The filter pipet was controlled to the same temperature with the liquid phase to avoid precipitation before sampling. The liquid phase was then placed in the sample bottle, which was already in the constant-temperature water circulating bath. The density and refractive index of the clarified solution were then measured at corresponding temperatures. If solid phases precipitate from the solutions during the whole process, the experimental procedure will be repeated. The solid phases were taken out for identification with the XRD method at the same time.


### 2.3. Analytical Methods

Hg(NO3)2 standard solution was used for volumetric titration to determine the concentration of Cl− [18]. The concentration of HCO3− was determined using hydrochloric acid solution and phenolphthalein in the presence of the double indicator method (phenolphthalein indicator and methyl orange reagent) [18]. The concentration of ammonium ion (NH4+) was determined by titration with a standard solution of NaOH using phenolphthalein as the indicator in the presence of methanal [19]. The relative errors of Cl−, HCO3−, and NH4+ among three parallel samples for measurement were less than 0.003. The concentration of Na+ was analyzed by an inductively coupled plasma optical emission spectrometer (ICP-OES, Prodigy, Leman Corporation, USA) with an uncertainty of ±0.01 and evaluated by ion balance. The density and refractive index were determined at corresponding temperatures with constant temperature water circulating bath (high precision temperature regulation, cc-k12, Hubble, Germany) to control temperature. The density was measured no less than three times. Considering instrument uncertainties, the largest uncertainty was from solution concentration and temperature fluctuation in the solution sampling, and the total uncertainties of the density and refractive index were within ±2.0 mg·cm−3 and 0.0010 at a 0.68 level of confidence.


## 2.1. Reagents and Instruments

The chemicals NaCl, NH4Cl, NaHCO3, and NH4HCO3 used in the experiments were all of the analytical grade, as shown in Table 1. All the water used in the experiment was double deionized water (DDW, pH = 6.60, conductivity = 1 × 10−4 S·m−1, at 298.15 K). The precision electronic balance (0.01 mg, Mettler Toledo, Swiss New Classic M) with an uncertainty of 0.2 mg was used for weighing. A magnetic stirring thermostatic water bath (HXC-500-6A, Beijing Fortune Joy Science Technology Co. Ltd., China) was used for the solid and liquid phase equilibrium [15–17]. The density was measured by DMA 4500 M high-precision vibrating tube densimeter (Anton Parr, Austria). The densimeter was calibrated at 293.15 K and atmospheric pressure with dry air and fresh deionized de-gas water. The precision of the densimeter (DMA 4500, Austria) is 1.0 × 10−5 g·cm−3 and the uncertainty is ±1.4 mg·cm−3. The density of deionized distilled de-gas water was in good agreement with the literature value. The Abbe refractometer was calibrated with double-deionized water at 293.15 K and atmospheric pressure was used for refractive index measurement with an uncertainty less than ±0.0001. An X-ray powder diffractometer (XRD, MSAL XD-3, Beijing Purkinje General Instrument Co., Ltd, China) was used to identify the solid equilibrium phase.Table 1
Reagents used in this work.
Chemical nameCAS reg. noGradeInitial mass fraction purityPurification methodFinal mass fraction purityAnalysis methodNaCl7647-14-5A.R0.99Recrystallization0.992Titration for Cl−NH4Cl12125-02-9A.R0.99Recrystallization0.992Titration for and NH4+NaHCO3144-55-8A.R0.99Recrystallization0.992Titration for HCO3−NH4HCO31066-33-7A.R0.99Recrystallization0.992Titration for HCO3− and NH4+


## 2.2. Experimental Methods

The isothermal solution equilibrium method was adopted for the solid and liquid phase equilibrium experiments, which was described in our previous work [15–17]. The reagents NaCl, NH4Cl, NaHCO3, NH4HCO3,and DDW were mixed in a different ratio in a series of sealed hard polyethylene bottles, and then the bottles were placed in a magnetic stirring constant temperature water bath at a stirring speed of 120 r/min to accelerate the solid and liquid equilibrium. After stirring for a period of time, the supernatant of the liquid phase in each bottle was taken out no less than twice for chemical analysis. About 5 mL liquid phases were filtered from the polyethylene bottles, weighed, and diluted into a 250 mL volumetric flask. If the relative error of two measurements is less than 0.003, it is considered that the solid and liquid equilibrium has reached. The result shows that the equilibrium state for this quaternary system can be attained in 30 d at 283.15 K and in 20 d at 313.15 K. The average concentrations were considered to be the solubilities of the salts. The equilibrium liquid phase was also taken out for physicochemical property measurement. Meanwhile, about 5.0 mL sample of the clarified solution was also taken out from the liquid phase through a filter pipet rapidly. The filter pipet was controlled to the same temperature with the liquid phase to avoid precipitation before sampling. The liquid phase was then placed in the sample bottle, which was already in the constant-temperature water circulating bath. The density and refractive index of the clarified solution were then measured at corresponding temperatures. If solid phases precipitate from the solutions during the whole process, the experimental procedure will be repeated. The solid phases were taken out for identification with the XRD method at the same time.


