Phase Equilibria in Multicomponent WaterâSalt Systems - Journal of

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Phase Equilibria in Multicomponent Water−Salt Systems Sherali Tursunbadalov* Department of Chemistry, Faculty of Natural and Applied Sciences, Nigerian Turkish Nile University, Plot 681, Cadastral Zone C-OO, Research & Institution Area, FCT Abuja 900001, Nigeria

Lutfullo Soliev Department of General and Inorganic Chemistry, Faculty of Chemistry, Tajik State Pedagogical University, Rudaki 121, 734003 Dushanbe, Tajikistan ABSTRACT: The translation method of determining phase equilibria and construction of phase diagrams for multicomponent systems was applied to investigate the phase equilibria in two quaternary Na, NH4//SO4, Cl−H2O (at 100 °C, 10 °C) and Na2SO4−K2SO4−MgSO4−H2O (at 35 °C) and three quinary Li, K//Cl, CO3, B4O7−H2O (at 0 °C), Na, K//Cl, SO4, B4O7−H2O (at 50 °C), and Na, K//Cl, CO3, B 4 O 7 − H 2 O (at 25 °C) water−salt systems. The comprehensive closed phase equilibria diagrams for each of the systems were constructed at the relevant temperatures. The constructed diagrams for the quinary systems were fragmented into trivariant crystallization volumes for each of the available individual solid phases in the systems. The available experimental results on each of the three investigated quinary systems compose only a portion of the phase equilibria data obtained by us using the techniques of translation method. Comparison of our results with the available literature data for the two quinary Li, K//Cl, CO3, B4O7−H2O (at 0 °C) and Na, K//Cl, SO4, B4O7 − H2O (at 50 °C) systems shows agreement. The “translation method” which is comprehensively described in the literature,7,8 was derived from the latter third principle of the physicochemical analysis and functions in accordance with Gibbs’ phase rule. The method which is employed for the determination of phase equilibria and construction of closed equilibria phase diagrams for multicomponent systems substantially alleviates the hardships in phase equilibria studies of multicomponent systems.

1. INTRODUCTION While the multicomponent systems are studied by eliminating existing phases in systems, the vagueness about the rest of the system remains without elucidation. In study of phase equilibria in Na+, NH4+//SO42−, HCO3−, Cl −−H2O; Na+, Mg2+, K+// SO42−, B4O72−−H2O; and Li+, Na+, K+//CO32−, B4O72−−H2O systems, the NaHCO3, MgB4O7·9H2O, and Li2CO3 phases were eliminated, respectively.1−3 However, the phase equilibria beyond the eliminated solid phases have been neither observed nor properly investigated. If the case is like this even in quinary systems, more complex systems are beyond the capabilities of most of the phase equilibria investigations. The prominent Russian scientist Nikolai Semenovich Kurnakov4 has significantly contributed to the development of theoretical and experimental investigations of multicomponent systems. The two basic “consistency” and “continuity” principles,5 as well as the subject and tasks of the physicochemical analysis, were formulated by him. As had been observed by Kurnakov, the geometrical figures of the subsystems extend into the composition of the global system by the addition of a new component.5 Later, the third compatibility principle was proposed by Goroshchenko6 as a theoretical justification of Kurnakov’s latter observation. Every geometrical figure of diagrams of subsystems and the overall system is involved in the phase diagram of the global composition according to the compatibility principle. © XXXX American Chemical Society

2. DETERMINATION OF PHASE EQUILIBRIA IN MULTICOMPONENT WATER−SALT SYSTEMS USING TRANSLATION METHOD The method involves three main “through, unilateral and intermediate”7,8 techniques which are employed in this section in the investigation of three different quaternary cases. The selected systems are among the experimentally studied ones,9−11 hence enabling comparison of results obtained by the translation method. Each case was chosen to show a different technique of the method. 2.1. Phase Equilibria in the Quaternary Na, NH4//SO4, Cl−H2O System at 100 °C. To predict the phase equilibria and construct a “schematic phase equilibria diagram”12 for the Na, NH4//SO4, Cl−H2O system at 100 °C only “through Received: October 15, 2015 Accepted: June 13, 2016

A

DOI: 10.1021/acs.jced.5b00875 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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translation” is required. The term schematic is entitled to show the absence of the coordinate axes in diagrams. The data on ncomponent subsystems are used for the investigation of the (n + 1)-component system using the translation method. The system is composed of the following four ternary systems: Na2SO4−NaCl−H2O, (NH4)2SO4−NH4Cl−H2O, Na2SO4− (NH4)2SO4−H2O, and NaCl−NH4Cl−H2O subsystems. The following equilibrium solid phases occur in the system at 100 °C: Na2SO4−thenardite (Tn), NaCl−halite (Hal), (NH4)2SO4 (A), and NH4Cl (B). The title system is characterized with the presence of four ternary invariant points and their relevant equilibrium solid phases in Table 1.13

rule at the (n + 1)-component global system. The only condition is that the translating points must vary from each other by one solid phase and locate in different n-component subsystems. Following the determination of the points at the (n + 1)-component composition, the required curves which extend between the points are determined. Four quaternary monovariant curves which are generated from the transformation of the relevant ternary invariant points intersect to generate two quaternary invariant points with the equilibrium solid phases in:

