Investigation of Phase Equilibria in Quinary WaterâSalt Systems

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Investigation of Phase Equilibria in Quinary 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: Isothermal methods of investigation of quinary systems and advantages of use of the translation method for investigation of quinary water−salt systems were discussed. Two quinary systemsLi, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2Owere investigated by means of the translation method at 15 and 25 °C, respectively. The comparison showed a good agreement between our results and the available literature data. There are 4 points, 13 curves, and 15 fields saturated with 4, 3, and 2 different equilibrium solid phases, respectively, in Li, Na, K//CO3, B4O7−H2O systems at 15 °C. The quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C involves 5 invariant points, 16 monovariant curves, and 18 divariant fields saturated with 4, 3, and 2 different equilibrium solid phases, respectively. The total phase equilibria diagrams of both of the quinary systems were constructed on the basis of obtained data. The obtained diagrams were fragmented into divariant cocrystallization fields saturated with two different equilibrium solid phases. The trivariant crystallization volumes, which reflect the structures of Jänecke dry-salt phase diagrams of the systems saturated with the relevant phases, were also extracted.

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INTRODUCTION Multicomponent systems compose a considerable part of raw materials for chemical industry. They involve both naturally occurring sources and industrial wastes. The contributions of van’t Hoff in investigation of multicomponent water−salt systems laid the basis of the main trends of studies. He had formulated guidelines in experimental investigation of quinary systems. Although more than a century has passed from the achievements of van’t Hoff, there are still challenges in the investigation of multicomponent systems and quinary water− salt systems per se. These challenges exist due to the number of components in the systems and the resulting large number of solid phases due to interactions of components. Consequently, investigation of quinary systems becomes time-consuming and requires a huge number of experimental trials. The other challenge is representation of the obtained results visually, which is one of the serious problems in the investigation of multicomponent systems. Different techniques are used by the experts to solve this problem. The most popular method is when a triangular prism is used, where the salt part of a quinary system is reflected. Different ways of simplification of systems are also tried, among which the selection of the part saturated with an equilibrium solid phase is considerably popular. In this case, the results are presented as Jänecke projections for the part of the system saturated with the latter solid phase which is eliminated. In the case of the oceanic Na, K, Mg//Cl, SO4−H2O system, two-dimensional Jänecke plots © XXXX American Chemical Society

in a Gibbs’ triangle are in use. With these diagrams, only solubility relations at saturation with NaCl are considered and as the coordinates K22+, Mg2+, and SO4− are chosen, where the relation K2 + Mg + SO4 = 100 holds.1 It is well-known that the water−salt systems holding five components are usually investigated isothermally with respect to some equilibrium solid phases. Obviously, these kinds of studies do not generate comprehensive phase equilibria knowledge of the systems, although they lead to a partial understanding of the system and leave the rest of the system in obscurity. The literature review shows that each of the quinary Li, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2O systems was investigated with respect to a solid phase at 15 and 25 °C, respectively, but total phase equilibria diagram was not obtained for any of the systems so far.2,3 However, the available results of experimental investigations facilitate further study of the systems and lead to more comprehensive knowledge of phase equilibria. In this work, the isothermal methods of investigation of quinary water−salt systems are discussed and results of investigation of two quinary Li, Na, K//CO3, B4O7− H2O and Na, K//Br, SO4, B4O7−H2O systems at 15 and 25 °C, respectively, by means of the translation method4 are presented. Received: September 6, 2017 Accepted: February 12, 2018

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DOI: 10.1021/acs.jced.7b00799 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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METHODOLOGY There are four types of quinary systems which are composed of the following: three cations and two anions, two cations and three anions, one cation and four anions, and four cations and one anion. For the representations of the first two types of quinary systems, the triangular prism in Figure 1 is used,

Figure 3. Space phase diagram of the quinary system Li, K//Cl, CO3, B4O7−H2O at 0 °C.6

Figure 1. Triangular prism used for representation of the salt part of quinary systems, with two cations and three anions and with three cations and two anions.

whereas, for the last two types, the prism in Figure 2 is used. The features of the first two types of quinary systems and the use of a prism in Figure 1 are explained in the literature.5

Figure 4. Space phase diagram of the quinary system Li, K, Rb, Mg// borate−H2O at 75 °C.7

anions, while the second system belongs to the type with four cations and one anion. The first system was investigated by the isothermal evaporation method, whereas the second one was investigated by means of an isothermal dissolution method. As an initial step, the composition of the quaternary invariant point, which involves three different solid phases in equilibrium, is saturated with a new solid phase from another quaternary subsystem at the temperature of investigation of the system. The mixture is thermostated and monitored until the composition becomes constant. The sample obtained at equilibrium is separated into liquid and solid parts. The chemical or instrumental analysis is used for the determination of composition of the liquid phases, while the solid phases are identified by the X-ray diffraction method. As a result of the experimentations of the systems, the values of solubilities, densities of solutions, refractive indices, and composition of equilibrated solid phases in the quinary systems are obtained which leads to the determination of Jänecke indices and relevant Jänecke projections along with space phase diagrams for the systems. While the space phase diagrams in Figures 3 and 4 were obtained as a result of isothermal experimental investigation of the systems Li, K//Cl, CO3, B4O7−H2O at 0 °C6 and Li, K, Rb, Mg//borate−H2O at 75 °C,7 the first system was investigated through more than 100 experimental trials that require determination of several of the

Figure 2. Triangular prism used for representation of the salt part of quinary systems, with four anions and one cation and with four cations and one anion.

The salt composition for solubility equilibria at one temperature requires one of the trigonal prisms in Figure 1 and Figure 2 due to the increased dimensionality in quinary systems. In the quinary systems, simultaneous saturation with four, three, two, and one salts provides the isothermal invariant points, monovariant curves, divariant fields, and trivariant volumes saturated at the same time with relevant liquid phases, respectively. Hence, within the prisms in Figures 1 and 2, volumes represent the composition ranges of one salt, surfaces the coexistence of two salts, lines of three salts, and points of four salts at a given temperature.1 Isothermal Methods of Investigation of Quinary Water−Salt Systems. Figure 3 and Figure 4 show two examples of trigonal prisms which represent the salt composition of two Li, K//Cl, CO3, B4O7−H2O at 0 °C6 and Li, K, Rb, Mg//borate−H2O at 75 °C7 quinary systems. The first system belongs to the type with two cations and three B