## 2.3. Analytical Methods

Hg(NO3)2 standard solution was used for volumetric titration to determine the concentration of Cl− [18]. The concentration of HCO3− was determined using hydrochloric acid solution and phenolphthalein in the presence of the double indicator method (phenolphthalein indicator and methyl orange reagent) [18]. The concentration of ammonium ion (NH4+) was determined by titration with a standard solution of NaOH using phenolphthalein as the indicator in the presence of methanal [19]. The relative errors of Cl−, HCO3−, and NH4+ among three parallel samples for measurement were less than 0.003. The concentration of Na+ was analyzed by an inductively coupled plasma optical emission spectrometer (ICP-OES, Prodigy, Leman Corporation, USA) with an uncertainty of ±0.01 and evaluated by ion balance. The density and refractive index were determined at corresponding temperatures with constant temperature water circulating bath (high precision temperature regulation, cc-k12, Hubble, Germany) to control temperature. The density was measured no less than three times. Considering instrument uncertainties, the largest uncertainty was from solution concentration and temperature fluctuation in the solution sampling, and the total uncertainties of the density and refractive index were within ±2.0 mg·cm−3 and 0.0010 at a 0.68 level of confidence.


## 3. Results and Discussion

### 3.1. Phase Diagrams at 283.15 K and 313.15 K

The solubility data in some ternary subsystems of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K were reported in the literature [12–14]. The comparison of the solubility data at invariant points for the ternary systems in this work and literatures was tabulated in Table 2. The relative error between the data in this work and literature data was less than 0.02, which shows the experimental data presented in this work are reliable.Table 2
The comparison of solubility data of ternary systems at 283.15 K, 313.15 K, and 0.1 MPaa.
NoComposition of liquid phase, 100wbSolid phasecReferenceNa+NH4+Cl−HCO3−283.15 K110.510.0015.800.59S + SBThis work24.257.2919.360.00A + S[13]4.966.2319.920.00A + SThis work30.009.0315.693.62AB + AThis work41.392.450.0012.00AB + SBThis work313.15 K111.210.0015.620.94S + SB[12]10.480.0015.620.99S + SBThis work26.0176.6322.050.00A + S[14]5.916.7322.410.00A + SThis work30.0012.2519.098.73AB + AThis work1.465.110.0021.20AB + SB[12]41.706.140.0025.30AB + SBThis workaStandard uncertainties u are u (T) = 0.1 K, u (p) = 0.005 MPa, ur (Na+) = 0.003, ur (NH4+) = 0.003, ur (Cl−) = 0.003, and ur (HCO3−) = 0.003. bw, Mass fraction, cA: NH4Cl, S: NaCl, AB: NH4HCO3, SB: NaHCO3.The experimental solubility data of quaternary systems (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K and 0.1 MPa were shown in Table 3. The composition of the liquid phase expressed in mass fraction for the quaternary system in Table 3 was converted into the Jänecke index, which is [J (mol/100 mol (Na+ + NH4+)]. The Jänecke necke index (JB) in Table 3 was calculated with the following equation:(1)JB=nBnNa++nNH4+×100.Table 3
Solubilities and physicochemical properties in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15, 313.15 K, and 0.1 MPaa.
NoComposition of liquid phase, 100wbComposition of liquid phase,Jc/[mol/100 mol (Na+ + NH4+)]Solid phasedNa+NH4+Cl−HCO3−H2ONH4+HCO3−H2O283.15 K1, A10.510.0015.800.5973.100.002.12887.58S + SB29.351.3416.810.4972.0115.511.67831.03S + SB37.893.2918.320.5969.9134.741.86738.34S + SB4, F17.454.2019.330.8368.1941.842.46679.69S + SB + A54.615.4917.131.4071.3760.324.54784.68A + SB62.727.1616.692.8070.6377.098.90760.91A + SB7, F22.368.1417.174.3567.9881.4812.84681.24A + AB + S8, B4.966.2319.920.0068.8942.890.00681.49A + S9, C0.009.0315.693.6271.6610011.84794.60A + B100.707.6414.173.4074.0993.2412.26905.89A + B11, D1.392.450.0012.0084.1669.171002380.03AB + SB121.442.691.889.7084.2970.4375.002209.46AB + SB131.252.892.768.3784.7374.6463.822191.78AB + SB141.463.495.426.3783.2675.3340.581798.43AB + SB152.015.169.796.0077.0476.6526.291144.99AB + SB162.095.9611.965.1974.8078.4520.17985.49AB + SB172.387.7516.055.0068.8280.5715.34716.50AB + SB313.15 K1, A′10.480.0015.620.9972.910.003.56887.81S + SB210.390.2816.060.9372.343.293.26859.00S + SB39.771.1216.770.9171.4312.743.06814.06S + SB48.782.7318.261.2069.0328.443.70718.56S + SB58.223.3418.441.4468.5634.164.35701.23S + SB6, F′16.076.8821.642.2563.1659.165.72543.18S + SB + A75.717.2721.702.5362.7961.886.35535.06SB + A85.657.3421.762.4862.7762.406.22533.85SB + A94.638.0121.043.3163.0168.828.39541.89SB + A10, F′21.6710.7616.8012.0258.7589.1829.39487.36SB + AB + A11, B′5.916.7322.410.0064.9559.210.00572.12S + A12, C′0.0012.2519.098.7359.9310021.02489.85AB + A13, D′1.706.140.0025.3066.8682.21100895.73AB + SB141.756.182.1621.8868.0381.8785.47901.85AB + SB151.7910.0413.3115.9058.9687.7340.99515.85AB + SBaStandard uncertainties u are u (T) = 0.1 K, u (p) = 0.005 MPa, ur (Na+) = 0.003, ur (NH4+) = 0.003, ur (Cl−) = 0.003, and ur (HCO3−) = 0.003. bw, Mass fraction, cJ = Jänecke index. dA: NH4Cl, S: NaCl, AB: NH4HCO3, and SB: NaHCO3.n (B) in equation (1) is the molar concentration of B. Using the Jänecke index J (NH4+), J (HCO3−) and J (H2O) in Table 3 as the X and Y axes, the equilibrium phase diagrams of the reciprocal quaternary system at 283.15 and 313.15 K were plotted in Figures 1 and 2. The phase diagrams in Figures 1(a) and 2(a) with no J (H2O) are the dry-salt phase diagram. Points A, B, C, and D in Figure 1(a) and A′, B′, C′, D′ in Figure 2(a) are the cosaturated points for the ternary systems NaCl-NaHCO3-H2O, NaCl-NH4Cl-H2O, NH4Cl-NH4CO3-H2O, and NaHCO3-NH4CO3-H2O at 283.15 K and 313.15 K. From Figures 1(a) and 2(a), the dry-salt phase diagrams in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K has four crystallization regions corresponding to NaHCO3, NH4HCO3, NaCl and NH4Cl, respectively. No solid solution or complex salt was found in the system at 283.15 and 313.15 K. The water phase diagrams of the system at 283.15 K and 313.15 K were shown in Figures 1(b) and 2(b). The Figures 1(b) and 2(b) shows that the Jänecke index of J (H2O) changes regularly with the increase of J (NH4+). There are two invariant points in each phase diagram in Figures 1(b) and 2(b) corresponding to F1 (F1′) and F2 (F2′). The Jänecke index of J (H2O) at F1 (F1′) is greater than F2 (F2′). The Jänecke index indicates the solubility of different salts. The X-ray diffraction patterns of solid phases for the invariant points in the system are shown in Figure 3. From Figure 3, the solid phases for the invariant points can be confirmed. F1 and F1′ are the invariant points saturated with three salts corresponding to NaCl, NaHCO3 and NH4Cl, respectively. F2 and F2′ are the invariant points saturated with NaHCO3, NH4CO3 and NH4Cl, respectively. There are five univariant curves in the diagram in Figures 1(a) and 2(a) corresponding to AF1 (A′F1′) saturated with NaCl and NaHCO3, BF1 (B′F1′) saturated with NaCl and NH4Cl, F1F2 (F1′F2′′) saturated with NaHCO3 and NH4Cl, F2C (F2′C′) saturated with NH4Cl and NH4HCO3, and F2D (F2′D′) saturated with NaHCO3 and NH4HCO3. The area of the four crystallization regions NaHCO3, NH4Cl, NH4Cl and NaCl decreases in sequence, which shows the solubility of the four salts increases in the same order. In the dry-salt phase diagram, more than two-thirds of the areas were occupied with NaHCO3, which indicates NaHCO3 can be easily crystallized from the solution. The J (H2O) changes regularly as the concentration changes in different curves. The concentration of salts can be roughly judged from the changing tendency of J (H2O) in different curves.Figure 1
Phase diagram of the quaternary system (Na+, NH4+//Cl−, and HCO3−-H2O) at 283.15 K: (a) dry-salt phase diagram; (b) water content diagram.
(a)(b)Figure 2
Phase diagram of the quaternary system (Na+, NH4+//Cl−, and HCO3−-H2O) at 313.15 K: (a) dry-salt phase diagram; (b) water content diagram.
(a)(b)Figure 3
X-ray diffraction patterns of solid phases for the invariant points in the systems NaCl + NH4Cl + NaHCO3 (a) and NH4HCO3 + NH4Cl + NaHCO3 (b).
(a)(b)A comparison of the dry-salt phase diagrams of the quaternary system at 273.15, 288.15, 308.15, 323.15 K from the literature [8–11] and 283.15 K and 323.15 K in this study is shown in Figure 4. Figure 4 shows that the areas of the regions for NaCl, NaHCO3, and NH4Cl increased obviously, whereas the area of the NH4HCO3 region decreased significantly with the increase in temperature from 283.15 to 323.15 K. The separation of NaHCO3 at high temperatures and recovery of NH4HCO3 at low temperatures can be sufficiently productive. The change in crystallization area can provide theoretical data for the separation and purification of sodium bicarbonate.Figure 4
Dry-salt diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 273.15, 283.15, 308.15, 313.15, and 323.15 K.