Table 1. Ternary Invariant Points and Their Respective Equilibrium Solid Phasesa in the Quaternary Na, NH4//SO4, Cl−H2O System at 100 °C13

The equilibrium solid phase compositions of subsystem (ternary in this case) invariant points that are translated to the global (quaternary in this case) composition reflect the equilibrium solid phase compositions of the latter type of curves. The equilibrium solid phases of invariant points presented in Table 1 and thereafter show also the composition of the relevant monovariant curves that are generated from them. Because the determined two E41 and E42 quaternary invariant points in eq 1 vary from each other by one equilibrium solid phase, the monovariant curve with equilibrium solid phases in the following correlation extends between them:

ternary system

invariant point

equilibrium solid phases

Na2SO4−(NH4)2SO4−H2O (NH4)2SO4−NH4Cl−H2O NaCl−NH4Cl−H2O Na2SO4−NaCl−H2O

E31 E32 E33 E34

Tn + A A+B Hal + B Tn + Hal

E13 + E 32 → E14 = A + B + Tn;

E33 + E34 → E 24 = Hal + Tn + B

(1)

a

Also the equilibrium solid phases at the quaternary monovariant curves which generate from the relevant ternary invariant points.

The capital letter “E” in Table 1 and thereafter denotes an invariant point, whose subscript and superscript indicate the serial number and the multiplicity (system complexity) of the point, respectively. The ternary level phase equilibria diagram of the system at 100 °C is shown as an unfolded prism in Figure 1 and is constructed according to the data in Table 1.

Since the obtained phase equilibria knowledge is employed in the internal part of the diagram in Figure 1, the final version of the phase equilibria diagram of the quaternary Na, NH4//SO4, Cl−H2O system at 100 °C is shown in Figure 2.

Figure 2. Schematic phase equilibria diagram of quaternary Na, NH4// SO4, Cl−H2O system at 100 °C constructed by translation method.

In Figure 2 the four divariant fields reflect the individual crystallization fields where a solid phase is in equilibrium with a relevant saturated solution. The five monovariant curves reflect the state of equilibrium, where two solid phases are in equilibrium with a relevant saturated solution. The two invariant points reflect the state of equilibrium, where three solid phases are in equilibrium with a relevant saturated solution. The monovariant curves are classified into two types: the curves that are formed on the (n + 1)-component level and the curves that are formed as a result of transformation of points at the n-component subsystems. In Figure 2 and thereafter throughout the diagrams and fragmentation segments of the present work, every thin solid curve belongs to the ncomponent subsystems (ternary in this case) and every dashed

Figure 1. Expansion of quaternary Na,NH4//SO4,Cl−H2O system phase diagram at 100 °C on the ternary level.

The approximate locations of invariant points in Figure 1 and thereafter are determined based on the solubility of the complexes at the relevant points. The through translation is accomplished when two or more points at the different ncomponent subsystems transform into the curves of the (n + 1)-component global composition and mutually intersect with each other. This intersection leads to the generation of invariant points which meet the requirements of Gibbs’ phase B



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translation of the latter E34 ternary point along with the NH4Cl phase:

and thick solid curve belongs to the (n + 1)-component overall system (quaternary in this case). Our obtained results on the Na, NH4//SO4, Cl−H2O system at 100 °C agree with the experimental data presented by Zhang et al.9 2.2. Phase Equilibria in the Quaternary Na, NH4//SO4, Cl−H2O System at 10 °C. The system is characterized with the presence of ternary invariant points with their relevant equilibrium solid phases shown in Table 2.13 There are five equilibrium solid phases: Na2SO4·10H2O−mirabillite (Mb), NaCl−halite (Hal), (NH4)2SO4 (A), NH4Cl (B), and Na2SO4· (NH4)2SO4·4H2O (C) in the system at 10 °C.

E34 + B → E34 = Mb + C + B

(4)

The final version of the phase equilibria diagram of the system at 10 °C is shown in Figure 4.

Table 2. Equilibrium Solid Phasesa at the Ternary Invariant Points of the Quaternary Na, NH4//SO4, Cl−H2O System at 10 °C13 ternary system

invariant point


(NH4)2SO4−NH4Cl−H2O NaCl−NH4Cl−H2O Na2SO4−NaCl−H2O Na2SO4−(NH4)2SO4−H2O

E31 E32 E33 E34 E35

A+B Hal + B Mb + Hal Mb + C C+A

Figure 4. Schematic phase equilibria diagram of the Na, NH4//SO4, Cl−H2O system at 10 °C constructed by translation method.

a


An unfolded prism form of the ternary level phase equilibria diagram shown in Figure 3 for the quaternary Na, NH4//SO4, Cl−H2O system at 10 °C is constructed according to the data in Table 2.