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Figure 5. Dry salt diagrams of the quinary Na, NH4//SO4, HCO3, Cl−H2O system saturated with NaHCO3.8

the composition of the quinary system, its points, curves, and fields transform into quinary curves, fields, and volumes, respectively. The conventional terminology used in this work includes “geometrical figures” to mean point, curve, field, and volume. In the case of the quinary system, the geometrical figures of quaternary subsystems generate the geometrical figures of the overall quinary system. The invariant points of the overall quinary system form as a result of the intersection of monovariant curves of this composition generated from transformation of invariant points of relevant quaternary subsystems. As invariant points of the quaternary system extend as monovariant curves of the quinary system, their linkage takes place in accordance with the reduced Gibbs’ phase rule. The Gibbs’ phase rule applied throughout this work is the form for isothermal−isobaric processes. Representation of quinary phase equilibria data by the translation method starts from the quaternary subsystems which are shown on an unfolded prism in Figure 6. The unfolded prism diagram in Figure 6 gives the reciprocal relation among quaternary geometrical figures in the quinary A, B, C// X,Y−H2O system at a temperature (T). The quaternary systems which share the same ternary subsystems are set nearby on the prism. In other words, the unfolded prism

latter parameters, whereas the second system was studied by about 40 trials analogously. Reduction of the complexity of the diagrams in Figures 3 and 4 is possible by selection of the parts saturated with a solid phase in the system. This solid phase can be a phase with little relation to the research or actual phase which saturates the investigated system at the moment of investigation. The diagrams for the saturated parts of the system are obtained by the Jänecke method. Such kinds of diagrams are shown in Figure 5 which represent the parts of the quinary Na, NH4// SO4, HCO3, Cl−H2O system saturated with NaHCO3 at different temperatures.8 As the elimination of halite in the oceanic Na, K, Mg//Cl, SO4−H2O system leads to the consideration of the system as a ternary system, 9 the elimination of NaHCO 3 in the investigation of the latter quinary Na, NH4//SO4, HCO3, Cl−H2O system enabled the authors to consider the system as a ternary NH4//SO4, Cl−H2O system.8 As reducing the dimension of the total phase diagram inevitably leads to a loss of information, it must be decided which information on the total phase diagram is needed to document given petrological information satisfactorily.10 The diagrams in Figure 5 show the parts of the quinary Na, NH4// SO4, HCO3, Cl−H2O system saturated with the eliminated phase from the system which has led to a loss of information about the system. It is worth mentioning that, although the parts saturated with a solid phase of quinary systems can be obtained isothermally, it is not possible to find complete data about the remaining parts of the investigated systems saturated with other equilibrium solid phases. Investigation of Quinary Water−Salt Systems by the Translation Method. The internal structures of the prisms in Figures 1−4 can be described by the translation method.4,16 The method has been used for investigation of various multicomponent water−salt systems11−16 so far. It uses the phase equilibria data in quaternary subsystems for the determination of phase equilibria in quinary systems. Initially, the equilibrium solid phases at the quinary invariant points are predicted, which leads to the determination of phase equilibria in quinary monovariant curves and divariant fields. The method considers the transformation of geometrical figures of ncomponent subsystems when the system enters into the composition of the (n + 1)-component overall system. The transformation of geometrical figures takes place as follows: when the ternary system enters into the overall quaternary system, its points and curves transform into quaternary curves and fields, respectively. When the quaternary system enters into

Figure 6. Unfolded prism used for representation of quaternary geometrical figures in a quinary A, B, C//X, Y−H2O system at a temperature of T °C. C



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in the quinary A, B, C//X, Y−H2O system at a particular temperature (T). There are two types of quinary curves: the ones generated as a result of extension of quaternary points and the ones that extend between the determined quinary invariant points. The dashed curves represent the ones extended from quaternary points, and the thick ones represent the curves extending between the quinary points. The selection of intersecting curves generated from the quaternary points and determination of the solid phase composition of the ones that extend between the quinary points both take place in accordance with the Gibbs’ phase rule. As can be seen in the total phase equilibria diagram, the number of intersecting curves changes as two and three depending on the part of the diagram. Since the quinary invariant points are saturated with four solid phases and a relevant liquid phase in equilibrium, the latter case happens due to the equilibrium solid phase composition of extending quaternary points. Here the condition is that the equilibrium solid phase composition of the point at intersection must be quinary where the degree of freedom is equal to zero. Hence, the number of equilibrium solid phases at the quinary point of intersection becomes four when two curves intersect, and sometimes when three different curves intersect with each other. As the most commonly used techniques to represent the total phase diagram in a lower dimension are projections, sections, and pseudosections; the fragmentation of the isothermal total phase equilibria diagrams, like the one in Figure 8 into crystallization volumes, produces the individual parts saturated with each of the equilibrium solid phases whose assemblage produces the total phase equilibria diagram. The latter individual projections form structures of relevant Jänecke projections. So far, it is not possible to find a complete set of Jänecke projections for any quinary water−salt system saturated with its equilibrium solid phases. What has been observed so far is that it is possible to obtain a complete set of structures of Jänecke projections as crystallization volumes of quinary water−salt systems by means of the translation method.4,15,16 One of the main differences of the diagrams constructed by the translation method from the traditional phase diagrams is representation of invariant points by capital letter E with the subscript showing the serial number of the point and the superscript showing the complexity of the relevant system to which the point belongs, while in traditional phase equilibria diagrams such as the ones mentioned in previous sections the points are shown by only intersection points of the curves representing the points of saturation of different solid phases in equilibrium. The invariant points throughout the rest of this work are denoted by capital letter “E”, whose subscript and superscript show the serial number of the point and complexity of the relevant system, respectively. As determination of phase equilibria by the translation method mainly establishes through the determination of phase equilibria at invariant points of overall composition of systems, such representation of points ensures better determination of the equilibrium composition of geometrical figures in multicomponent water−salt systems. A traditional view can still be given following the determination of solid phase equilibria at geometrical figures of diagram for better clarity. The only crystallization volumes saturated with equilibrium solid phases will be given without the “E” notation of the points by the end of this work.

diagram is set in a way that when it is folded the same ternary subsystems meet each other. Combination of common crystallization fields in quaternary subsystems generates the transition diagram in Figure 7. There are six solid P1, P2, P3, P4,

Figure 7. Transition phase diagram of the quinary A, B, C//X, Y− H2O system at T °C.

P5, and P6 phases at equilibrium in the system at this particular temperature (T). The divariant fields of five of the phases are shown together, and the other completing phase P4 is shown separately in a transition diagram. The latter diagram reflects the surface of the prism that is formed by folding the prism in Figure 6. The reason why the latter type of diagram is called the “transition phase equilibria diagram” is that it reflects the reciprocal relation of quaternary geometrical figures of the quinary water−salt system. In other words, it does not show the quinary geometrical figures of the quinary system but the quaternary geometrical figures. The quinary geometrical figures are superimposed on the transition diagram to obtain the total phase equilibria diagram of the system. The main techniques of determination of quinary geometrical figures in quinary systems were discussed in our previous works in detail.4,14,16 The total phase equilibria diagram in Figure 8 reflects the reciprocal relation of quinary geometrical figures and relevant quaternary geometrical figures

Figure 8. Total phase equilibria diagram of the quinary A, B, C//X, Y−H2O system at T °C. D