### 3.2. Density and Refractive Index at 283.15 K and 313.15 K

According to the density and refractive index data of the quaternary system in Table4 at two temperatures, the density and refractive index diagrams of the system at 283.15 K and 313.15 K were plotted with 100 J (NH4+) as the abscissa, as shown in Figures 5 and 6. The density for point D′ in Figure 6(a) was the calculated data because there was no experimental data. The column numbers in Table 4 correspond to those in Table 3. The density and refractive index change regularly as J (NH4+) changes in different univariant curves. The density curves in Figure 5(a) is the similar to those in Figure 6(a). The density decreases from A (A′) to C (C′) as 100 J (NH4+) increases, with the maximum data at point A (A′) and the minimum data at point C (C′). The refractive indices are more complicated in Figures 5(b) and 6(b). The refractive index increases from A to F1 in Figure 5(b), reaching the maximum data at point F1. From F1 to F2, the refractive index decreases firstly and then increases. The refractive indices show a downward trend from F2 to C. In the curve DF2, the refractive index increases sharply from 1.3609 to 1.3926, with the minimum data at point D. The changing regularity for the refractive index in Figure 6(b) is a little different from those in Figure 5(b). The minimum value is at point D in Figure 5(b) but at point A′ in Figure 6(b). The maximum refractive index is at point F1, almost the same as point F2 in Figure 5(b). However, the refractive index has the maximum value at point F2 in Figure 6(b). The difference in the density and refractive index diagrams for the quaternary system at 283.15 K and 313.15 K shows the concentration change at different temperatures.Table 4
Physicochemical properties in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at T = 283.15, 313.15 K, and p = 0.1 MPaa.
No.bComposition of liquid phase, 100wcnDρ/g·cm−3Solid phaseeNaClNaHCO3NH4ClNH4HCO3Experimental valueCalculated valueRelative errord, (%)Experimental valueCalculated valueRelative error, (%)283.15 K1, A26.410.430.000.001.38211.38340.091.208541.210930.20S + SB223.780.003.950.261.38571.3854−0.021.199781.19819−0.13S + SB320.070.009.780.241.39041.3891−0.091.188681.18684−0.15S + SB4, F118.950.0012.480.381.39281.3921−0.051.182831.187370.38S + SB + A511.720.0016.320.591.38901.3872−0.131.138481.141700.28A + SB66.920.0021.281.171.38721.38860.101.119801.122220.22A + SB7, F26.010.0024.191.821.39261.39290.021.129871.12756−0.20A + AB + S8, B18.340.0012.620.001.39171.3908−0.071.179541.180810.11A + S9, C0.000.0015.1413.231.38551.3841−0.101.085401.105451.85A + B100.000.9621.663.291.38591.3827−0.231.0874801.090300.26A + B11, D0.005.080.0010.761.36091.36390.221.095491.103770.76AB + SB120.001.991.1512.571.36381.36380.001.091831.08075−1.01AB + SB130.004.576.723.981.36741.3648−0.191.092441.08736−0.47AB + SB142.450.008.286.011.36731.3666−0.051.097981.06906−2.63AB + SB155.110.0015.342.511.37481.37770.211.103811.09535−0.77AB + SB165.320.0017.712.171.38001.38150.111.109361.10288−0.58AB + SB176.060.0023.032.091.38831.39140.221.122091.125480.30AB + SB313.15 K1, A′26.110.980.000.001.37811.37770.031.199421.19055−0.74S + SB226.430.390.850.001.37841.3790−0.051.193511.19313−0.03S + SB324.851.252.470.001.38061.38060.001.189411.18918−0.02S + SB422.331.656.990.001.38451.3852−0.051.180441.184510.34S + SB520.911.988.550.001.38571.3859−0.021.179211.179280.01S + SB6, F1′15.443.1018.300.001.39661.39640.021.164321.170140.50S + SB + A714.520.0021.611.081.39661.3970−0.031.164951.16361−0.12SB + A814.370.0021.821.041.39671.3970−0.021.164621.16291−0.15SB + A911.770.0023.811.411.39571.3960−0.021.151071.14978−0.11SB + A10, F2′4.250.0031.985.021.40151.4030−0.111.137391.12932−0.71SB + AB + A11, B′15.050.0020.000.001.39541.39270.201.157551.158690.10S + A12, C′0.000.0029.1810.891.39931.39860.051.104191.110750.59AB + A13, D′0.006.170.0026.971.37971.3805−0.05—f1.11204—AB + SB144.456.210.0021.311.38031.37980.04—1.12491—AB + SB154.556.540.0029.951.39811.39770.03—1.16039—AB + SBaStandard uncertainties u, u (T) = 0.1 K, u (p) = 0.005 MPa (ambient pressure change), ur (w (NaCl)) = 0.003, ur (w (NaHCO3)) = 0.003, ur (w (NH4Cl)) = 0.003, ur (w (NH4HCO3)) = 0.003, u (ρ) = 1.0 mg·cm−3, u (nD) = 0.0010. bThe points correspond to those in Table 2cw, mass fraction. dRelative error = 100% × (calculated value−experimental value)/experimental value. eA: NH4Cl, S: NaCl, AB: NH4HCO3, SB: NaHCO3. f—, not determined.Figure 5
Physicochemical properties versus composition diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 K (a) density versus J (NH4+); (b) refractive index versus J (NH4+).
(a)(b)Figure 6
Physicochemical properties versus composition diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) O at 313.15 K (a) density versus J (NH4+); (b) refractive index versus J (NH4+).
(a)(b)The density and refractive index can be calculated using the empirical equations from the literature [20, 21]. The equations used in the calculation were as follows:(2)lnρρ0=∑Aiwi,(3)lnnDnD0=∑Biwi.The density values of solution and pure water at the same temperature are expressed byρ and ρ0 in equation (2). The ρ0 of purified water is 0.9997 g·cm−3 at 283.15 K and 0.9922 g·cm−3 at 313.15 K [22]. The nD and nD0 in equation (3) represent the refractive indices of the solution and the pure water. The nD0 of purified water is 1.33369 at 283.15 K and 1.33061 at 313.15 K [23]. The coefficients for density and refractive index of the i-th component in the solution were expressed by Ai and Bi, respectively. According to the above empirical formula, the coefficients Ai and Bi were fitted to the experimental data, as shown in Table 5. The concentration for the four salts was used in Table 4 for convenience which were calculated with the mass fraction of ions in Table 3, were used for density and refractive index calculation for convenience. The calculated densities and refractive indices were also tabulated in Table 4. The maximum relative error between the experimental and calculated data for the density and refractive index is 2.63% and 0.23%, except for some points. The agreement between the experimental and calculated data shows that the coefficients obtained in this work are reliable.Table 5
The fitting parameters of the refractive and density at 283.15, 313.15 K, and 0.1 MPaa.
NaClNaHCO3NH4ClNH4HCO3283.15 KAi0.0070890.0104190.0028920.004293Bi0.0011550.0011860.0012040.001006313.15 KAi0.0068400.0037360.0026090.003372Bi0.0016830.0014940.0015430.001415aStandard uncertainties u, u (T) = 0.1 K, u (p) = 0.005 MPa (ambient pressure change).


