Crystallization and Dissolution in Multicomponent WaterâSalt Systems

Article pubs.acs.org/jced

Crystallization and Dissolution in Multicomponent Water−Salt Systems Sherali Tursunbadalov* Department of Chemistry, Faculty of Natural and Applied Sciences, Nile University of Nigeria, 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, Dushanbe, Tajikistan ABSTRACT: Phase equilibria in three quinary systems of Li, Na, K, Sr//Cl−H2O at 25 °C, Li, Na, K//SO4, B4O7−H2O at 0 °C, and Na, K, Mg//SO4, B4O7−H2O at 15 °C were investigated by means of translation method. The quinary invariant points, monovariant curves, divariant fields, and trivariant volumes which are saturated with four, three, two, and one solid phases with relevant equilibrium liquid phases, respectively, were determined in each of the systems. Two points, seven curves, and nine fields were determined in the Li, Na, K, Sr//Cl−H2O system at 25 °C. Six points, 18 curves, and 19 fields were found in the Li, Na, K//SO4, B4O7−H2O system at 0 °C. Seven points, 20 one curves, and 20 two fields were determined in the Na, K, Mg//SO4, B4O7−H2O system at 15 °C on the quinary level. The total phase equilibria diagrams of each of the systems were constructed. The constructed diagrams were fragmented into trivariant crystallization volumes of equilibrium solid phases. The obtained volumes reflected the structures of projected diagrams of systems saturated with relevant equilibrium solid phases and involved the recent experimental results on KCl, Li2B4O7 along with Na2B4O7, and MgB4O7·9H2O saturated parts of the quinary systems: Li, Na, K, Sr//Cl−H2O at 25 °C, Li, Na, K//SO4, B4O7− H2O at 0 °C, and Na, K, Mg//SO4, B4O7−H2O at 15 °C, respectively. The obtained results clarified the reciprocal relations of phase conglomerates in the systems comprehensively.

1. INTRODUCTION The determination of conditions of crystallization and dissolution of salts in aqueous multicomponent systems has an exceptional importance for the synthesis of complex inorganic materials besides the extraction of individual compounds. As the multicomponent systems constitute valuable natural resources of chemical manufacturing, the comprehensive utilization of such kind of resources requires theoretical guides particularly phase equilibria knowledge. In this respect, crystallization and dissolution processes which depend mainly on phase equilibria principles are considered as the two main utilization techniques. Crystallization is used at some stage in nearly all processing industries as a method of production, purification, or recovery of solid materials.1 Elucidation of the latter two processes in multicomponent systems is required in most of the extraction processes and valued particularly for the systems with four and more than four component systems due to complexity of the systems. In this study, we present the results of prediction of phase equilibria and construction of total phase diagrams2 for the three Li, Na, K, Sr//Cl−H2O,3 Li, Na, K//SO4, B4O7−H2O4 and Na, K, Mg//SO4, B4O7−H2O5 quinary systems by means of the translation method6 to show possible crystallization−dissolution © 2017 American Chemical Society

pathways in the systems. The processes of crystallization and dissolution of salts in these systems can be identified by the principles of relevant phase equilibria. The latter three systems have recently been investigated with regard to KCl, Li2B4O7 along with Na2B4O7, and MgB4O7·9H2O equilibrium solid phases respectively, as such our investigation will consider the systems comprehensively neither eliminating any of the solid phases nor focusing on a specific phase of interest. The data on n-component subsystems are used in prediction of phase equilibria and construction of total phase diagrams2 for (n + 1)-component systems by means of the translation method.6

2. ASSESSMENT OF QUATERNARY DATA AND DETERMINATION OF QUINARY PHASE EQUILIBRIA The translation method6 is derived from the compatibility principle7 of geometrical figures of n-component subsystems with geometrical figures of (n + 1)-component overall system. It considers the extension of geometrical figures, points, curves, and fields of subsystems into the composition of overall system, and Received: January 29, 2017 Accepted: August 2, 2017 Published: August 18, 2017 3053