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INVESTIGATION OF QUINARY PHASE EQUILIBRIA The Quinary Li, Na, K//CO3, B4O7−H2O System at 15 °C. The quinary Li, Na, K//CO3, B4O7−H2O system involves five quaternary subsystems: Li, Na//CO3, B4O7−H2O; Na, K// CO 3 , B 4 O 7 −H 2 O; Li, K//CO 3 , B 4 O 7 −H 2 O; Li 2 CO 3 − Na2CO3−K2CO3−H2O; and Li2B4O7−Na2B4O7−K2B4O7− H2O. The first three of the listed quaternary subsystems were studied experimentally.17−19 The latter available quaternary data and results obtained by Sang et al.2 on the Li2CO3 saturated part of the system facilitate further determination of phase equilibria in the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C. There are seven solid phasesLi2CO3 (LC), Li2B4O7·3H2O (LB3), Na2B4O7·10H2O (NB10), NaKCO3· 6H2O (NK6), K2B4O7·4H2O (KB4), K2CO3·1.5H2O (K1.5), and Na2CO3·10H2O (NC10)in equilibrium at 15 °C of this quinary system. The phase equilibria in the last two quaternary Li2CO3−Na 2CO3−K2CO3−H2O and Li2B4O7−Na2B4O7− K2B4O7−H2O subsystems were determined, and relevant phase equilibria diagrams were constructed by the translation method using the available ternary phase equilibria data in the literature.20 The translation that is an extension of invariant points in subsystems takes place by the virtue of the compatibility principle of physicochemical analysis, whereas the linkage of the generated geometrical figures on the overall quaternary systems take place in accordance with Gibbs’ phase rule. The Quaternary Li2CO3−Na2CO3−K2CO3−H2O System at 15 °C. There are two invariant points in the ternary Na2CO3− K2CO3−H2O system, while each of the other two ternary Li2CO3−Na2CO3−H2O and Li2CO3−K2CO3−H2O subsystems of this quaternary Li2CO3−Na2CO3−K2CO3−H2O system involves one invariant point. The total number of equilibrium solid phases in the system thus is four that require two invariant points saturated with three different solid phases along with relevant liquid phases. The point E41 in the diagram in Figure 9 constructed by the translation method for this

only one invariant point and the system involves only three solid phases in equilibrium, the system requires a quaternary point saturated with the latter solid phases in equilibrium. The translation of the three ternary invariant points as quaternary monovariant curves into overall composition generates three quaternary curves that intersect on a quaternary point saturated with three equilibrium solid phases in the system. Figure 10 shows the phase equilibria diagram of the quaternary Li2B4O7− Na2B4O7−K2B4O7−H2O system constructed by the translation method.

Figure 10. Schematic phase equilibria diagram of the Li2B4O7− Na2B4O7−K2B4O7−H2O system at 15 °C.

The equilibrium solid phases at the invariant points of quaternary subsystems of the quinary Li, Na, K//CO3, B4O7− H2O system are given in Table 1. The table includes the data available in the literature17−19 and the ones obtained in this work in the Li2CO3−Na2CO3−K2CO3−H2O and Li2B4O7− Na2B4O7−K2B4O7−H2O subsystems. Table 1. Equilibrium Solid Phases at Quaternary Points in the Li, Na, K//CO3, B4O7−H2O System at 15 °C points E49 E410 E41 E42 E44 E45 E46 E43

Figure 9. Schematic phase equilibria diagram of the Li2CO3− Na2CO3−K2CO3−H2O system at 15 °C.

E47 E48

quaternary Li2CO3−Na2CO3−K2CO3−H2O system is saturated with NC10, NK6, and LC phases, while the point E42 is saturated with NK6, K1.5, and LC phases. The curve that extends between the two E41 and E42 quaternary points is saturated with the LC and NK6 phases along with a liquid phase, since the system is a four-component system and the number of equilibrium phases is three, which require a monovariant curve between the points according to the reduced Gibbs’ phase rule for isothermal−isobaric processes. The direction of arrows in Figure 9 and thereafter shows the direction of translation of invariant points of subsystems into the composition of the overall system. The Quaternary Li2B4O7−Na2B4O7−K2B4O7−H2O System at 15 °C. Since each of the three ternary subsystems of the quaternary Li2B4O7−Na2B4O7−K2B4O7−H2O system involves

composition Li, Na//CO3, B4O7−H2O LC+NB10+NC10 LC+NB10+LB3 Li2CO3−Na2CO3−K2CO3−H2O LC+NK6+NC10 LC+NK6+K1.5 Na, K//CO3, B4O7−H2O NB10+NC10+KB4 K1.5+NK6+KB4 KB4+NK6+NC10 Li2B4O7−Na2B4O7−K2B4O7−H2O LB3+NB10+KB4 Li, K//CO3, B4O7−H2O K1.5+LC+KB4 LB3+LC+KB4

The quaternary diagrams arranged on an unfolded prism in Figure 11 are set on the basis of data in Table 1. The latter diagram involves the final versions of ones constructed by the translation method for the two quaternary Li2CO3−Na2CO3− K2CO3−H2O and Li2B4O7−Na2B4O7−K2B4O7−H2O subsystems and the ones corresponding to the structures of the phase equilibria diagrams available in the literature for three Li, Na// CO3, B4O7−H2O; Na, K//CO3, B4O7−H2O; and Li, K//CO3, B4O7−H2O subsystems. The thin monovariant curves belong to n-component subsystems, whereas the thick and dashed curves belong to (n + 1)-component overall systems throughout this work. The thin curves are ternary curves, whereas the thick and dashed curves are quaternary curves in the diagram in Figure 11. The dashed arrows used in Figures 9 E



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Figure 11. Reciprocal relationship among the quaternary geometrical figures in the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C.

form of the unfolded prism, the outlines of all seven equilibrium solid phases in the system were traced on the unfolded prism in Figure 11 and arranged in a way to enable the superimposition of quinary points, the curves extending from quaternary points and also the curves that extend between the points. For example, NC10, which occurs in three quaternary subsystems, is outlined with four E49, E44, E46, and E14 points. The NK6, which occurs in two quaternary subsystems, is outlined with four E41, E42, E45, and E46 points. At the same time, these two fields are adjacent on the E41 and E46 points and the curve extending between them. There are a total of four quinary invariant points produced as a result of the intersection of quinary monovariant curves generated from the transformation of quaternary points in the subsystem. The two conditions for this intersection of curves extended from quaternary points are the difference of equilibrium solid phases at the points by one solid phase and the location of points in different subsystems. Two of the quinary points in eqs 1 and 2 are formed by intersection of curves extended from two quaternary points, and the other two points in eqs 3 and 4 are formed by intersection of curves extended from three quaternary invariant points to the overall quinary composition. Conventionally, the generation of the first two points and last two points, in latter equations, is called the formation of quinary points as a result of the double and triple translations of the quaternary points, respectively.

and 10 and thereafter in initial versions of diagrams constructed by the translation method will be shown as dashed curves when the diagrams are used in unfolded prisms, for better visualization. The transition phase equilibria diagram in Figure 12 is obtained by the combination of common crystallization

Figure 12. Transition phase equilibria diagram of the Li, Na, K//CO3, B4O7−H2O system at 15 °C.