The system involves five fields, seven curves, and three points on the quaternary level. Five out of seven curves are generated as a result of translation of ternary invariant points. Because the determined quaternary E41 point varies from E43 by one solid phase and point E43 varies from E42 by one solid phase, the monovariant curves with relevant equilibrium solid phases in eq 5 extend between the latter pairs of quaternary points: The same number of geometrical figures, seven quaternary monovariant curves and three quaternary invariant points, were detected experimentally9 in the system, which shows the reliability of our obtained results. The composition of the system at 10 °C is more complex than it is at 100 °C due to the formation of a fifth Na2SO4· (NH4)2SO4·4H2O phase. Hence, the number of geometrical figures increases proportionally since there are two invariant points at 100 °C and three points at 10 °C. Five curves were determined at 100 °C, whereas seven curves exist at 10 °C of the systems. In order to complete the phase equilibria data and construct a closed schematic phase equilibria diagram of the system, the only through translation was adequate at 100 °C, whereas along with the through translation of the four ternary invariant points there is also need for the unilateral translation of one of the ternary points to the higher quaternary composition. 2.3. Phase Equilibria in the Quaternary Na2SO4− K2SO4−MgSO4−H2O System at 35 °C. The system is composed of the three ternary subsystems: Na2SO4−MgSO4− H2O, MgSO4−K2SO4−H2O, and K2SO4−Na2SO4−H2O. The systems are characterized with the invariant points and their relevant equilibrium solid phases shown in Table 3.13 There are six equilibrium solid phases in the system at 35 °C: MgSO4· 7H2O−epsomite (Eps); Na2SO4−thenardite (Tn); K2SO4− arcanite (Ar); K2SO4·MgSO4·6H2O−shenite (Sch); 3K2SO4· Na2SO4−glaserite (Gs); Na2SO4·MgSO4·4H2O−astrakhanite (Ast).

Figure 3. Expansion of the Na, NH4//SO4, Cl−H2O quaternary system phase diagram at 10 °C on the ternary level.

The through translation of four ternary points generates the two E41 and E42 quaternary points with their equilibrium solid phases in: E13 + E35 → E14 = A + B + C;

E 32 + E33 → E 24 = Hal + Mb + B

(3)

The ternary invariant point which does not find its pair from the other subsystems is translated by “unilateral translation” to quaternary composition. One more quaternary point E43 with the relevant equilibrium solid phases in the following correlation is generated as a result of unilateral E34

C



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Table 3. Ternary Invariant Points and Relevant Equilibrium Solid Phasesa in the Quaternary Na2SO4−K2SO4−MgSO4− H2O System at 35 °C13 ternary system

invariant point


MgSO4−Na2SO4−H2O

E31 E32 E33 E34 E35 E36

Eps + As As + Tn Tn + Gs Gs + Ar Ar + Sch Sch + Eps

Na2SO4−K2SO4−H2O K2SO4−MgSO4−H2O a


Figure 6. Schematic phase equilibria diagram of the Na2SO4−K2SO4− MgSO4−H2O system at 35 °C constructed by translation method.

The ternary level phase equilibria diagram shown as an unfolded prism in Figure 5 is constructed based on the data in Table 3.

Thus, the quaternary Na2SO4−K2SO4−MgSO4−H2O system at 35 °C is characterized with four invariant points, nine monovariant curves, and six divariant fields which are in agreement with experimentally obtained results.10,11

3. PHASE EQUILIBRIA IN QUINARY WATER−SALT SYSTEMS In this section three different quinary systems whose complexity grows from first to the third are investigated using through translation technique. The systems had previously been studied experimentally with regard to specific solid phases,14−16 whereas our investigations of these quinary systems by translation method lead to the comprehensive phase equilibria knowledge on the systems. Although the conditions, the temperatures per se for the systems are presented; the main emphasis in this section is the composition of the systems and the structures of their relevant phase diagrams. 3.1. Phase Equilibria in the Quinary Li, K//Cl, CO3, B4O7−H2O System at 0 °C. This system is a subsystem of salt lake brines in different parts of the world.17 The Li2CO3 saturated part of system was previously obtained by Wang et al.14 We have investigated the comprehensive phase equilibria in the system at 0 °C using the translation method. It involves five quaternary subsystems: Li, K//Cl, CO3−H2O; Li, K//CO3, B4O7−H2O; Li, K//Cl, B4O7−H2O; Li//Cl, CO3, B4O7−H2O; K//Cl, CO3, B4O7−H2O. Six equilibrium solid LiCl·H2O (L1), KCl (KC), LiBO2·8H2O (LB8), K2B4O7·4H2O (KB4), Li2CO3 (LC), and K2CO3·1.5H2O (K1.5) phases occur in the system at 0 °C. The data which are obtained using the translation method are shown in Table 4.