DOI: 10.1021/acs.jced.7b00094 J. Chem. Eng. Data 2017, 62, 3053−3063

Journal of Chemical & Engineering Data

Article

the subsequent combination of generated geometrical figures of the overall composition in accordance with Gibbs’ phase rule. In other words, as the geometrical figures of subsystems extend into the composition of overall system they transform into one unit higher dimensional geometrical figures of overall system and combine in accordance with Gibbs’ phase rule. This transformation generates volumes, fields, and curves of the overall composition from the fields, curves, and points of subsystems, respectively. In this section we will compile the available quaternary data and construct transition phase diagrams6 which show the reciprocal phase relations in the investigated three quinary systems. Afterward, the prediction results of quinary phase equilibria and construction of relevant total phase diagrams2 will be presented. The quinary invariant points are generated as the quaternary points extend into the quinary compositions transforming into curves. This extension takes place mainly by “through” and “unilateral translation”6 techniques in the investigated three quinary systems. In “through translation”, invariant points of subsystems extend simultaneously, whereas in “unilateral translation”, a point extends along with a completing solid from another subsystem. The latter simultaneously extending quaternary invariant points vary from each other by one solid phase and situate in different subsystems. As the quaternary invariant points of origin vary from each other by a solid phase, they generate an invariant point which holds four different solid phases and a relevant liquid phase in equilibrium. Following the prediction of phase equilibria in quinary invariant points, the monovariant curves extending between the points are determined where in every operation the Gibbs’ phase rule is obeyed. 2.1. The Quinary Li, Na, K, Sr//Cl−H2O System at 25 °C. The quinary Li, Na, K, Sr//Cl−H2O system comprises the four which are Li, Na, K//Cl−H2O; Li, Na, Sr//Cl−H2O; Na, K, Sr// Cl−H2O, and Li, K, Sr//Cl−H2O quaternary subsystems. There are five LiCl·H2O (Li1); KCl (Syl); NaCl (Hal); SrCl2·6H2O (Sr6); SrCl2·2H2O (Sr2) solid phases in equilibrium in this quinary system at 25 °C. The quaternary phase equilibria data found in literature8−10 and complemented by means of “translation method”6 are given in Table 1. The capital “E” denotes an invariant point with subscript showing serial number and superscript showing the point complexity throughout this work.

fragmentation tables in this work. Likewise, the thin curves in Figure 1 belong to the ternary subsystems, whereas the thick ones and dotted arrows belong to the quaternary systems. The transition phase equilibria diagram6 in Figure 2 is obtained by the combination of common crystallization fields in quaternary diagrams in Figure 1. The overall reciprocal relation of quaternary geometrical figures is reflected on the diagram in Figure 2. The separate segment for SrCl2·2H2O phase completes the surface of the prism which reflects the composition of the quinary system on the quaternary level. The translationthat is, the extension of quaternary invariant points in this systemtakes place by means of the only “through translation”.6 As the quaternary invariant points transform into quinary monovariant curves and extend into the overall composition, they generate the quinary invariant points. This transformation of points and combination of generated curves produces two quinary points in the Li, Na, K, Sr//Cl−H2O system at 25 °C. Table 2 shows the generation of the quinary invariant points along with their relevant equilibrium solid phases produced from the translation of the quaternary points into the overall quinary composition. The two determined quinary E51 and E52 invariant points vary from each other by one equilibrium solid phase, hence the quinary monovariant curve in Table 3, which holds all the three shared equilibrium Hal, Syl, and Sr2 solid phases by both of the points extends between them. The determined quinary geometrical figures (points and curves) were superimposed on the transition diagram in Figure 2 to obtain the total phase diagram in Figure 3. The curves generated from the extension of quaternary points to the quinary composition are shown as dashes, whereas the curve extending between the determined quinary invariant points is shown as a thick curve. The diagram in Figure 3 involves every quaternary and quinary geometrical figure hence considered as a total phase equilibria diagram2 of the quinary Li, Na, K, Sr//Cl−H2O system at 25 °C. 2.2. The Quinary Li, Na, K//SO4, B4O7−H2O System at 0 °C. The quinary Li, Na, K//SO4, B4O7−H2O system involves five quaternary systems which are Li, Na//SO4, B4O7−H2O; Na, κ// SO4, B4O7−H2O; Li, K//SO4, B4O7−H2O; Li2SO4−Na2SO4− K2SO4−H2O and Li2B4O7−Na2B4O7−K2B4O7−H2O subsystems whose equilibrium solid phase compositions are given in Table 4.4 There are eight mirabilite−Na2SO4·10H2O (Mb); arcanite−K2SO4 (Ar); Borax−Na2B4O7·10H2O (NB10); LiBO2· 8H2O (LB8); KLiSO4 (KLS); 3Na2SO4·Li2SO4·12H2O (NL12); Li2SO4·H2O (LS1); K2B4O7·4H2O (KB4), solid phases in equilibrium in this quinary system at 0 °C. The data in Table 4 enable the construction of a set of quaternary phase equilibria diagrams in Figure 4. The quaternary diagrams in Figure 4 are arranged in a way to reflect the composition of the quinary Li, Na, K//SO4, B4O7−H2O system on the quaternary level. The combination of common crystallization fields of quaternary diagrams in Figure 4 produces a transition diagram6 in Figure 5 which reflects the reciprocal relation of quaternary geometrical figures in the system. A separate segment for arcanite in Figure 5 completes the surface of the prism which reflects the composition of the system on quaternary level. The four quinary points given along with relevant equilibrium solid phases in Table 5 are generated by “through translation” in this system. Here, the number of quaternary points participating in generation of the latter quinary invariant points varies as two and three. The first quinary E51 point is generated by triple