fields in quaternary diagrams in Figure 11. The KB4 segment of the diagram in Figure 12 completes the surface of the prism which reflects the quaternary composition of the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C. The curves and points of the latter segment are all the ones involved in the main body of the transition diagram that will be used as a matrix of the quinary phase equilibria diagram. The seven equilibrium solid phases in the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C depending on the location of phases occur in two and three different quaternary subsystems of the system that can be traced through relevant quaternary points and the curves linking them. In combination of common divariant crystallization fields and in construction of the transition diagram in Figure 12, which is the compacted

E44 + E 94 → E53 = NC10 + NB10 + KB4 + LC

(1)

E14 + E64 → E54 = NC10 + NK6 + KB4 + LC

(2)

4 E34 + E84 + E10 → E52 = LB3 + KB4 + LC + NB10

(3)

E 24 + E54 + E 74 → E15 = NK6 + LC + K1.5 + KB4

(4)

The translation method classifies the monovariant curves of (n + 1)-component overall systems into two types: the ones generated as a result of transformation of invariant points of nF



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monovariant curve saturated with solid LC, KB4, and NB10 phases and which extends between the two quinary E52 and E53 invariant points according to eq 7. The diagram in Figure 13 is composed of the parts saturated with each of the equilibrium solid phases and hence involves the structures of all dry-salt phase diagrams given as Jänecke projections for the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C saturated with its relevant equilibrium solid phases. The Quinary Na, K//Br, SO4, B4O7−H2O System at 25 °C. Recently, the title quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C was studied with respect to the Na2B4O7· 10H2O phase.3 The authors have isothermally investigated the system generating the projection of the system saturated with the latter solid phase. A total of 5 invariant points, 11 univariant curves, and 7 crystallization fields have been found. Every determined geometrical figure by the authors was saturated with the Na2B4O7·10H2O phase. The complexity which gives the objective of this work needs to be clarified for this system along with the first quinary Li, Na, K//CO3, B4O7−H2O system that had also been studied isothermally at 15 °C with respect to a specific equilibrium solid phase. There are eight solid phasesNaBr·2H2O (NB2), KBr (KB), 3K2SO4·Na2SO4 (Gla), Na2B4O7·10H2O (NB10), K2B4O7·4H2O (KB4), K2SO4 (Ar), Na2SO4 (NS), and Na2SO4·10H2O (Mb)in equilibrium at 25 °C of the Na, K//Br, SO4, B4O7−H2O system. The data on four-component subsystems are used for the prediction of phase equilibria in five-component global systems by means of the translation method. The quinary Na, K//Br, SO4, B4O7−H2O system involves five quaternary subsystems: Na, K//Br, SO4−H2O; Na, K//Br, B4O7−H2O; Na, K//SO4, B4O7−H2O; NaBr−Na2SO4−Na2B4O7−H2O; and KBr − K2SO4 − K2B4O7−H2O. The quaternary Na, K//Br, SO4− H2O subsystem was studied experimentally.21 The phase equilibria in the other four quaternary subsystems were determined in this work by means of the translation method on the basis of relevant ternary data20 and in accordance with the results obtained by Ruizhi et al.3 The study completed by Ruizhi et al. shows the composition of Na2B4O7·10H2O containing invariant points in three quaternary Na, K//Br, B4O7−H2O; Na, K//SO4, B4O7−H2O; and NaBr−Na2SO4− Na2B4O7−H2O subsystems, whereas the quaternary KBr− K2SO4−K2B4O7−H2O subsystem is a simple system with only one invariant point. Table 2 compiles the equilibrium solid phases at the quaternary invariant points of subsystems of the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C. It includes the data available in the literature and also the ones obtained in this work. The compiled data in Table 2 are reflected on the quaternary phase equilibria diagrams arranged on an unfolded prism in Figure 14. The unfolded prism which reflects the composition of the quinary Na, K//Br, SO4, B4O7−H2O system on the quaternary level includes the final versions of quaternary phase equilibria diagrams for four subsystemsNa, K//Br, B 4 O 7 −H 2 O; Na, K//SO 4, B 4 O 7 −H 2 O; NaBr− Na2SO4−Na2B4O7−H2O; and KBr−K2SO4−K2B4O7−H2O constructed by the translation method and presents the reciprocal arrangement of all quaternary phase equilibria diagrams. The quaternary monovariant curves generated from relevant ternary points are shown as dashed lines for better visualization. The details about the construction of phase equilibria diagrams for Na, K//Br, B4O7−H2O; Na, K//SO4, B 4 O7 −H 2O; NaBr−Na 2 SO 4 −Na 2B 4 O7 −H 2O; and KBr−

component subsystems and the ones extending between the invariant points of the overall (n + 1)-component system. Hence, in determination of curves of the overall (n + 1)component system, the translation of invariant points of ncomponent subsystems to the overall composition is considered first. In the title quinary Li, Na, K//CO3, B4O7− H2O system at 15 °C, the transformation and extension of quaternary invariant points to the overall composition generate 10 quinary monovariant curves with their identical equilibrium solid phase compositions in Table 1. In other words, the quaternary invariant points generate 10 quinary monovariant curves that extend in accordance with eqs 1−4. There are three quinary monovariant curves in eqs 5−7 extending between the determined four quinary points in eqs 1−4. Since the curves extend between the points that vary from each other by one equilibrium solid phase, the equilibrium solid phases at the monovariant curves in eqs 5−7 are the three common phases shared by two linked points. E15−E54 = NK6, KB4, LC

(5)

E53−E54 = LC, KB4, NC10

(6)

E52−E53 = LC, KB4, NB10

(7)

To obtain a comprehensive phase equilibria diagram of the system in Figure 13, the determined quinary geometrical figures

Figure 13. Total phase equilibria diagram of the quinary Li, Na, K// CO3, B4O7−H2O system at 15 °C.

are superimposed on the transition phase equilibria diagram in Figure 12. Every relevant geometrical figure (point, curve, field, volume) to the available seven equilibrium solid phases in the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C takes part in the diagram in Figure 13. The total phase equilibria diagram in Figure 13 presents the reciprocal relation of geometrical figures of the quinary level with the geometrical figures of the quaternary level of the system. The diagram exposes the internal structure of the prism which reflects the composition of the quinary Li, Na, K//CO3, B4O7−H2O system at 15 °C. The geometrical figures inside the prism and the ones on the surfaces of the prism represent the quinary and relevant quaternary geometrical figures, respectively. The extending quinary monovariant curves as dashed lines from quaternary points to the quinary points are located according to eqs 1−4, whereas the thick curves which also represent the quinary monovariant curves extending between the quinary points are set according to eqs 5−7. For example, the point E52 forms at the intersection of the three curves extending from E43, E48, and E410 points, while the point E53 forms at the intersection of two curves extending from E44 and E49 points according to eq 3 and eq 1, respectively. There is a G