Figure 5. Expansion of the quaternary Na2SO4−K2SO4−MgSO4−H2O system phase diagram at 35 °C on the ternary level.

All six ternary points are translated by through translation to the quaternary composition. The monovariant curves which are formed as a result of transformation of ternary invariant points into quaternary curves generate the three quaternary invariant points in eq 6:

Table 4. Equilibrium Solid Phases at the Quaternary Invariant Points in the Li, K//Cl, CO3, B4O7−H2O System at 0 °Ca

Since the three fields for astrakhanite, scheirerite and glaserite are not enclosed on the quaternary level, the intermediate E44 point with equilibrium solid phases in the following correlation is found to enclose the diagram on the quaternary level. E44 = As + Gs + Sch

quaternary system Li, K//Cl, CO3−H2O Li, K//CO3, B4O7−H2O

(7)

Hence, the three quaternary monovariant curves with relevant equilibrium solid phases in eq 8 extend between the determined four quaternary points:

Li, K//B4O7, Cl−H2O LiCl−Li2CO3−Li2B4O7−H2O KCl−K2CO3−K2B4O7−H2O

The implementation of all these phase equilibria findings is shown on the diagram in Figure 6.

invariant point


E41 E42 E43 E44 E45 E46 E47 E48

L1 + LC + KC K1.5 + LC + KC K1.5 + LC + KB4 LB8 + LC + KB4 LB8 + KC + KB4 LB8 + KC + L1 L1 + LC + LB8 KC + K1.5 + KB4

a

Also the equilibrium solid phases at the quinary monovariant curves which generate from relevant quaternary invariant points.

D



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Figure 7. Development of the salt part of the quinary Li, K//Cl, CO3, B4O7−H2O system phase diagram at 0 °C on the quaternary level.

Two of the quaternary; Li//Cl, CO3, B4O7−H2O and K//Cl, CO3, B4O7−H2O − H2O subsystems at 0 °C are simple eutonic ones with a single invariant point each. Observe that there are two invariant points in each of three Li, K//Cl, B4O7−H2O; Li, K//CO3, B4O7−H2O; and Li, K//Cl, CO3−H2O subsystems at 0 °C. The quaternary level diagram shown as an unfolded prism in Figure 7 is constructed according to the data in Table 4. The “transition diagram” in Figure 8 is obtained following the unification of individual solid phase regions in Figure 7. The

E 24 + E34 + E84 → E15 = KC + LC + K1.5 + KB4

(9a)

E14 + E64 + E 74 → E52 = L1 + KC + LC + LB8

(9b)

E44 + E54 → E53 = KB4 + LB8 + LC + KC

(9c)

E51

As the quinary invariant point varies from the E53 point and the E53 invariant point varies from the E52

invariant invariant point by one equilibrium solid phase; two quinary monovariant curves with relevant equilibrium solid phases in eq 10 extend between them: These phase equilibria findings are implemented on the transition diagram in Figure 8 to produce the final version of the phase equilibria diagram in Figure 9. In Figure 9 12 thin solid lines represent quaternary curves whereas eight dotted curves represent quinary curves which are generated from the translation of quaternary points to the overall composition. The total number of quinary curves in the system thus becomes 10, where eight are generated from the translation of quaternary points to the quinary level and two more are the latter two curves in eq 10 extending between the determined quinary points. 3.2. Phase Equilibria in the Quinary Na, K//Cl, SO4, B4O7 − H2O System at 50 °C. The part of the system saturated with Na2B4O7·10H2O phase was previously studied by Sang et al.15 The comprehensive phase equilibria data for this quinary Na, K//Cl, SO4, B4O7 − H2O system at 50 °C are required to exploit the resources of salt lakes.17 The following seven equilibria, NaCl (NC), KCl (KC), 3K2SO4·Na2SO4 (GS), Na2B4O7·10H2O (NB10), K2B4O7·4H2O (KB4), K2SO4 (KS), and Na2SO4 (NS), solid phases occur in the system at 50 °C. The system involves the Na, K//Cl, SO4−H2O; Na, K//SO4, B4O7−H2O; Na, K//Cl, B4O7−H2O; Na//Cl, SO4, B4O7− H2O; and K//Cl, SO4, B4O7−H2O quaternary subsystems. There are two invariant points in the Na, K//Cl, B4O7−H2O system at 50 °C. The two K//Cl, SO4, B4O7−H2O and Na //Cl, SO4, B4O7−H2O quaternary systems at 50 °C are simple

Figure 8. Transition phase equilibria diagram constructed by translation method for the quinary Li, K//Cl, CO3, B4O7−H2O system at 0 °C.