Table 1. Equilibrium Solid Phases at the Quaternary Points in Li, Na, K, Sr//Cl−H2O System at 25 °C (Also at the Quinary Curves Which Generate from Relevant Points) system

invariant point

solid phases

Li, Na, K//Cl−H2O Na, K, Sr//Cl−H2O Li, Na, Sr//Cl−H2O

E41 E46 E42 E43 E44 E45

Li1 + Hal + Syl Hal + Sr6 + Syl Hal + Sr2 + Li1 Sr2 + Sr6 + Hal Li1 + Sr2 + Syl Syl + Sr6 + Sr2

Li, K, Sr//Cl−H2O

The quaternary phase equilibria diagrams in Figure 1 were constructed on the basis of data in Table 1. The arrangement is made according to the sides of diagrams that share the same ternary subsystems. The thin curves belong to n-component subsystems, whereas thick ones and dotted arrows belong to (n + 1)-component overall systems throughout diagrams and 3054



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Figure 1. Reciprocal relationship among the quaternary geometrical figures in quinary Li, Na, K, Sr//Cl−H2O system at 25 °C.

Figure 2. Transition phase equilibria diagram of quinary Li, Na, K, Sr// Cl−H2O system at 25 °C from quaternary to quinary composition.

Figure 3. Total phase equilibria diagram of the quinary Li, Na, K, Sr// Cl−H2O system at 25 °C.

Table 2. Generation of Quinary Invariant Points from the Quaternary Original Points along with the Respective Equilibrium Solid Phases at the Quinary Points quaternary points of origin

translation

quinary points and their solid phases

E41 + E42 + E44 E43 + E45 + E46

→ →

E51 = Li1 + Hal + Syl + Sr2 E52 = Sr6 + Hal + Syl + Sr2

Table 4. Equilibrium Solid Phases at Invariant Points of Quaternary Subsystems in Quinary Li, Na, K//SO4, B4O7− H2O System at 0 °C (Also at the Quinary Curves Which Generate from the Points) system Na, K//SO4, B4O7− H2O

Table 3. Solid Phases at Quinary Curve between Quinary Points in the Li, Na, K, Sr//Cl−H2O System at 25 °C quinary points and curve between them E51E52

Li2B4O7−Na2 B4O7−K2 B4O7−H2O Li, Na//SO4, B4O7− H2O

equilibrium solid phases

= Hal + Syl + Sr2 Li, K//SO4, B4O7− H2O

translation, whereas the other three E52, E53, and E54 points are generated by double translation of relevant quaternary points. 4 In this quinary system there are three E24, E44, and E11 quaternary points among which one must extend unilaterally and two others simultaneously by “through translation”. There are two options here: first option, if E42 and E44 points extend 4 simultaneously and generate a quinary point, then the E11 4 quaternary point extends unilaterally; second option, if E4 and E411 points extend simultaneously, then the E42 point extends unilaterally.

Li2SO4−Na2SO4−K2SO4−H2O

point

solid phases

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

NB10 + KB4 + Ar NB10 + Mb + Ar KB4 + NB10 + LB8 LS1 + NL12 + NB10 Mb + NL12 + NB10 LS1 + LB8 + NB10 LS1 + LB8 + KLS Ar + LB8 + KLS Ar + LB8 + KB4 Mb + KLS + NL12 KLS + NL12 + LS1 Mb + Ar + KLS

In determination of quinary points from the latter three E42, E44, and E411 points, the reciprocal relations between the determined quinary geometrical figures were taken into account. The second option mentioned above gives a quinary point with LB8, KLS, Ar, 3055



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Figure 4. Reciprocal relationship among the quaternary geometrical figures in the quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C.

point, with KLS, Ar, Mb, and NB10 phases, that shares three phases with the E54 point. On the other hand, the unilateral translation of E411 point along with NB10 generates a quinary point that links with two of the determined E51 and E52 points and at the same time with the point generated from the simultaneous translation of the latter two E42 and E44 points. The above-mentioned prediction is also in agreement with the results obtained by Zeng et al.4 Each of the six quinary invariant points determined experimentally by Zeng et al. involves the NB10 phase; hence, we have to ensure the presence of the latter phase in generating the fifth and sixth quinary points. The simultaneous translation of E44 and E411 points does not meet this requirement as none of the latter points involves the required NB10 phase. As a result of simultaneous extension of E42 and E44 points and unilateral extension of the remaining E411 point with NB10 phase, we obtain the other two invariant points of quinary composition in eqs 1 and 2.