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geometrical figure due to 0 and 1 degrees of freedom, respectively. The diagrams in Figures 15−18 show the initial versions of quaternary phase equilibria diagrams of the Na, K//Br, B4O7−

Table 2. Equilibrium Solid Phases at Quaternary Invariant Points in the Na, K//Br, SO4, B4O7−H2O System at 25 °C (Also at the Quinary Curves Generated from These Points) points E45 E46 E411 E412 E48 E49 E410 E47 E41 E42 E43 E44

composition Na, K//Br, B4O7−H2O NB10+NB2+KB NB10+KB+KB4 NaBr−Na2SO4−Na2B4O7−H2O NS+NB2+NB10 NS+Mb+NB10 Na, K//SO4, B4O7−H2O Ar+KB4+NB10 NB10+Ar+Gla NB10+Mb+Gla KBr−K2SO4−K2B4O7−H2O KB+KB4+Ar Na, K//Br, SO4−H2O Ar+KB+Gla Gla+KB+NS NS+KB+NB2 Gla+Mb+NS

Figure 15. Schematic phase equilibria diagram of the Na, K//Br, B4O7−H2O system at 25 °C.

K2SO4−K2B4O7−H2O subsystems by means of the translation method will be given in the forthcoming pages. The geometrical figures inside the quaternary phase equilibria diagrams are determined where they meet the requirements of the reduced Gibbs’ phase rule for isobaric− isothermal processes. The point is available between three different solid phases, while the curve lies between two different solid phases in the system. In the first case, the point is considered as an invariant geometrical figure, while, in the second case, the curve is considered as a monovariant

H2O; Na, K//SO4, B4O7−H2O; NaBr−Na2SO4−Na2B4O7− H2O; and KBr−K2SO4−K2B4O7−H2O systems constructed by the translation method. The translation that is an extension of ternary invariant points and generation of relevant quaternary monovariant curves are shown by arrows for better clarity of the construction. Hence, both the arrows and thick solid lines represent the quaternary monovariant curves. The dashed arrows that show the direction of translation of ternary invariant points were shown as dashes in the unfolded prism in Figure 14 for better readability of the diagrams. The phase

Figure 14. Reciprocal relationship among the quaternary geometrical figures in the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C. H



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while the E48 point represents the state of equilibrium between Ar, KB4, and NB10 phases. It is notable to state that, for the determination of phase equilibria in the last two Na, K//Br, B4O7−H2O and Na, K// SO4, B4O7−H2O quaternary systems, the composition of the quaternary points involving the NB10 phase in the results obtained by Ruizhi et al.3 was also considered. The quaternary points that extend as quinary monovariant curves into the crystallization volume of the Na2B4O7·10H2O phase show the composition of the quaternary points involving the latter phase. The Quaternary NaBr−Na2SO4−Na2B4O7−H2O System at 25 °C. Figure 17 gives the phase equilibria diagram of the

equilibria diagrams in Figures 15−18 were constructed on the basis of ternary phase equilibria data in the literature where the number of invariant points along with relative positions can be found.20 The Quaternary Na, K//Br, B4O7−H2O System at 25 °C. Figure 15 gives the phase equilibria diagram of the quaternary Na, K//Br, B4O7−H2O system at 25 °C constructed by the translation method. There are two quaternary invariant points, saturated with three solid phases and relevant liquid phases, determined in this system. Each of the ternary subsystems of the system involves only one invariant point whose extension into the quaternary composition generates four monovariant curves, and as a result produces the latter two quaternary invariant points. The relative locations of the ternary points in subsystems must be considered in this system in order to get correct invariant points forming at the intersection point of curves. The curve which extends between the determined points of the system is saturated with NB10 and KB phases. This curve is required to represent the state of equilibrium between three phases: the latter two solid phases along with a relevant liquid phase. The Quaternary Na, K//SO4, B4O7−H2O System at 25 °C. The phase equilibria diagram of the quaternary Na, K//SO4, B4O7−H2O system constructed by the translation method is given in Figure 16. This system is one of the complicated

Figure 17. Schematic phase equilibria diagram of the NaBr−Na2SO4− Na2B4O7−H2O system at 25 °C.

NaBr−Na2SO4−Na2B4O7−H2O system. There are two invariant points in the ternary NaBr−Na2SO4−H2O system, while each of the other two ternary subsystems of the quaternary system NaBr−Na2SO4−Na2B4O7−H2O involves one invariant point. Two quaternary invariant points are formed from extension and intersection of the monovariant curves generated from the latter four ternary invariant points in the system NaBr−Na2SO4−Na2B4O7−H2O. The two quaternary E411 and E412 points in Figure 17 are linked through the fifth monovariant curve extending between the points. The curve which lies between the quaternary points represents the state of equilibrium between two solid NS and NB10 phases along with the relevant liquid phase. The Quaternary KBr−K2SO4−K2B4O7−H2O System at 25 °C. The initial version of the phase equilibria diagram of the KBr−K2SO4−K2B4O7−H2O system at 25 °C is given in Figure 18. Each of the ternary subsystems of this quaternary system

Figure 16. Schematic phase equilibria diagram of the Na, K//SO4, B4O7−H2O system at 25 °C.

subsystems of the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C. It involves four ternary subsystemsNa2SO4− K2SO4−H2O, Na2B4O7−K2B4O7−H2O, Na2SO4−Na2B4O7− H 2 O, and K 2 B 4 O 7 −K 2 SO 4 −H 2 Oamong which the Na2SO4−K2SO4−H2O system includes two invariant points that generate two quaternary monovariant curves. Each of the other three ternary subsystems generates one quaternary monovariant curve, since each of them involves only one ternary invariant point. There are two E48 and E410 quaternary invariant points in this system formed as a result of double translation of ternary invariant points into the composition of the quaternary system, and one more E49 point is formed as a result of unilateral translation of the remaining ternary point along with the solid NB10 phase in the Na2SO4−K2SO4−H2O system. The latter point E49, which is generated as a result of unilateral translation, represents the state of equilibrium between Gla, Ar, and NB10 phases. The point E410 represents the state of equilibrium between Mb, Gla, and NB10 phases,

Figure 18. Schematic phase equilibria diagram of the KBr−K2SO4− K2B4O7−H2O system at 25 °C.

involves only one invariant point whose extension as quaternary monovariant curves generates only one quaternary point between three equilibrium solid phases of the system. In other words, the three different solid phases in the quaternary KBr−K2SO4−K2B4O7−H2O system at 25 °C require only one point in between where the solid phases are in equilibrium with a relevant liquid phase in accordance with Gibbs’ phase rule. The transition phase equilibria diagram in Figure 19 is obtained by the combination of common crystallization fields in I



Article 4 4 E44 + E10 + E12 → E53 = NB10 + NS + Mb + Gla

(10)

Double “through translation” E14 + E 94 → E54 = KB + NB10 + Gla + Ar

(11)

Unilateral translation E 24 + NB10 → E55 = NS + KB + Gla + NB10

The next step of determination of quinary monovariant curves involves the curves extending between determined quinary points in eqs 8−12. As the general principles, each of the quinary points that is formed by triple “through translation”, double “through translation”, and “unilateral translation” is linked to one, two, and three other quinary invariant points, respectively, by means of monovariant curves.4 The other principle needing consideration is that the curves of the overall composition extend between two different points varying by one equilibrium solid phase. The following four curves in eqs 13−16 extend between the determined quinary points in eqs 8−12.