## 3.1. Phase Diagrams at 283.15 K and 313.15 K

The solubility data in some ternary subsystems of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K were reported in the literature [12–14]. The comparison of the solubility data at invariant points for the ternary systems in this work and literatures was tabulated in Table 2. The relative error between the data in this work and literature data was less than 0.02, which shows the experimental data presented in this work are reliable.Table 2
The comparison of solubility data of ternary systems at 283.15 K, 313.15 K, and 0.1 MPaa.
NoComposition of liquid phase, 100wbSolid phasecReferenceNa+NH4+Cl−HCO3−283.15 K110.510.0015.800.59S + SBThis work24.257.2919.360.00A + S[13]4.966.2319.920.00A + SThis work30.009.0315.693.62AB + AThis work41.392.450.0012.00AB + SBThis work313.15 K111.210.0015.620.94S + SB[12]10.480.0015.620.99S + SBThis work26.0176.6322.050.00A + S[14]5.916.7322.410.00A + SThis work30.0012.2519.098.73AB + AThis work1.465.110.0021.20AB + SB[12]41.706.140.0025.30AB + SBThis workaStandard uncertainties u are u (T) = 0.1 K, u (p) = 0.005 MPa, ur (Na+) = 0.003, ur (NH4+) = 0.003, ur (Cl−) = 0.003, and ur (HCO3−) = 0.003. bw, Mass fraction, cA: NH4Cl, S: NaCl, AB: NH4HCO3, SB: NaHCO3.The experimental solubility data of quaternary systems (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K and 0.1 MPa were shown in Table 3. The composition of the liquid phase expressed in mass fraction for the quaternary system in Table 3 was converted into the Jänecke index, which is [J (mol/100 mol (Na+ + NH4+)]. The Jänecke necke index (JB) in Table 3 was calculated with the following equation:(1)JB=nBnNa++nNH4+×100.Table 3
Solubilities and physicochemical properties in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15, 313.15 K, and 0.1 MPaa.
NoComposition of liquid phase, 100wbComposition of liquid phase,Jc/[mol/100 mol (Na+ + NH4+)]Solid phasedNa+NH4+Cl−HCO3−H2ONH4+HCO3−H2O283.15 K1, A10.510.0015.800.5973.100.002.12887.58S + SB29.351.3416.810.4972.0115.511.67831.03S + SB37.893.2918.320.5969.9134.741.86738.34S + SB4, F17.454.2019.330.8368.1941.842.46679.69S + SB + A54.615.4917.131.4071.3760.324.54784.68A + SB62.727.1616.692.8070.6377.098.90760.91A + SB7, F22.368.1417.174.3567.9881.4812.84681.24A + AB + S8, B4.966.2319.920.0068.8942.890.00681.49A + S9, C0.009.0315.693.6271.6610011.84794.60A + B100.707.6414.173.4074.0993.2412.26905.89A + B11, D1.392.450.0012.0084.1669.171002380.03AB + SB121.442.691.889.7084.2970.4375.002209.46AB + SB131.252.892.768.3784.7374.6463.822191.78AB + SB141.463.495.426.3783.2675.3340.581798.43AB + SB152.015.169.796.0077.0476.6526.291144.99AB + SB162.095.9611.965.1974.8078.4520.17985.49AB + SB172.387.7516.055.0068.8280.5715.34716.50AB + SB313.15 K1, A′10.480.0015.620.9972.910.003.56887.81S + SB210.390.2816.060.9372.343.293.26859.00S + SB39.771.1216.770.9171.4312.743.06814.06S + SB48.782.7318.261.2069.0328.443.70718.56S + SB58.223.3418.441.4468.5634.164.35701.23S + SB6, F′16.076.8821.642.2563.1659.165.72543.18S + SB + A75.717.2721.702.5362.7961.886.35535.06SB + A85.657.3421.762.4862.7762.406.22533.85SB + A94.638.0121.043.3163.0168.828.39541.89SB + A10, F′21.6710.7616.8012.0258.7589.1829.39487.36SB + AB + A11, B′5.916.7322.410.0064.9559.210.00572.12S + A12, C′0.0012.2519.098.7359.9310021.02489.85AB + A13, D′1.706.140.0025.3066.8682.21100895.73AB + SB141.756.182.1621.8868.0381.8785.47901.85AB + SB151.7910.0413.3115.9058.9687.7340.99515.85AB + SBaStandard uncertainties u are u (T) = 0.1 K, u (p) = 0.005 MPa, ur (Na+) = 0.003, ur (NH4+) = 0.003, ur (Cl−) = 0.003, and ur (HCO3−) = 0.003. bw, Mass fraction, cJ = Jänecke index. dA: NH4Cl, S: NaCl, AB: NH4HCO3, and SB: NaHCO3.n (B) in equation (1) is the molar concentration of