Figure 5. Transition phase equilibria diagram of the quinary Li, Na, K// SO4, B4O7−H2O system at 0 °C from quaternary to quinary composition.

Table 5. Generation of Quinary Invariant Points from the Quaternary Points by Means of “Through Translation” and Respective Equilibrium Solid Phases at the Quinary Points quaternary points of origin E41 E48 E45 E43

+ + + +

E49 + E410 E46 E47

E412

translation → → → →

(1)

4 E11 + NB10 → E56 = KLS + Ar + LB8 + NB10

(2)

The six curves in Table 6 extend between the pairs of determined six quinary E51, E52, E53, E54, E55, and E56 invariant points that vary by one equilibrium solid phase. The determined quinary geometrical figures were superimposed on transition diagram in Figure 5 to obtain the final version of the quinary phase diagram in Figure 6. 2.3. The Quinary Na, K, Mg//SO4, B4O7−H2O System at 15 °C. This quinary system involves five Na2SO4−K2SO4− MgSO4−H2O; Na2B4O7−K2B4O7−MgB4O7−H2O; K, Mg// SO4, B4O7−H2O; Na, Mg//SO4, B4O7−H2O, and Na, K//

quinary points and their solid phases E51 E52 E53 E54

E 24 + E44 → E55 = KLS + NB10 + Mb + Ar

= KB4 + Ar + LB8 + NB10 = NB10 + LB8 + KLS + LS1 = NL12 + LS1 + KLS + NB10 = Mb + KLS + NL12 + NB10

and Mb phases which will not have linkage with any of the available four E51, E52, E53, and E54 quinary points, whereas the first option where E42 and E44 points extend simultaneously gives a 3056



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Table 6. Equilibrium Solid Phases at Quinary Monovariant Curves Extending between Quinary Points in the Li, Na, K//SO4, B4O7−H2O System at 0 °C quinary points and curves between them E51E56 E52E53

= =


quinary points and curves between them

NB10, LB8, Ar NB10, KLS, LS1

E54E55 E52E56

= =

SO4, B4O7−H2O quaternary subsystems. There are nine MgSO4· 7H2O epsomite (Eps); Na2SO4·10H2O mirabilite (Mb); K2SO4 arcanite (Ar); Na2B4O7·10H2O Borax (NB10); MgB4O7·9H2O hungchaoite (MB9); K2SO4·MgSO4·6H2O schoenite (Sch); Na2SO4·MgSO4·4H2O astrakhanite (Ast); Na2SO4·3K2SO4 glaserite (Gs); K2B4O7·4H2O (KB4) solid phases in equilibrium in this system at 15 °C. The data on three reciprocal K, Mg// SO4, B4O7−H2O;11 Na, Mg//SO4, B4O7−H2O12 and Na, K// SO4, B4O7−H2O13 subsystems are available in literature. As the phase equilibria data on the other two, Na2SO4−K2SO4− MgSO4−H2O and Na2B4O7−K2B4O7−MgB4O7−H2O subsystems are missing at 15 °C, we have determined the phase equilibria in these systems by means of “translation method”6 on the basis of their relevant ternary phase equilibria data.9 Table 7 presents the equilibrium solid phases at the quaternary invariant points in the quinary Na, K, Mg//SO4, B4O7−H2O

Na2B4O7−K2B4O7−MgB4O7−H2O K, Mg//SO4, B4O7−H2O

Na, Mg//SO4, B4O7−H2O

Na2SO4−K2SO4−MgSO4−H2O

point

solid phases

E41 E42 E43 E414 E411 E412 E413 E48 E49 E410 E44 E45 E46 E47

NB10 + KB4 + Ar NB10 + Gs + Ar NB10 + Gs + Mb NB10 + KB4 + MB9 Eps + Sch + MB9 Ar + Sch + MB9 Ar + KB4 + MB9 NB10 + Mb + MB9 Ast + Mb + MB9 Ast + Eps + MB9 Mb + Gs + Ast Gs + Ast + Sch Gs + Ar + Sch Eps + Ast + Sch