separate segments of the transition diagrams in Figure 8 and thereafter complete the surfaces of the prisms which represent the composition of relevant quinary systems on the quaternary level. The two E51 and E52 quinary invariant points in eqs 9a and 9b, respectively, are produced by the triple translation, and the E53 point in eq 9c is produced by double translation of the quaternary points to the quinary composition of the system. E



Article 4 E54 + E64 + E10 → E15 = KC + NB10 + KS + KB4

(11a)

E14 + E 24 + E84 → E52 = NC + GS + NS + NB10

(11b)

E34 + E 74 → E53 = NB10 + GS + NC + KC

(11c)

E44 + E 94 → E54 = NB10 + KS + GS + KC

(11d)

There are three quinary monovariant curves with relevant equilibrium solid phases in eq 12 extending between the determined four quinary invariant points.

The total number of quinary monovariant curves becomes 13 curves, 10 of which were generated as a result of translation of 10 quaternary invariant points to the quinary composition and the latter three in eq 12 which extended between the determined quinary invariant points. These findings are employed on the “transition phase equilibria diagram” in Figure 11 which is obtained as a result of combination of identical crystallization fields of quaternary subsystems in unfolded prism in Figure 10. The final version of the schematic phase equilibria diagram of the quinary Na, K//Cl, SO4, B4O7−H2O system at 50 °C is shown in Figure 12. This system is more complex than the previous quinary system as it involves four points and 13 curves whereas the previous one had three points and 10 curves on the global composition. 3.3. Phase Equilibria in the Quinary Na, K//Cl, CO3, B4O7−H2O System at 25 °C. This system is considered as an important part of salt lake brines due to its valuable solid phases.17 Although the KCl saturated part of the system had been studied by Zeng et al.,16 it still lacks comprehensive phase equilibria knowledge at 25 °C. There are eight, NaCl (NC), KCl (KC), Na2CO3·K2CO3·6H2O (NK6), Na2B4O7·10H2O (NB10), K 2 B4 O 7 ·4H 2O (KB4), K2 CO 3 ·1.5H 2 O (K1.5), Na2CO3·10H2O (N10), and Na2CO3·7H2O (N7), equilibrium solid phases in the system at 25 °C. The system comprises the following five quaternary subsystems: Na, K//Cl, CO3−H2O; Na, K//CO3, B4O7−H2O; Na, K//Cl, B4O7−H2O; Na //Cl, CO3, B4O7−H2O; K//Cl, CO3, B4O7−H2O. Two of the quaternary subsystems have been studied experimentally.18 The quaternary Na, K//Cl, CO3−H2O system was investigated by Blasdale.19 The author has determined four quaternary points and two quaternary curves with the (Na2CO3·10H2O + KCl) and (NaKCO3·6H2O + KCl) equilibrium solid phases. The Na, K//Cl, B4O7−H2O quaternary18 system was studied from 20 to 60 °C with intervals of 10 °C where the authors gave equilibrium solid phase compositions for the two invariant points and two more monovariant curves. Their presented data on the system show that the composition of the system does not change between 20 and 50 °C; hence we have used the same data for the 25 °C analysis. We have predicted the phase equilibria in three Na// Cl, CO3, B4O7−H2O, K//Cl, CO3, B4O7−H2O, and Na, K// CO3, B4O7−H2O remaining subsystems by the translation method using the data on their relevant ternary subsystems.13 The data available in the literature and complemented by

Figure 9. Phase equilibria diagram constructed by translation method for the quinary Li, K//Cl, CO3, B4O7−H2O system at 0 °C.

systems with a single point each. The two Na, K//Cl, SO4− H2O and Na, K//SO4, B4O7−H2O systems at 50 °C each involve three points. We have determined the phase equilibria in the Na, K//SO4, B4O7−H2O system at 50 °C using the translation method. Table 5 presents data taken from the Table 5. Equilibrium Solid Phases at the Quaternary Invariant Points in the Na, K//Cl, SO4, B4O7−H2O System at 50 °Ca quaternary system Na, K//Cl, SO4−H2O

Na, K//SO4, B4O7−H2O

Na, K// Cl, B4O7−H2O NaCl−Na2SO4−Na2B4O7−H2O KCl−K2SO4−K2B4O7−H2O

invariant point


E42 E43 E44 E48 E49 E410 E46 E47 E41 E45

NC + NS + GS NC + KC + GS KC + KS + GS NB10 + NS + GS NB10 + KS + GS NB10 + KS + KB4 KB4 + KC + NB10 NB10 + KC + NC NC + NS + NB10 KC + KS + KB4

a

Also the equilibrium solid phases at the quinary monovariant curves which generate from the relevant quaternary invariant points.

available literature18 for four of the subsystems and the data complemented for the Na, K//SO4, B4O7−H2O quaternary system using the translation method. The schematic phase equilibria diagrams for each of the quaternary subsystems are constructed according to the data in Table 5 and associated as an unfolded prism in Figure 10. Four quinary invariant points in eqs 11a−11d are generated by means of through translation of 10 available quaternary points in the Na, K//Cl, SO4, B4O7−H2O system at 50 °C. Two quinary E51 and E52 points in eqs 11a and 11b, respectively, are generated as a result of triple translation, whereas two quinary E53 and E54 points in eqs 11c and 11d, respectively, are generated as a result of double translation of quaternary points. F



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Figure 10. Development of the salt part of the quinary Na, K//Cl, SO4, B4O7−H2O system phase diagram at 50 °C on the quaternary level.