B. Using the Jänecke index J (NH4+), J (HCO3−) and J (H2O) in Table 3 as the X and Y axes, the equilibrium phase diagrams of the reciprocal quaternary system at 283.15 and 313.15 K were plotted in Figures 1 and 2. The phase diagrams in Figures 1(a) and 2(a) with no J (H2O) are the dry-salt phase diagram. Points A, B, C, and D in Figure 1(a) and A′, B′, C′, D′ in Figure 2(a) are the cosaturated points for the ternary systems NaCl-NaHCO3-H2O, NaCl-NH4Cl-H2O, NH4Cl-NH4CO3-H2O, and NaHCO3-NH4CO3-H2O at 283.15 K and 313.15 K. From Figures 1(a) and 2(a), the dry-salt phase diagrams in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K has four crystallization regions corresponding to NaHCO3, NH4HCO3, NaCl and NH4Cl, respectively. No solid solution or complex salt was found in the system at 283.15 and 313.15 K. The water phase diagrams of the system at 283.15 K and 313.15 K were shown in Figures 1(b) and 2(b). The Figures 1(b) and 2(b) shows that the Jänecke index of J (H2O) changes regularly with the increase of J (NH4+). There are two invariant points in each phase diagram in Figures 1(b) and 2(b) corresponding to F1 (F1′) and F2 (F2′). The Jänecke index of J (H2O) at F1 (F1′) is greater than F2 (F2′). The Jänecke index indicates the solubility of different salts. The X-ray diffraction patterns of solid phases for the invariant points in the system are shown in Figure 3. From Figure 3, the solid phases for the invariant points can be confirmed. F1 and F1′ are the invariant points saturated with three salts corresponding to NaCl, NaHCO3 and NH4Cl, respectively. F2 and F2′ are the invariant points saturated with NaHCO3, NH4CO3 and NH4Cl, respectively. There are five univariant curves in the diagram in Figures 1(a) and 2(a) corresponding to AF1 (A′F1′) saturated with NaCl and NaHCO3, BF1 (B′F1′) saturated with NaCl and NH4Cl, F1F2 (F1′F2′′) saturated with NaHCO3 and NH4Cl, F2C (F2′C′) saturated with NH4Cl and NH4HCO3, and F2D (F2′D′) saturated with NaHCO3 and NH4HCO3. The area of the four crystallization regions NaHCO3, NH4Cl, NH4Cl and NaCl decreases in sequence, which shows the solubility of the four salts increases in the same order. In the dry-salt phase diagram, more than two-thirds of the areas were occupied with NaHCO3, which indicates NaHCO3 can be easily crystallized from the solution. The J (H2O) changes regularly as the concentration changes in different curves. The concentration of salts can be roughly judged from the changing tendency of J (H2O) in different curves.Figure 1
Phase diagram of the quaternary system (Na+, NH4+//Cl−, and HCO3−-H2O) at 283.15 K: (a) dry-salt phase diagram; (b) water content diagram.
(a)(b)Figure 2
Phase diagram of the quaternary system (Na+, NH4+//Cl−, and HCO3−-H2O) at 313.15 K: (a) dry-salt phase diagram; (b) water content diagram.
(a)(b)Figure 3
X-ray diffraction patterns of solid phases for the invariant points in the systems NaCl + NH4Cl + NaHCO3 (a) and NH4HCO3 + NH4Cl + NaHCO3 (b).
(a)(b)A comparison of the dry-salt phase diagrams of the quaternary system at 273.15, 288.15, 308.15, 323.15 K from the literature [8–11] and 283.15 K and 323.15 K in this study is shown in Figure 4. Figure 4 shows that the areas of the regions for NaCl, NaHCO3, and NH4Cl increased obviously, whereas the area of the NH4HCO3 region decreased significantly with the increase in temperature from 283.15 to 323.15 K. The separation of NaHCO3 at high temperatures and recovery of NH4HCO3 at low temperatures can be sufficiently productive. The change in crystallization area can provide theoretical data for the separation and purification of sodium bicarbonate.Figure 4
Dry-salt diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 273.15, 283.15, 308.15, 313.15, and 323.15 K.