NB10, Mb, KLS NB10, KLS, LB8

E53E54 E55E56

equilibrium solid phases = =

NB10, NL12, KLS NB10, Ar, KLS

3. RESULTS AND DISCUSSION The determination of phase equilibria in multicomponent systems by means of the translation method is based on the third principle of physicochemical analysis, which relates the geometrical figures of n-component subsystems with geometrical figures of global (n + 1)-component system along with the Gibbs’ phase rule. The transformation of geometrical figures of subsystems takes place in accordance with the latter principle, whereas the combination of generated geometrical figures on overall system takes place in accordance with the Gibbs’ phase rule. Since finding a suitable representation of total phase diagram in a lower and drawable dimension is a very important step in the construction of meaningful phase diagrams,2 the obtained total diagrams in Figures 3, 6, and 9 can be sliced into lower dimensional figures divariant fields and trivariant volumes. The compositions of quinary invariant points and monovariant curves were presented in the previous sections. In the forthcoming section, to visualize the phase relations in the systems more

Table 7. Equilibrium Solid Phases at Quaternary Points in the Na, K, Mg//SO4, B4O7−H2O System at 15 °C (Also, at the Quinary Curves Which Generate from the Points) system


system at 15 °C. Figure 7 shows the quaternary phase equilibria diagrams of the system which were constructed and compacted for the quinary composition of the system in accordance with the data in Table 7. The transition diagram in Figure 8 which reflects the reciprocal relationship among quaternary geometrical figures is obtained as the common crystallization fields of different quaternary diagrams in Figure 7 are merged together. The separate segment in the latter diagram shown for arcanite completes the surface of prism which reflects the composition of this quinary system on the quaternary level. The figures (curves and points) of the arcanite segment are same geometrical figures involved in the main part of the transition diagram. There are two E56 and E54 quinary invariant points that are generated by triple extension of relevant quaternary invariant points in Table 8. Each of the three E52, E51, and E55 invariant points in Table 9 are generated by extension of two different quaternary invariant points to the overall composition. Two quaternary E42 and E45 invariant points which do not extend by means of “through translation” extend unilaterally along with a completing solid phase from other quaternary subsystems. The quinary invariant E53 and E57 points in Table 10 were determined by “unilateral translation” of latter two points to the quinary composition; Three of equilibrium solid phases of latter type of points belong to the extending quaternary invariant points, and the fourth solid phase is the completing equilibrium solid phase. The curves in Table 11 were determined between the quinary invariant points in Tables 8−10. To create the final version of phase equilibria diagram in Figure 9, the obtained quinary geometrical figures were superimposed on the transition diagram in Figure 8. The diagram in Figure 9 involves every quaternary and quinary geometrical figure in the quinary Na, K, Mg//SO4, B4O7−H2O system at 15 °C.

Figure 6. Total phase equilibria diagram of the quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C.

Na, K//SO4, B4O7−H2O


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Figure 7. Reciprocal relationship among the quaternary geometrical figures in quinary Na, K, Mg//SO4, B4O7−H2O system at 15 °C.

Figure 8. Transition phase equilibria diagram of quinary Na, K, Mg//SO4, 4O7−H2O system at 15 °C from quaternary to quinary composition.

Table 8. Generation of Quinary Points by “Triple through Translation” and Respective Equilibrium Solid Phases at the Generated Points quaternary points of origin

translation


E47 + E410 + E411 E41 + E413 + E414

→ →

E56 = MB9 + Eps + Ast + Sch E54 = KB4 + MB9 + NB10 + Ar

vividly, the obtained total diagrams in Figures 3, 6, and 9 will be fragmented into trivariant volumes saturated with each of the equilibrium solid phases in the systems. Since the volumes are generated as result of extension of relevant divariant fields there is only one solid phase in equilibrium with a relevant liquid phase in trivariant volumes. They reveal the structure of the dry-salt phase diagrams of the 3058



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Table 9. Generation of Quinary Points by “Double through Translation” and Respective Equilibrium Solid Phases at the Points quaternary points of origin

translation


E48 + E43 E44 + E49 E412 + E46

→ → →

E52 = NB10 + MB9 + Gs + Mb E51 = MB9 + Gs + Mb + Ast E55 = MB9 + Eps + Ar + Gs

Table 10. Generation of Quinary Points by “Unilateral Translation” and Respective Equilibrium Solid Phases at the Points quaternary points E42 E45