Table 6. Equilibrium Solid Phases at Quaternary Invariant Points in the Na, K//Cl, CO3, B4O7−H2O System at 25 °Ca quaternary system Na, K//Cl, B4O7−H2O Na, K//CO3, B4O7−H2O

Na, K//Cl, CO3−H2O

Figure 11. Transition phase diagram of the quinary Na, K//Cl, SO4, B4O7 − H2O system at 50 °C constructed by the translation method.

NaCl−Na2CO3−Na2B4O7−H2O KCl−K2CO3−K2B4O7−H2O

invariant point


E43 E42 E45 E46 E47 E48 E49 E410 E411 E412 E44 E41

NB10 + NC + KC NB10 + KC + KB4 N10 + KB4 + NB10 N10 + N7 + KB4 NK6 + N7 + KB4 NK6 + K1.5 + KB4 NK6 + K1.5 + KC NK6 + N7 + KC N10 + N7 + KC N10 + NC + KC N10 + NC + NB10 KC + K1.5 + KB4

a

Also the equilibrium solid phases at the quinary monovariant curves which generate from the relevant quaternary invariant points.

The schematic phase equilibria diagrams for the quaternary subsystems are constructed according to the data in Table 6 and arranged in the form of an unfolded prism in Figure 13. As it was done in the previous two quinary systems, the reciprocally relevant quaternary diagrams are arranged to render the composition of the system on the quaternary level. The transition phase equilibria diagram in Figure 14 is obtained when common crystallization fields in quaternary diagrams are combined. Five quinary invariant points in eqs 13a−13e are produced as quaternary invariant points in different subsystems transform into quinary curves and combine on the overall composition. Two of these quinary points in eqs 13a and 13b are generated as a result of triple translation, and three points in eqs 13c−13e are generated as a result of double translation of quaternary points.

Figure 12. Phase equilibria diagram of the Na, K//Cl, SO4, B4O7 − H2O system at 50 °C constructed by the translation method.

translation method for the latter three subsystems at 25 °C are presented in Table 6.

E14 + E84 + E 94 → E15 = NK6 + K1.5 + KB4 + KC (13a) G



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Figure 13. Development of the salt part of the quinary Na, K//Cl, CO3, B4O7−H2O system phase diagram at 25 °C on the quaternary level.

Figure 15. Quinary phase equilibria diagram constructed by translation method for Na, K//Cl, CO3, B4O7 − H2O system at 25 °C.

Figure 14. Transition phase diagram constructed by translation method for Na, K//Cl, CO3, B4O7 − H2O system at 25 °C.

previous first and second quinary systems showed three and four points, respectively.

4 E34 + E44 + E12 → E52 = N10 + NC + NB10 + KC

(13b)

E 24 + E54 → E53 = KB4 + NB10 + N10 + KC

(13c)

4 E64 + E11 → E54 = N10 + KB4 + N7 + KC

(13d)

4 E 74 + E10 → E55 = N7 + KB4 + NK6 + KC

(13e)

4. RESULTS AND DISCUSSION The main limitation of application of translation method is the formation of a new solid phase on the global (n + 1)component composition. Hence the prediction using this method gives the most reliable results for the four- and highercomponent systems, where the probability of the formation of a new solid phase of the quaternary structure is negligible and a phase of five- and higher-component compositions is not real due to the thermodynamic instabilities of phases. Although, the “unilaterally” or “intermediately” generated geometrical figures which are presented in eqs 4 and 7 were not observed in the three quinary systems, these two important; unilateral and intermediate techniques of the method that generate the inevitable and complementary geometrical figures of phase diagrams must be attended soundly. Many examples of unilaterally and intermediately generated geometrical figures can be seen in structures of quaternary diagrams. All three “through, unilateral, and intermediate” techniques of the method were required in prediction of phase equilibria and

Four quinary monovariant curves in the following correlations extend between the determined five quinary invariant points in eqs 13a−13e:

All of these findings are implemented on the transition diagram in Figure 14 to render the comprehensive phase equilibria diagram in Figure 15. The complexity of this system is clearly seen in the obtained diagram in Figure 15 showing five quinary points, whereas the H



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Figure 16. Trivariant crystallization volumes for the individual solid phases: (a) K2B4O7·4H2O, (b) Li2B4O7·4H2O, (c) LiCl·H2O, (d) KCl, (e) K2CO3·1.5H2O, and (f) Li2CO3 in the quinary Li, K//Cl, CO3, B4O7−H2O system at 0 °C.