## 3.2. Density and Refractive Index at 283.15 K and 313.15 K

According to the density and refractive index data of the quaternary system in Table4 at two temperatures, the density and refractive index diagrams of the system at 283.15 K and 313.15 K were plotted with 100 J (NH4+) as the abscissa, as shown in Figures 5 and 6. The density for point D′ in Figure 6(a) was the calculated data because there was no experimental data. The column numbers in Table 4 correspond to those in Table 3. The density and refractive index change regularly as J (NH4+) changes in different univariant curves. The density curves in Figure 5(a) is the similar to those in Figure 6(a). The density decreases from A (A′) to C (C′) as 100 J (NH4+) increases, with the maximum data at point A (A′) and the minimum data at point C (C′). The refractive indices are more complicated in Figures 5(b) and 6(b). The refractive index increases from A to F1 in Figure 5(b), reaching the maximum data at point F1. From F1 to F2, the refractive index decreases firstly and then increases. The refractive indices show a downward trend from F2 to C. In the curve DF2, the refractive index increases sharply from 1.3609 to 1.3926, with the minimum data at point D. The changing regularity for the refractive index in Figure 6(b) is a little different from those in Figure 5(b). The minimum value is at point D in Figure 5(b) but at point A′ in Figure 6(b). The maximum refractive index is at point F1, almost the same as point F2 in Figure 5(b). However, the refractive index has the maximum value at point F2 in Figure 6(b). The difference in the density and refractive index diagrams for the quaternary system at 283.15 K and 313.15 K shows the concentration change at different temperatures.Table 4
Physicochemical properties in the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at T = 283.15, 313.15 K, and p = 0.1 MPaa.
No.bComposition of liquid phase, 100wcnDρ/g·cm−3Solid phaseeNaClNaHCO3NH4ClNH4HCO3Experimental valueCalculated valueRelative errord, (%)Experimental valueCalculated valueRelative error, (%)283.15 K1, A26.410.430.000.001.38211.38340.091.208541.210930.20S + SB223.780.003.950.261.38571.3854−0.021.199781.19819−0.13S + SB320.070.009.780.241.39041.3891−0.091.188681.18684−0.15S + SB4, F118.950.0012.480.381.39281.3921−0.051.182831.187370.38S + SB + A511.720.0016.320.591.38901.3872−0.131.138481.141700.28A + SB66.920.0021.281.171.38721.38860.101.119801.122220.22A + SB7, F26.010.0024.191.821.39261.39290.021.129871.12756−0.20A + AB + S8, B18.340.0012.620.001.39171.3908−0.071.179541.180810.11A + S9, C0.000.0015.1413.231.38551.3841−0.101.085401.105451.85A + B100.000.9621.663.291.38591.3827−0.231.0874801.090300.26A + B11, D0.005.080.0010.761.36091.36390.221.095491.103770.76AB + SB120.001.991.1512.571.36381.36380.001.091831.08075−1.01AB + SB130.004.576.723.981.36741.3648−0.191.092441.08736−0.47AB + SB142.450.008.286.011.36731.3666−0.051.097981.06906−2.63AB + SB155.110.0015.342.511.37481.37770.211.103811.09535−0.77AB + SB165.320.0017.712.171.38001.38150.111.109361.10288−0.58AB + SB176.060.0023.032.091.38831.39140.221.122091.125480.30AB + SB313.15 K1, A′26.110.980.000.001.37811.37770.031.199421.19055−0.74S + SB226.430.390.850.001.37841.3790−0.051.193511.19313−0.03S + SB324.851.252.470.001.38061.38060.001.189411.18918−0.02S + SB422.331.656.990.001.38451.3852−0.051.180441.184510.34S + SB520.911.988.550.001.38571.3859−0.021.179211.179280.01S + SB6, F1′15.443.1018.300.001.39661.39640.021.164321.170140.50S + SB + A714.520.0021.611.081.39661.3970−0.031.164951.16361−0.12SB + A814.370.0021.821.041.39671.3970−0.021.164621.16291−0.15SB + A911.770.0023.811.411.39571.3960−0.021.151071.14978−0.11SB + A10, F2′4.250.0031.985.021.40151.4030−0.111.137391.12932−0.71SB + AB + A11, B′15.050.0020.000.001.39541.39270.201.157551.158690.10S + A12, C′0.000.0029.1810.891.39931.39860.051.104191.110750.59AB + A13, D′0.006.170.0026.971.37971.3805−0.05—f1.11204—AB + SB144.456.210.0021.311.38031.37980.04—1.12491—AB + SB154.556.540.0029.951.39811.39770.03—1.16039—AB + SBaStandard uncertainties u, u (T) = 0.1 K, u (p) = 0.005 MPa (ambient pressure change), ur (w (NaCl)) = 0.003, ur (w (NaHCO3)) = 0.003, ur (w (NH4Cl)) = 0.003, ur (w (NH4HCO3)) = 0.003, u (ρ) = 1.0 mg·cm−3, u (nD) = 0.0010. bThe points correspond to those in Table 2cw, mass fraction. dRelative error = 100% × (calculated value−experimental value)/experimental value. eA: NH4Cl, S: NaCl, AB: NH4HCO3, SB: NaHCO3. f—, not determined.Figure 5