completing phase + +

MB9 MB9

quinary points and their solid phases → →

E53 = NB10 + MB9 + Gs + Ar E57 = MB9 + Ast + Sch + Gs

systems saturated with the respective solid phases and crystallization−dissolution sequences can be traced within the relevant volumes, where every geometrical figure (point, curve, and field) is saturated with relevant phases depending on the saturation conditions of the solutions. There are two types of quinary divariant fields the fields that are generated as a result of extension of quaternary curves and the fields that are created within the quinary geometrical figures. Quinary divariant fields are saturated with two different solid phases along with a relevant equilibrium liquid phases. 3.1. The Quinary Li, Na, K, Sr//Cl−H2O System at 25 °C. To expose the internal structure of total phase equilibria diagram of this system in Figure 3, the trivariant crystallization volumes in Figure 10 were extracted from it. The reciprocal arrangement of geometrical figures in latter volumes gives the structures of drysalt diagrams of system saturated with equilibrium solid phases. The work performed by Meng et al.3 generated diagram of the system saturated with KCl. The segment which is saturated with the latter phase is shown in Figure 10e. Table 12 compiles the total number of quaternary and quinary geometrical figures in the Li, Na, K, Sr//Cl−H2O system at 25 °C. 3.2. The Quinary Li, Na, K//SO4, B4O7−H2O System at 0 °C. In individual crystallization volumes in Figure 11, which were extracted from the total phase equilibria diagram of this system in Figure 6, every geometrical figure (point, curve, and field) is saturated with the relevant solid phases. The parts of this system which were experimentally observed and investigated by Zeng et al. are schematically shown in Figure 11e and h. The volume in Figure 11e involves the three quinary points, seven monovariat curves, and five divariant fields saturated with the LiBO4·8H2O, whereas the volume in Figure 11h involves the six quinary points, twelve monovariant curves, and seven divariant fields saturated with the Na2B4O7·10H2O. Each of the respective projected diagrams presented by Zeng et al. involves the same number of geometrical figures and identical

Figure 9. Total phase equilibria diagram of the quinary Na, K, Mg//SO4, B4O7−H2O system at 15 °C.

equilibrium solid phases shown in Figure 11e and h. The reciprocal locations of nearby crystallization phases in the latter volumes in Figure 11e and h are in well agreement with the results of Zeng et al.4 Table 13 compiles the findings in the quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C. 3.3. The Quinary Na, K, Mg//SO4, B4O7−H2O System at 15 °C. There are nine trivariant crystallization volumes in this system at 15 °C which are generated as a result of extension of available equilibrium solid phases into the quinary composition of the system. The volumes in Figure 12 were extracted from the total phase equilibria diagram of the system in Figure 9. The experimentally investigated part of the system by Shi-Hua et al.5 is shown in Figure 12i. The latter segment involves the seven quinary points, fourteen monovariant curves, and eight divariant fields saturated with the MgB4O7·9H2O which are equivalent to the corresponding geometrical figures of the drysalt diagram presented by Shi-Hua et al. The reciprocal locations of nearby crystallizing phases in Figure 12i are in well agreement with the results of Shi-Hua et al. Table 14 compiles the total number of quaternary and quinary geometrical figures in the Na, K, Mg//SO4, B4O7−H2O system at 15 °C. 3.4. Some Features of Geometrical Figures in Multicomponent Water−Salt Systems. 3.4.1. Invariant Points and Monovariant Curves. The invariant points of overall quinary compositions in this study were mainly generated by “through translations” where the points are generated as a result of extension of two or three points of four-component subsystems. The latter two types of simultaneous translations mainly depend on the composition of the systems and relevant structures of phase diagrams of the subsystems. The points which do not extend by “through translations” extend unilaterally where

Table 11. Equilibrium Solid Phases at the Quinary Curves Extending between the Quinary Points in the Na, K, Mg//SO4, B4O7− H2O System at 15 °C quinary points and curves between them E51E52 E52E53 E55E53

= = =



MB9, Gs, Mb NB10, MB9, Gs MB9, Ar, Gs

E55E57 E51E57

= =

3059



MB9, Sch, Gs MB9, Ast, Gs

E53E54 E56E57

equilibrium solid phases = =

MB9, NB10, Ar Ast, Sch, MB9



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Figure 10. (a−e) Trivariant crystallization volumes of equilibrium solid phases in the quinary Li, Na, K, Sr//Cl−H2O system at 25 °C. (a) LiCl·H2O, (b) SrCl·6H2O, (c) NaCl, (d) SrCl·2H2O, (e) KCl.

