Solid-Liquid Phase Equilibria of the Quaternary System NaCl + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O at 283.15 and 313.15 K

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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].Te ammoniaalkali method, also known as the Solvoir method, uses ammonia and carbon dioxide as raw materials to prepare sodium carbonate, but the utilization coefcient of raw materials is low [4].Te 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].Te 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 + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) [7].With the diference in solubilities for diferent 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 + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) is necessary and meaningful for the production of sodium bicarbonate.
Te phase equilibrium data of this quaternary system at 273.15 K, 288.15 K, 308.15 K, and 323.15K were reported in the literature [8][9][10][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 313.15K were not complete.Te solubility data in its subsystems at 283.15 K and 313.15K can be found in the literature [12][13][14].No double salts and solid solutions form in the subsystems.Te solubility of sodium bicarbonate, which is smaller than sodium carbonate, sodium chloride and sodium bicarbonate, increases as temperature increases [12][13][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 + NH 4 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).Te 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][16][17].Te density was measured by DMA 4500 M high-precision vibrating tube densimeter (Anton Parr, Austria).Te densimeter was calibrated at 293.15 K and atmospheric pressure with dry air and fresh deionized de-gas water.Te precision of the densimeter (DMA 4500, Austria) is 1.0 × 10 −5 g•cm −3 and the uncertainty is ±1.4 mg•cm −3 .Te density of deionized distilled de-gas water was in good agreement with the literature value.Te 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 difractometer (XRD, MSAL XD-3, Beijing Purkinje General Instrument Co., Ltd, China) was used to identify the solid equilibrium phase.

Experimental Methods.
Te isothermal solution equilibrium method was adopted for the solid and liquid phase equilibrium experiments, which was described in our previous work [15][16][17].Te reagents NaCl, NH 4 Cl, NaHCO 3 , NH 4 HCO 3 ,and DDW were mixed in a diferent 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 fltered from the polyethylene bottles, weighed, and diluted into a 250 mL volumetric fask.If the relative error of two measurements is less than 0.003, it is considered that the solid and liquid equilibrium has reached.Te 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. Te average concentrations were considered to be the solubilities of the salts.Te equilibrium liquid phase was also taken out for physicochemical property measurement.Meanwhile, about 5.0 mL sample of the clarifed solution was also taken out from the liquid phase through a flter pipet rapidly.Te flter pipet was controlled to the same temperature with the liquid phase to avoid precipitation before sampling.Te liquid phase was then placed in the sample bottle, which was already in the constant-temperature water circulating bath.Te density and refractive index of the clarifed solution were then measured at corresponding temperatures.If solid phases precipitate from the solutions during the whole process, the experimental procedure will be repeated.Te solid phases were taken out for identifcation with the XRD method at the same time.
2.3.Analytical Methods.Hg(NO 3 ) 2 standard solution was used for volumetric titration to determine the concentration of Cl − [18].Te concentration of HCO 3 − was determined using hydrochloric acid solution and phenolphthalein in the presence of the double indicator method (phenolphthalein indicator and methyl orange reagent) [18].Te concentration of ammonium ion (NH 4 + ) was determined by titration with a standard solution of NaOH using phenolphthalein as the indicator in the presence of methanal [19].Te relative errors of Cl − , HCO 3 − , and NH 4 + among three parallel samples for measurement were less than 0.003.Te 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.Te 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.Te density was measured no less than three times.Considering instrument uncertainties, the largest uncertainty was from solution concentration and temperature fuctuation 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 confdence.[12][13][14].Te comparison of the solubility data at invariant points for the ternary systems in this work and literatures was tabulated in Table 2. Te 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.