Figure 17. Trivariant crystallization volumes for individual solid phases: (a) 3K2SO4·Na2SO4, (b) NaCl, (c) K2SO4, (d) KCl, (e) Na2B4O7·10H2O, (f) K2B4O7·4H2O, and (g) Na2SO4 in the quinary Na, K//Cl, SO4, B4O7−H2O system at 50 °C.

results in sections 2 for the quaternary systems agree with the available experimental results in literature. The investigation of quinary systems by translation method has revealed a set of data which unravels the internal structures of the systems whereas the previous experimental results were limited mainly

construction of phase diagrams for the much more complicated quinary Na, K//CO3, HCO3, SO4−H2O system20−23 and many other investigations whose results are available in the literature. Usually, the quaternary water−salt systems do not involve ambiguity as much as the quinary systems, and the obtained I



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Figure 18. Trivariant crystallization volumes for the individual solid: (a) Na2CO3·7H2O, (b) Na2CO3·K2CO3·H2O, (c) Na2B4O7·10H2O, (d) NaCl, (e) K2CO3·1.5H2O, (f) Na2CO3·10H2O, (g) K2B4O7·4H2O, and (h) KC phases in the quinary Na, K//Cl, CO3, B4O7−H2O system at 25 °C.

to the parts saturated with the Li2CO3, Na2B4O7·10H2O and KCl phases. In this section we will emphasize mainly our results obtained in investigation of quinary systems using the translation method. 4.1. Quinary Li, K//Cl, CO3, B4O7−H2O System at 0 °C. This quinary Li, K//Cl, CO3, B4O7−H2O system at 0 °C involves six equilibrium solid phases that generate three invariant points, 10 monovariant curves, and 12 divariant fields on the quinary level. The six trivariant crystallization volumes in Figure 16 for the equilibrium solid phases are extracted from the diagram in Figure 9. The volumes in Figure 16 reflect the schematic structure and composition of the relevant dry-salt diagrams of the systems saturated with relevant equilibrium solid phases. They involve the equivalent number of geometrical figures saturated with the relevant solid phases at 0 °C. This system at 0 °C had previously been investigated by Wang et al.14 They have obtained the projected phase diagram for the system saturated with Li2CO3 phase, where three invariant points, seven monovariant curves, and 5 crystallization fields of the quinary composition were determined. The work by Wang et al. has produced the part of the system which is schematically shown in a crystallization volume in Figure 16f. The geometrical figures, five divariant fields, seven monovariant curves, and three invariant points, saturated with Li2CO3 phase are reflected in Figure 16f, which are equivalent to the results

obtained by Wang et al. In the results of experimental investigation performed by Wang et al., the only part of the system saturated with the Li2CO3 phase was mentioned whereas our obtained volumes in Figure 16 present the internal structure of the system revealing the individual segments where the system is saturated with each of the available equilibrium solid phases. Because the saturation of the quinary Li, K//Cl, CO3, B4O7−H2O system depends on the conditions, the six volumes guide the crystallization and dissolution processes in the system at 0 °C. 4.2. Quinary Na, K//Cl, SO4, B4O7 − H2O system at 50 °C. The quinary Na, K//Cl, SO4, B4O7 − H2O system at 50 °C involves seven equilibrium solid phases that generate four points, 13 curves, and 15 fields on the quinary composition. The seven crystallization volumes in Figure 17 for each of the equilibrium solid phases of the system are extracted from the diagram in Figure 12. These quinary volumes guide one to further investigate the system with regard to equilibrium solid phases and lay the basis of technological extraction of the relevant solid phases from the Na, K//Cl, SO4, B4O7−H2O system at 50 °C. The part of the Na, K//Cl, SO4, B4O7−H2O system at 50 °C saturated with Na2B4O7·10H2O phase had previously been investigated by Sang et al.15 The authors found four invariant points, nine monovariant curves, and six divariant crystallization fields which schematically correspond to the trivariant crystallization volume J



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CO3−H2O subsystem of the same quinary system at 25 °C, which was studied by Blasdale19 and found to involve four quaternary invariant points, which enabled us to construct its schematic closed phase equilibria diagram in Figure 13. The data on which we have relied upon include the one on the latter quaternary Na, K//Cl, CO3−H2O subsystem19 and also the works of Osaka,24 Hill and Miller,25 and Blasdale,19 etc., on the ternary Na2CO3−K2CO3−H2O subsystem at 25 °C. Hence, two more quinary points in dry-salt diagram16 of the system do not exist as they are shown with the involvement of the Na2CO3.H2O. The presented results by Zeng et al. on the phase equilibria in the quinary Na, K//Cl, CO3, B4O7−H2O system at 25 °C hence can be developed accordingly.