Table 12. Total Number of Quaternary and Quinary Geometrical Figures in the Li, K, Na, Sr//Cl−H2O System at 25 °C

Table 13. Total Number of Quaternary and Quinary Geometrical Figures in the Quinary Li, Na, K//SO4, B4O7− H2O System at 0 °C

level

quaternary

quinary

level

quaternary

quinary

invariant points monovariant curves divariant fields trivariant volumes

6 9 5

2 7 9 5


12 18 8

6 18 19 8

As it has been observed in this study, the extension of invariant points of subsystems into the overall composition leads to the extension of the other geometrical figures. The extension of curves and fields of n-component subsystems generate the fields and volumes of (n + 1)-component overall composition. The translation method which has undoubtedly achieved a degree of

the extending point completes its composition by a solid phase in another subsystem. The third type of invariant points is required to link the invariant points generated as a result of the latter two “through” and “unilateral translations”. This type of point which is conventionally called intermediate point was not considered in this work.

Figure 11. (a−h) Trivariant crystallization volumes of equilibrium solid phases in the quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C: (a) K2B4O7· 4H2O; (b) 3Na2SO4·LiSO4·12H2O; (c) LiSO4·H2O; (d) Na2SO4·10H2O; (e) LiBO2·8H2O; (f) K2SO4; (g) KLiSO4, and (h) Na2B4O7·10H2O. 3060



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Figure 12. (a−i) Trivariant crystallization volumes of equilibrium solid phases in the quinary Na, K, Mg//SO4, B4O7−H2O system at 15 °C. (a) Na2SO4· MgSO4·4H2O; (b) K2SO4; (c) K2SO4·MgSO4·6H2O; (d) MgSO4·7H2O; (e) K2B4O7·4H2O; (f) Na2B4O7·10H2O; (g) Na2SO4·3K2SO4; (h) Na2SO4· 10H2O; (i) MgB4O7·9H2O.

dimensionality of the space and complicated compositions of the systems. Although the Gibbs diagrams obtained for halite saturated oceanic systems14 are widely used and some sort of eliminations are done in investigations,15 there is no guarantee of such kind of saturation in every multicomponent water−salt system; hence, the parts of the systems saturated with other solid phases are also needed to fully exploit the systems. The fragmentation of obtained total diagrams in Figures 3, 6, and 9 into segments is the response to most of the questions about the systems. The saturation of the parts by each of the available solid phases in the system, nearby crystallization fields in those parts, and paragenetic formation of solid phases from the contents of the systems which show the crystallization pathways during crystallization of the contents of system, among others, are all shown. 3.4.3. Divariant Fields and Trivariant Volumes. There are two types of divariant fields in multicomponent systems: the fields generated as a result of extension of monovariant curves of subsystems to the overall compositions of systems and the fields created on the (n + 1)-component composition by the geometrical figures of this level. Hence, the total number of divariant fields is the sum of these two types of fields in the systems. The second type of field is not observed in simple systems with a few number of equilibrium solid phases. Although one diagram for each quinary Li, Na, K, Sr//Cl− H2O system (at 25 °C) and Na, K, Mg//SO4, B4O7−H2O system (at 15 °C) and two diagrams for the quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C were available in literature for the relevant parts of the systems,1−3 the systems were not characterized in terms of the rest of the equilibrium solid phases. Our study demonstrated the complete sets of phase equilibria

Table 14. Total Number of Quaternary and Quinary Geometrical Figures in Quinary Na, K, Mg//SO4, B4O7−H2O System at 15 °C level

quaternary

quinary


14 21 9

7 21 22 9

maturity classifies the monovariant curves of (n + 1)-component overall systems into two types: the curves generated as a result of extension of invariant points of n-component subsystems and the curves extending between the invariant points of overall system. These two types of curves which have different nature of formation must be considered separately in investigation of multicomponent water−salt systems. The number of the curves which extend between the points of overall composition depends on the nature of formation of points; the curves generated by “triple through”, “double through”, and “unilateral translations” are linked with one, two, and three other invariant points of the overall composition. The intermediate points of the overall composition which were not observed in this work are linked to four invariant points of the overall composition.6 3.4.2. Total Phase Equilibria Diagrams. The schematic diagrams in Figures 3, 6, and 9, which were constructed without elimination of any of the phases in the systems, involve the whole contents of the investigated quinary systems and, hence, are considered as the total phase diagrams of the systems. What is widely used today is the part of the multicomponent water−salt systems saturated with a solid phase which is due to the 3061