Results and Discussion
Te experimental solubility data of quaternary systems (NaCl + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) at 283.15 and 313.15K and 0.1 MPa were shown in Table 3. Te 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 + + NH 4 + )].Te Jänecke necke index (J B ) in Table 3 was calculated with the following equation: n (B) in equation ( 1) is the molar concentration of B. Using the Jänecke index J (NH 4 + ), J (HCO 3 − ) and J (H 2 O) in Table 3 as the X and Y axes, the equilibrium phase diagrams of the reciprocal quaternary system at 283.15 and 313.15K were plotted in Figures 1 and 2. Te phase diagrams in Figures 1(a Tere are two invariant points in each phase diagram in Figures 1(b) and 2(b) corresponding to F 1 (F 1 ′) and F 2 (F 2 ′).Te Jänecke index of J (H 2 O) at F 1 (F 1 ′) is greater than F 2 (F 2 ′).Te Jänecke index indicates the solubility of diferent salts.Te X-ray difraction 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 confrmed.F 1 and F 1 ′ are the invariant points saturated with three salts corresponding to NaCl, NaHCO 3 and NH 4 Cl, respectively.F 2 and F 2 ′ are the invariant points saturated with NaHCO 3 , NH 4 CO 3 and NH 4 Cl, respectively.Tere are fve univariant curves in the diagram in Figures 1(a A comparison of the dry-salt phase diagrams of the quaternary system at 273. 15    ) as the abscissa, as shown in Figures 5 and 6.Te density for point D′ in Figure 6(a) was the calculated data because there was no experimental data.Te column numbers in Table 4 correspond to those in Table 3. Te   Te density and refractive index can be calculated using the empirical equations from the literature [20,21].Te equations used in the calculation were as follows:    Journal of Chemistry ln Te density values of solution and pure water at the same temperature are expressed by ρ and ρ 0 in equation (2).Te ρ 0 of purifed water is 0.9997 g•cm −3 at 283.15 K and 0.9922 g•cm −3 at 313.15 K [22].The n D and n D0 in equation (3) represent the refractive indices of the solution and the pure water.Te n D0 of purifed water is 1.33369 at 283.15 K and 1.33061 at 313.15 K [23].Te coefcients for density and refractive index of the i-th component in the solution were expressed by A i and B i , respectively.According to the above empirical formula, the coefcients A i and B i were ftted to the experimental data, as shown in Table 5. Te 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.Te calculated densities and refractive indices were also tabulated in Table 4. Te 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.Te agreement between the experimental and calculated data shows that the coefcients obtained in this work are reliable.Journal of Chemistry    Journal of Chemistry

Conclusions
Te solid-liquid phase equilibria for the quaternary system (NaCl + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) at 283.15 and 313.15K were studied with the isothermal solution method.Te space phase diagrams were plotted with the experimental solubilities.Tere are four single salt crystallization regions of NaCl, NH 4 Cl, NaHCO 3 , and NH 4 HCO 3 , fve 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.Te area of the four crystallization regions NaHCO 3 , NH 4

3. 1 .
Phase Diagrams at 283.15 K and 313.15 K. Te solubility data in some ternary subsystems of the quaternary system (NaCl + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) at 283.15 and 313.15K were reported in the literature ) and 2(a) with no J (H 2 O) 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-NaHCO 3 -H 2 O, NaCl-NH 4 Cl-H 2 O, NH 4 Cl-NH 4 CO 3 -H 2 O, and NaHCO 3 -NH 4 CO 3 -H 2 O 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 + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) at 283.15 and 313.15K has four crystallization regions corresponding to NaHCO 3 , NH 4 HCO 3 , NaCl and NH 4 Cl, respectively.No solid solution or complex salt was found in the system at 283.15 and 313.15 K. Te water phase diagrams of the system at 283.15 K and 313.15K were shown in Figures 1(b) and 2(b).Te Figures 1(b) and 2(b) shows that the Jänecke index of J (H 2 O) changes regularly with the increase of J (NH 4 + ).
) and 2(a) corresponding to AF 1 (A′F 1 ′) saturated with NaCl and NaHCO 3 , BF 1 (B′F 1 ′) saturated with NaCl and NH4 Cl, F 1 F 2 (F 1 ′F 2 ′′) saturated with NaHCO 3 and NH 4 Cl, F 2 C (F 2 ′C′) saturated with NH 4 Cl and NH 4 HCO 3 , and F 2 D (F 2 ′D′) saturated with NaHCO 3 and NH 4 HCO 3 .Te area of the four crystallization regions NaHCO 3 , NH 4 Cl, NH4 Cl 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 NaHCO 3 , which indicates NaHCO 3 can be easily crystallized from the solution.Te J (H 2 O) changes regularly as the concentration changes in diferent curves.Te concentration of salts can be roughly judged from the changing tendency of J (H 2 O) in diferent curves.