Figure 19. Transition phase equilibria diagram of the Na, K//Br, SO4, B4O7−H2O system at 25 °C.

quaternary diagrams in Figure 14. There are eight solid phases, in equilibrium in the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C, which occur in different quaternary subsystems of the system, as shown in Figure 14. The outlines of the divariant fields saturated with each of the eight phases can easily be traced on the unfolded prism. For instance, the KB4 phase is outlined with quaternary E46, E47, and E48 points and the monovariant curves extending between them. Arkanite is outlined with E41, E47, E48, and E49 points and monovariant curves extending between them. These two KB4 and arkanite phases are adjacent at the same time on the E47 and E48 points and the curve that extends between them. The unification of the diagram through the combination of the eight fields whose outlines can similarly be traced leads to the construction of the transition diagram in Figure 19, which is arranged in a way that facilitates the superimposition of the qunary invariant points, the curves extending from quaternary points and the curves that link the quinary points. The glaserite segment of the diagram in Figure 19 completes the surface of the prism which reflects the quaternary solid phase composition of the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C. The extension of invariant points of quaternary subsystems to the overall five-component composition generates 12 quinary curves with the identical equilibrium solid phase compositions of points in Table 2. There are five quinary invariant points formed as a result of translation of latter points to the quinary composition of the system. The quinary points in eqs 8−10 are generated as a result of triple translation of quaternary invariant points. The point in eq 11 is formed as a result of double translation of quaternary points, while the last point in eq 12 is formed by the unilateral translation of the quaternary E42 point along with the NB10 phase. Hence, at each of the first three quinary invariant E51, E52, and E53 points, three monovariant curves extending from three different quaternary points intersect, and at the point E54, two different curves intersect, while the E55 point is generated by extension of only one curve. (8)

E64

(9)

+

E 74

+

E84

→

E52

= KB4 + KB + NB10 + Ar

E15−E55 = NB10, KB, NS

(13)

E55−E53 = NB10, Gla, NS

(14)

E55−E54 = NB10, KB, Gla

(15)

E54−E52 = NB10, KB, Ar

(16)

A total phase equilibria diagram of the system in Figure 20 is obtained by superimposition of quinary geometrical figures on

Figure 20. Total phase equilibria diagram of the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C.

the transition phase diagram in Figure 19. The diagram in Figure 20 involves every equilibrium solid phase and relevant geometrical figures in the quinary Na, K//Br, SO4, B4O7−H2O system at 25 °C. Hence, it includes quinary invariant points and the curves intersecting at the points and also the curves extending between the quinary points. All of these geometrical figures ensure the translation of each of the quaternary geometrical figures into the composition of the quinary system. There is a monovariant curve extending from each of

Triple “through translation” 4 E34 + E54 + E11 → E15 = NB10 + NB2 + KB + NS

(12)

J



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the quaternary invariant points in the transition diagram in Figure 19 into the composition of the quinary system. That extension is represented as dashed curves in the total phase equilibria diagram. The extension and intersection of generated quaternary monovariant curves follows the findings in eqs 8−12. For example, the quinary E52 point is at the intersection point of three curves extending from E46, E47, and E48 points, while the E54 point is at the intersection point of two curves extending from E41 and E49. The quinary curve that is saturated with NB10, KB, and Ar phases extends between that latter two quinary E52 and E54 points according to eq 16.

Table 3. Equilibrium Solid Phases and Outlines of Quinary Divariant Cocrystallization Fields in the Li, Na, K//CO3, B4O7−H2O System at 15 °C

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RESULTS AND DISCUSSION The dry-salt diagrams obtained experimentally for the two quinary Li, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2O systems2,3 partially clarify the phase equilibria in the systems at the relevant temperatures. The results obtained by the translation method show that this method avoids loss of information on phase equilibria and leads to more comprehensive knowledge of the systems that can be used in development of systematic approaches for derivation of optimal separation sequences required for each of equilibrium solid phases in investigated quinary systems. The phase equilibria at the invariant points and monovariant curves of the two quinary Li, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2O systems, at 15 and 25 °C, respectively, have been determined in the previous section. In the forthcoming sections, the phase equilibria in quinary divariant fields and trivariant volumes will be presented and obtained results will be compared with available literature data.2,3 The fragmentation of the total phase equilibria diagrams in Figures 13 and 20 into parts saturated with each of the equilibrium solid phases leads to more readable diagrams that can be used for tracking crystallization sequences in the systems.16 For better visualization and readability of the crystallization volumes, which are extracted from total phase equilibria diagrams of the systems, the invariant points will be shown as intersection points of the curves where the solid phases crystallize together and also all of the quinary curves will be given as thick solid curves. The Quinary Li, Na, K//CO3, B4O7−H2O System at 15 °C. There are 15 monovariant curves on the quaternary level of the Li, Na, K//CO3, B4O7−H2O system. The extension of latter quaternary curves to the quinary composition of a system generates 15 divariant fields in the system. The equilibrium solid phases and outlines of divariant fields in Table 3 are extracted from the total phase equilibria diagram in Figure 13. The cocrystallizing solid phases at the quinary fields in Table 3 are the phases that saturate the relevant quaternary curves at their origin in the transition diagram in Figure 12. For example, the divariant field generated from extension of the curve between the E410 and E43 points in the transition diagram into the quinary composition of the system is also saturated with solid LB3 and NB10 phases. The field generated from extension of the curve between the E49 and E44 points is saturated with the same solid NC10 and NB10 phases. Divariant fields generated on the overall quinary composition that is with participation of only quinary geometrical figures are not observed in this system. Each of the equilibrium solid phases in the system participates in the following number of divariant cocrystallization fields: KB4 - 6, LC - 6, NB10 - 4, NC10 - 4, NK6 - 4, K1.5 - 3, LB3 - 3.