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H2O system at 15 °C presenting the total phase equilibria diagrams and unraveling simultaneously the structures of total phase equilibria diagrams of the systems. This study completed the sets of phase equilibria diagrams for the parts of systems saturated with each of the relevant equilibrium solid phases. The five phase equilibria diagrams of quinary Li, Na, K, Sr//Cl−H2O system at 25 °C, eight phase equilibria diagrams of quinary Li, Na, K//SO4, B4O7−H2O system at 0 °C and nine phase equilibria diagrams of quinary Na, K, Mg//SO4, B4O7−H2O system at 15 °C that correspond to the relevant crystallization volumes of equilibrium solid phases were obtained. The obtained phase equilibria diagrams exposed the internal structures of the total phase diagrams more clearly, revealing the individual solid phase regions that can be used to follow the crystallization and dissolution sequences in the systems. The diagrams suggest at the same time the requirements or optionality of the experimental investigation of the systems with respect to each of the equilibrium solid phases. Our results can be used as guides in geochemical investigation and geological observation of mineral ores involving the contents of the quinary Li, Na, K, Sr//Cl− H2O system at 25 °C, Li, Na, K//SO4, B4O7−H2O system at 0 °C, and Na, K, Mg//SO4, B4O7−H2O system at 15 °C. They can also be used as references to understand the physical chemistry of relevant complex mixtures. These results serve as theoretical references in comprehensive utilization and exploitation of these three quinary water−salt systems at the relevant temperatures.

diagrams for the parts of these quinary systems saturated with each of the relevant equilibrium solid phases. Structures of the dry-salt phase diagrams of the systems saturated with each of the equilibrium solid phases have been obtained in Figures 10, 11, and 12. The latter diagrams which were extracted from the relevant quinary diagrams have valued the importance and usage in the field of chemical manufacturing. They can be used in industrial separation processes of individual solid phases from the relevant mixtures. Crystallization and dissolution pathways in the systems follow the sequences reflected in diagrams in Figures 10, 11, and 12 depending on the relevant conditions. The first and last crystallizing solid phases determine the rest of the processes which can be traced on the latter diagrams. The simplified diagrams which do not give quantitative relations but which show common crystallizing phases along with their crystallization sequences are also valued well particularly in physicochemical and mineralogical studies of multicomponent systems. These simplified or as sometimes called qualitative diagrams have great importance in paragenetic investigation of minerals, for example, the observation of laws of their coexistence in rocks.16 3.4.4. Tracking Crystallization Sequences. The obtained results in this work allow one to follow crystallization pathways in the investigated systems at the relevant temperatures. For example, there are nine solid phases in equilibrium in the Na, K, Mg//SO4, B4O7−H2O system at 15 °C. The crystallization volume of the Na2SO4·10H2O is shown in Figure 12h. Let the system be saturated with the latter phase at 15 °C, and the figurative point of the system lies in the field saturated with Na2SO4·10H2O and Na2B4O7·10H2O phases where these two phases crystallize together. In this case, there are three pathways to follow depending on the composition of the preliminary mixture: (i) Toward the curve extending between the E48 and E52 points where the third phase MgB4O7·9H2O will crystallize; afterward, the path follows through the curve toward the quinary E52 point where the fourth phase glaserite Na2SO4·3K2SO4 crystallizes and where the sequence ends. (ii) Toward the curve extending between the E43 and E52 points where the third phase Na2SO4·3K2SO4 will crystallize afterward, the path follows through the curve toward the quinary E52 point where the path ends with the crystallization of fourth phase MgB4O7·9H2O. (iii) The straight direction of crystallization toward the quinary E52 point is also possible, as the third path, where the common crystallization of two Na2SO4·3K2SO4 and MgB4O7·9H2O phases starts. 3.4.5. Future Work. The investigation of the systems studied with respect to some solid phases can be expanded similar to this work and be explored in more vivid details as there is a need for more systematic ways of investigation of water−salt systems.17 Likewise, the three investigated quinary systems in this work for the halite saturated oceanic quinary Na, K, Mg//Cl, SO4−H2O system18,19 along with related multicomponent systems that have been studied both thermodynamically and experimentally can also be investigated with respect to other equilibrium solid phases in the systems by means of the translation method.6

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +2348050692118, e-mail: s.tursunbadalov@ nileuniversity.edu.ng. ORCID

Sherali Tursunbadalov: 0000-0002-2642-3111 Notes

The authors declare no competing financial interest.

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REFERENCES

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4. CONCLUSIONS The obtained results reveal the comprehensive phase equilibria in quinary Li, Na, K, Sr//Cl−H2O system at 25 °C, Li, Na, K// SO4, B4O7−H2O system at 0 °C, and Na, K, Mg//SO4, B4O7− 3062



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Crystallization and Dissolution in Multicomponent WaterâSalt Systems

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