a 4 +) 3 −)
Standard uncertainties u are u (T) � 0.1 K, u (p) � 0.005 MPa, u r (Na + ) � 0.003, u r (NH � 0.003, u r (Cl − ) � 0.003, and u r (HCO � 0.003.b w, Mass fraction, c A: NH 4 Cl, S: NaCl, AB: NH 4 HCO 3 , SB: NaHCO 3 . density and refractive index change regularly as J (NH 4 + ) changes in diferent univariant curves.Te density curves in Figure 5(a) is the similar to those in Figure 6(a).Te density decreases from A (A′) to C (C′) as 100 J (NH 4 + ) increases, with the maximum data at point A (A′) and the minimum data at point C (C′).Te refractive indices are more complicated in Figures 5(b) and 6(b).Te refractive index increases from A to F 1 in Figure 5(b), reaching the maximum data at point F 1 .From F 1 to F 2 , the refractive index decreases frstly and then increases.Te refractive indices show a downward trend from F 2 to C. In the curve DF 2 , the refractive index increases sharply from 1.3609 to 1.3926, with the minimum data at point D. Te changing regularity for the refractive index in Figure 6(b) is a little diferent from those in Figure 5(b).Te minimum value is at point D in Figure 5(b) but at point A′ in Figure 6(b).Te maximum refractive index is at point F 1 , almost the same as point F 2 in Figure 5(b).However, the refractive index has the maximum value at point F 2 in Figure 6(b).Te diference in the density and
Cl, NH 4 Cl, and NaCl decreases in sequence.A comparison of the phase diagrams at 283.15 and 308.15K shows that the areas of the regions for NaCl, NaHCO 3 , and NH 4 Cl increase obviously, and the area of the NH 4 HCO 3 region decreases signifcantly with temperature increasing from 283.15 to 313.15 K. Te J (H 2 O), density, and refractive index change regularly as J (NH 4 + ) changes in diferent univariant curves.Te calculated densities and refractive indices in the quaternary system at two temperatures with the empirical equations were in agreement using the experimental values.Tese results on the phase diagram of (NaCl + NH 4 Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) can provide a theoretical basis for the recovery and utilization of sodium bicarbonate in the production industry of sodium carbonate.
Cl + NaHCO 3 + NH 4 HCO 3 + H 2 O) at 283.15 K and 313.15K were presented.Te phase diagram and physicochemical property diagrams were plotted.
2.1.Reagents and Instruments.Te chemicals NaCl, NH 4 Cl, NaHCO 3 , and NH 4 HCO 3 used in the experiments were all of the analytical grade, as shown in Table

Table 2 :
Te comparison of solubility data of ternary systems at 283.15 K, 313.15 K, and 0.1 MPa a .

Table 1 :
Reagents used in this work.Figure4shows that the areas of the regions for NaCl, NaHCO 3 , and NH 4 Cl increased obviously, whereas the area of the NH 4 HCO 3 region decreased signifcantly with the increase in temperature from 283.15 to 323.15 K. Te separation of NaHCO 3 at high temperatures and recovery of NH 4 HCO 3 at low temperatures can be sufciently productive.Te change in crystallization area can provide theoretical data for the separation and purifcation of sodium bicarbonate.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 Table4at two temperatures, the density and refractive index diagrams of the system at 283.15 K and 313.15K were plotted with 100 J (NH 4 +

Table 4 :
Physicochemical properties in the quaternary system (NaCl + NH

Table 5 :
Te ftting parameters of the refractive and density at 283.15, 313.15 K, and 0.1 MPa a .