There are seven trivariant volumes generated as a result of extension of quaternary divariant fields to the quinary composition of the system. A solid phase is in equilibrium with its relevant liquid phase throughout all geometrical figures of each of the volumes. The crystallization volumes in Figure 21 are extracted from the total phase equilibria diagram in Figure 13 for each of the equilibrium solid phases. The number of geometrical figures and their reciprocal arrangement in dry-salt phase diagrams of the system saturated with equilibrium solid phases are reflected in relevant crystallization volumes in Figure 21. The results obtained from experimental investigation by Sang et al.2 are schematically shown in the crystallization volume of the Li2CO3 phase in Figure 21g. The latter volume has four quinary invariant points, nine quinary monovariant curves, and six quinary divariant fields saturated with four, three, and two solid phases involving Li2CO3. The number of geometrical figures and their reciprocal arrangement in the volume of Li2CO3 are all in agreement with results of Sang et al.2 It is worth stating that the isothermal solution saturation method used for investigation of quinary water−salt systems follows the same paths shown on crystallization volumes in Figure 21. The authors of the experimental work of Sang et al. had traced the same curves in volume for Li2CO3. They have added the fourth component to the mixture of the quaternary invariant point to obtain the quinary invariant point. The crystallization field of LB3, which is located on the right side of the Li2CO3 volume, is outlined with two curves saturated with NB10+LB3 and KB4+LB3 phases. The two quinary monovariant curves extending from quaternary invariant points intersect at the point saturated with LB3, KB4, and NB10 which represents the point F1 of the experimental authors. Tracing the curve after the point saturated with LB3, KB4, and NB10 phases, another invariant point saturated with solid NC10, KB4, and NB10 phases is found which in turn represents the point F2 of the diagram constructed by Sang et al.2 After the point saturated with NC10, KB4, and NB10 phases, the monovariant curve leads to the point saturated with NC10, KB4, and NK6 phases which represents the composition of the point shown as F3 by Sang et al.2 After this point, the K



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Figure 21. Trivariant crystallization volumes of equilibrium solid phases in the Li, Na, K//CO3, B4O7−H2O system at 15 °C.

quinary geometrical figures. Eighteen fields are generated as a result of translation of quaternary monovariant curves in Figure 19 to the quinary composition of the Na, K//Br, SO4, B4O7− H2O system at 25 °C. No field is observed on the quinary level that forms in participation of only quinary geometrical figures of the system. Table 5 gives the listing and outlines of divariant cocrystallization fields extracted from the total phase equilibria diagram in Figure 20. Each of the solid phases in the Na, K// Br, SO4, B4O7−H2O system at 25 °C participates in the

monovariant curve leads to the point saturated with the last quinary invariant point saturated with K1.5, KB4, and NK6 phases along with Li2CO3. This last quinary invariant point represents the F4 point of Sang et al. The coexistence of Li2CO3 and other solid phases can also be observed in other geometrical figuresfields, curves, and pointsof quinary composition with lower dimensionality in more details. There are six divariant cocrystallization fields (#3, 5, 7, 11, 13, and 15) generated with the involvement of the Li2CO3 phase in Table 3. The number of monovariant curves generated from the transformation of quaternary points that involve the Li2CO3 phase generate six curves which can also be seen in Table 1. Also, each of three curves in eqs 5−7 extending between determined quinary points involve the Li2CO3 phase. Hence, the number of curves which involve Li2CO3 becomes 9. Each of the points determined on the quinary level in eqs 1−4 involves Li2CO3. As mentioned above, all of these findings are in agreement with data in the crystallization volume of Li2CO3 in Figure 21g. Table 4 compiles the quaternary and quinary geometrical figures in the Li, Na, K//CO3, B4O7−H2O system at 15 °C. The Quinary Na, K//Br, SO4, B4O7−H2O System at 25 °C. The primary step of determination of divariant fields in quinary systems is consideration of fields generated as a result of extension of quaternary monovariant curves into the overall composition, whereas the next step is the determination fields generated on the overall composition in participation of only

Table 5. Equilibrium Solid Phases and Outlines of Quinary Divariant Cocrystallization Fields in the Na, K//Br, SO4, B4O7−H2O System at 25 °C

Table 4. Total Number of Quaternary and Quinary Geometrical Figures in the Li, Na, K//CO3, B4O7−H2O System at 15 °C level

quaternary

quinary

invariant points monovariant curves divariant fields trivariant volumes

10 15 7

4 13 15 7 L



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Figure 22. Trivariant crystallization volumes of equilibrium solid phases in the Na, K//Br, SO4, B4O7−H2O system at 25 °C.

et al. involves 5 points, 11 curves, and 7 fields saturated with Na2B4O7·10H2O that correspond to the geometrical figures in the volume of Na2B4O7·10H2O in Figure 22g. It can also be seen in Table 5 that 7 of the divariant fields (#2, 6, 9, 12, 16, 17, and 18) among the listed 18 fields are saturated with NB10. In the crystallization volume of Na2B4O7·10H2O in Figure 22g, the point which is at the left bottom and saturated with KB4, KB, and Ar phases represents the point E3 given by Ruizhi et al.; tracing the quinary monovariant curve leads to the point saturated with Gla, KB, and Ar phases which represents the point E2 of Ruizhi et al. The next point saturated with NS, KB, and Gla phases and which represents the point E1 given by Ruizhi et al. is found on the trace of the curve saturated with Gla and KB. At this latter point saturated with NS, KB, and Gla, two more monovariant curves intersect; the one on the right side saturated with Gla and NS leads to the quinary invariant point saturated with Mb, NS, and Gla phases which at the same time represents the point E4 of the diagram presented by Ruizhi et al. Following the curves saturated with NS and KB phases on the left side leads to the point saturated with NB2, NS, and KB phases which represents the point E5 given by Ruizhi et al.3 Each of the rest of the volumes in Figure 22 involves the same reciprocal arrangement of geometrical figures and relevant locations of equilibrium solid phases corresponding to Jänecke dry-salt diagrams of the system. Since saturation of the Na, K// Br, SO4, B4O7−H2O system at 25 °C basically depends on conditions and under different conditions different phase diagrams are required, the diagrams in Figure 22 guide the crystallization of salts as they are easily comprehended in a qualitative sense. Table 6 compiles the total number of

following number of divariant fields: NB10 - 7; KB - 6; Gla - 5; NS - 5; Ar - 4; KB4 - 3; Mb - 3; NB2 - 3. The equilibrium solid phase composition of quinary divariant fields generated from translation of the quaternary monovariant curves into the quinary composition is determined on the basis of the solid phase composition of curves at the transition diagram in Figure 19. For example, the quinary divariant field saturated with KB and KB4 phases is generated from extension of the curve between E46 and E47 points in the transition diagram in Figure 19, whereas the field saturated with NB10 and KB4 phases is generated from extension of the curve between E46 and E48 points. Figure 22 presents the crystallization volumes for each of the equilibrium solid phases in the system. This fragmentation is done by extracting the relevant geometrical figures to each of the solid phases from the total phase equilibria diagram in Figure 20. Since the most viable representation of the quinary systems is possible for the parts saturated with a solid phase in the systems, the diagrams in Figure 22 present the maximum obtainable qualitative information about phase relations in the Na, K//Br, SO4, B4O7−H2O system at 25 °C. Every geometrical figurefield, curve, and pointin the latter diagrams is saturated with relevant equilibrium solid phases. The Na2B4O7·10H2O saturated part of the Na, K//Br, SO4, B4O7−H2O system at 25 °C was obtained by Ruizhi et al.3 experimentally. A total of 5 quinary invariant points, 11 monovariant curves, and 7 divariant fields saturated with the Na2B4O7·10H2O were determined by the authors. The rest of the system was not investigated, and the literature review shows no data which can reveal the relevant obscurity in this quinary system. The dry-salt diagram of the system obtained by Ruizhi M



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quaternary and quinary geometrical figures in the Na, K//Br, SO4, B4O7−H2O system at 25 °C.

systems. They reflect the structures of relevant dry-salt diagrams of the system. Obtained results in this work can be used as guides in exploitation and comprehensive utilization of the systems. Required technological schemes can be derived from the obtained crystallization diagrams of the systems.