Physicochemical properties versus composition diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 K (a) density versus J (NH4+); (b) refractive index versus J (NH4+).
(a)(b)Figure 6
Physicochemical properties versus composition diagram of the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) O at 313.15 K (a) density versus J (NH4+); (b) refractive index versus J (NH4+).
(a)(b)The density and refractive index can be calculated using the empirical equations from the literature [20, 21]. The equations used in the calculation were as follows:(2)lnρρ0=∑Aiwi,(3)lnnDnD0=∑Biwi.The density values of solution and pure water at the same temperature are expressed byρ and ρ0 in equation (2). The ρ0 of purified water is 0.9997 g·cm−3 at 283.15 K and 0.9922 g·cm−3 at 313.15 K [22]. The nD and nD0 in equation (3) represent the refractive indices of the solution and the pure water. The nD0 of purified water is 1.33369 at 283.15 K and 1.33061 at 313.15 K [23]. The coefficients for density and refractive index of the i-th component in the solution were expressed by Ai and Bi, respectively. According to the above empirical formula, the coefficients Ai and Bi were fitted to the experimental data, as shown in Table 5. The concentration for the four salts was used in Table 4 for convenience which were calculated with the mass fraction of ions in Table 3, were used for density and refractive index calculation for convenience. The calculated densities and refractive indices were also tabulated in Table 4. The maximum relative error between the experimental and calculated data for the density and refractive index is 2.63% and 0.23%, except for some points. The agreement between the experimental and calculated data shows that the coefficients obtained in this work are reliable.Table 5
The fitting parameters of the refractive and density at 283.15, 313.15 K, and 0.1 MPaa.
NaClNaHCO3NH4ClNH4HCO3283.15 KAi0.0070890.0104190.0028920.004293Bi0.0011550.0011860.0012040.001006313.15 KAi0.0068400.0037360.0026090.003372Bi0.0016830.0014940.0015430.001415aStandard uncertainties u, u (T) = 0.1 K, u (p) = 0.005 MPa (ambient pressure change).


## 4. Conclusions

The solid-liquid phase equilibria for the quaternary system (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) at 283.15 and 313.15 K were studied with the isothermal solution method. The space phase diagrams were plotted with the experimental solubilities. There are four single salt crystallization regions of NaCl, NH4Cl, NaHCO3, and NH4HCO3, five univariant solubility curves, and two invariant points saturated with the three coexisting solid phases in the phase diagrams at the two temperatures. Neither solid solutions nor double salts were found. The area of the four crystallization regions NaHCO3, NH4Cl, NH4Cl, and NaCl decreases in sequence. A comparison of the phase diagrams at 283.15 and 308.15 K shows that the areas of the regions for NaCl, NaHCO3, and NH4Cl increase obviously, and the area of the NH4HCO3 region decreases significantly with temperature increasing from 283.15 to 313.15 K. The J (H2O), density, and refractive index change regularly as J (NH4+) changes in different univariant curves. The calculated densities and refractive indices in the quaternary system at two temperatures with the empirical equations were in agreement using the experimental values. These results on the phase diagram of (NaCl + NH4Cl + NaHCO3 + NH4HCO3 + H2O) can provide a theoretical basis for the recovery and utilization of sodium bicarbonate in the production industry of sodium carbonate.



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*Source: 9296099-2023-03-02.xml*