in Figure 17e. In Figure 17e, there are corresponding quinary geometrical figures whose equilibrium solid phases are identical with the equilibrium solid phases of the respective geometrical figures in the dry-salt diagram.15 The composition of nine curves which involve the Na2B4O7· 10H2O phase were determined by Sang et al., but the curves without Na2B4O7·10H2O phase were not given due to the restriction of the study to Na2B4O7·10H2O phase. The examination of the phase equilibria diagram in Figure 12 reveals that the four quinary curves, which involve the (NC + NS + GS), (NC + KC + GS), (KC + KS + GS), and (KC + KS + KB4) equilibrium solid phases, exist in the system. These curves are generated as a result of translation of four E42, E43, E44, and E45 quaternary invariant points to the quinary composition where the Na2B4O7·10H2O phase is not involved. Every quinary divariant field in the title system is generated as a result of translation of quaternary monovariant curves to the quinary level as shown in Figure 12. There are six quaternary monovariant curves having the Na2B4O7·10H2O phase and nine more monovariant curves which do not hold this phase making the total number of quaternary monovariant curves 15, and concurrently the total number of quinary divariant fields which will be generated from them are 15 fields. Six of them were determined by Sang et al. whereas the nine remaining were not observed. 4.3. Quinary Na, K//Cl, CO3, B4O7−H2O System at 25 °C. This system is the most complicated among the three investigated quinary systems in this work. There are eight equilibrium solid phases which generate quinary geometrical figures, namely, five points, 16 curves, and 18 divariant fields, shown in Figure 15. Figure 18 presents the crystallization volumes extracted from the diagram in Figure 15 for the existing eight equilibrium solid phases in the system. The KCl saturated part of the systems at 25 °C had been previously investigated by Zeng et al.;16 the obtained results by these authors involve some flaws such as the inconsistency between the sets of concentration ranges and the equilibrium solid phases of relevant precipitates and the discrepancy of obtained results with the Gibbs’ phase rule. The authors of the latter study were prone to conclude on these defective data due to the complexity of the system and the lack of a theoretical basis of investigation of phase equilibria in the system. The volume for the KCl phase is shown in Figure 18h where five invariant points, 11 monovariant curves, and seven divariant fields saturated with the KCl phase are shown, whereas the drysalt diagram given by Zeng et al.16 involves seven invariant points, 14 monovariant curves, and eight divariant crystallization fields saturated with KCl phase. One of the quinary invariant points involving the NaCl + KCl + Na 2 CO 3 ·10H 2 O + Na 2 CO 3 ·7H 2 O solid phase composition does not exist in the dry-salt diagram given by Zeng et al.16 The equilibrium solid phase composition of the latter point is K2B4O7·4H2O + KCl + Na2CO3·10H2O + Na2CO3·7H2O, since its content meets the requirements of Gibbs’ phase rule and since the composition of its liquid phase involves the B4O72− ions as shown by the authors.16 Two invariant points are eliminated due to the nonexistence of the Na2CO3·H2O hydrate in the system at 25 °C. There is more than adequate evidence of the occurrence of Na2CO3 phase in three hydrate forms at 25 °C, Na2CO3·7H2O, Na2CO3·10H2O, and Na2CO3·K2CO3.·6H2O, while no data can be found on the presence of the Na2CO3·H2O hydrate at 25 °C. One piece of evidence of its occurrence is already the quaternary Na, K//Cl,

5. CONCLUSIONS The phase equilibria in the quaternary Na, NH4//SO4, Cl− H2O system at 100 and 10 °C were studied using the through translation and the combination of through and unilateral translation techniques, respectively. The phase equilibria in the quaternary Na2SO4−K2SO4−MgSO4−H2O system at 35 °C were also studied using the through and intermediate translation techniques together. Only the through translation technique was required to comprehensively determine the phase equilibria in three quinary Li, K//Cl, CO3, B4O7−H2O (0 °C); Na, K//Cl, SO4, B4O7 − H2O (50 °C); and Na, K//Cl, CO3, B4O7−H2O (25 °C) systems. The phase equilibria diagrams which involve every existing solid phase and their relevant geometrical figures in the latter three quinary systems were presented. The trivariant crystallization volumes for each of the existing solid phases in quinary systems have been extracted from the obtained diagrams. Our results show that individual segments saturated with solid phases in quinary systems form the structures of dry-salt diagrams of systems saturated with relevant phases. The results obtained by translation method for the two Li, K//Cl, CO3, B4O7−H2O (0 °C) and Na, K//Cl, SO4, B4O7−H2O (50 °C) quinary systems included segments similar to available literature data.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +2348050692118. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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