Table 6. Total Number of Quaternary and Quinary Geometrical Figures in the Na, K//Br, SO4, B4O7−H2O System at 25 °C level

quaternary

quinary

invariant points monovariant curves divariant fields trivariant volumes

12 18 8

5 16 18 8

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AUTHOR INFORMATION

Corresponding Author

*Phone: +2348050692118. E-mail: s.tursunbadalov@ nileuniversity.edu.ng. ORCID

Sherali Tursunbadalov: 0000-0002-2642-3111 Notes

Since the quinary oceanic Na, K, Mg//Cl, SO4−H2O system is always saturated with halite and the Jänecke projections of the system are constructed for the part saturated with the latter phase, for every quinary water−salt system, it is preferred to eliminate a solid phase in the same manner to simplify the investigations. The obtained results as crystallization volumes in Figures 21 and 22, which are the combination of fields, curves, and points saturated with the relevant equilibrium solid phases, visualize structures of each of those projections of the two investigated quinary Li, Na, K//CO3, B4O7−H2O and Na, K// Br, SO4, B4O7−H2O systems at 15 and 25 °C, respectively. The findings in this work besides the crystallization sequences and reciprocal relation of phases in the systems imply also about the solubility of salts in the system; the higher solubility of the phase under the given conditions, the fewer the number of involved geometrical figures and vice versa.

The authors declare no competing financial interest.

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REFERENCES

(1) Voigt, W. What we know and still not know about oceanic salts. Pure Appl. Chem. 2015, 87, 1099−1126. (2) Sang, S.-h.; Yin, H.-a.; Tang, M.-l. (Liquid + Solid) Equilibria in the Quinary System Li+ + Na+ + K+ + CO32‑, B4O72‑ + H2O at 288K. J. Chem. Eng. Data 2005, 50, 1557−1559. (3) Cui, R.; Sang, S.; Wang, D. Liquid-Solid Equilibria in the Quinary Na, K//Br, SO4, B4O7−H2O System at 298K. Russ. J. Inorg. Chem. 2016, 61, 1325−1330. (4) Tursunbadalov, S.; Soliev, L. Phase equilibria in multicomponent water−salt systems. J. Chem. Eng. Data 2016, 61, 2209−2220. (5) Usdowski, E.; Dietzel, M. Atlas and Data of Solid-Solution Equilibria of Marine Evaporites; Springer-Verlag: Berlin, Heidelberg, 1998. (6) Wang, R.; Zeng, Y. Metastable Phase Equilibrium of the Quinary Aqueous System Li+ + K+ + Cl− + CO32− + B4O72− + H2O at 273.15 K. J. Chem. Eng. Data 2014, 59, 903−911. (7) Yu, X.; Zeng, Y.; Guo, S.; Zhang, Y. Stable Phase Equilibrium and Phase Diagram of the Quinary System Li+, K+, Rb+, Mg2+// Borate−H2O at T = 348.15 K. J. Chem. Eng. Data 2016, 61, 1246− 1253. (8) Zhang, Y.; Hong, B. X.; Chang, L. L.; Yi, Z.; Li, L. P.; Peng, H. Q.; Jun, H. H.; Ke, H. L. Phase Equilibria of Na+, NH4+//SO42−, HCO3−, Cl−−H2O Quinary System. J. Chem. Eng. Data 2013, 58, 2095−2099. (9) Braitsch, O. Salt Deposits Their Origin and Composition; SpringerVerlag: New York, Heidelberg, Berlin, 1971. (10) Will, T. M. Phase equilibria in methamorphic rocks: thermodynamic background and petrological applications; SpringerVerlag: Heidelberg, Berlin, 1998. (11) Soliev, L.; Tursunbadalov, Sh. Phase equilibria in the Na,K// SO4,CO3,HCO3−H2O system at 25 °C. Russ. J. Inorg. Chem. 2008, 53, 805−811. (12) Soliev, L.; Tursunbadalov, Sh. Phase equilibria in the Na,K// SO4,CO3,HCO3−H2O system at 0 °C. Russ. J. Inorg. Chem. 2010, 55, 1295−1300. (13) Soliev, L.; Tursunbadalov, Sh Phase equilibria in quinary Na, K//SO4, CO3, HCO3−H2O system at 50 °C. IOP Conf. Ser.: Mater. Sci. Eng. 2013, 47, 012050. (14) Tursunbadalov, S.; Soliev, L. Phase equilibria in the Na,K// SO4,CO3,HCO3−H2O system at 75 °C. J. Solution Chem. 2015, 44, 1626−1639. (15) Tursunbadalov, S.; Soliev, L. Determination of phase equilibria and construction of comprehensive phase diagram for the quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C. J. Chem. Eng. Data 2017, 62, 698−703. (16) Tursunbadalov, S.; Soliev, L. Crystallization and dissolution in multicomponent water−salt systems. J. Chem. Eng. Data 2017, 62, 3053−3063. (17) Sang, S.-H.; Yin, H.-A.; Tang, M.-L.; Zeng, Y. (Liquid + Solid) Phase Equilibria in Quaternary System Na2CO3 + K2B4O7 + K2CO3 + Na2B4O7 + H2O at 288 K. J. Chem. Eng. Data 2004, 49, 1775−1777.

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CONCLUSIONS Isothermal studies of multicomponent water−salt systems are tedious and time-consuming. This study discusses isothermal investigation of quinary water−salt systems and presents the results of investigation of two quinary systems Li, Na, K//CO3, B4O7−H2O at 15 °C and Na, K//Br, SO4, B4O7−H2O at 25 °C by means of the translation method. It explores better understanding of phase equilibria and overcomes hardships in investigation of quinary water−salt systems. The results of this work considerably broaden the phase equilibria data in quinary Li, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2O systems and pave the way for understanding how geometrical figures can be interrelated in quinary water−salt systems. The coexistence of geometrical figures for four, three, and two equilibrium solid phases of the systems was determined as points, curves, and fields. The phase equilibria relevant to every equilibrium solid phase were observed, as none of the solid phases in the systems was eliminated. The determined divariant fields are generated as a result of extension of quaternary monovariant curves, and no field that is generated by the participation of only quinary geometrical figures of the systems was observed. The total phase equilibria diagrams for the quinary Li, Na, K//CO3, B4O7−H2O and Na, K//Br, SO4, B4O7−H2O systems, at 15 and 25 °C, respectively, were obtained in this study. The diagrams reflect the reciprocal relation of all geometrical figurespoints, curves, and fieldsin the systems. The obtained diagrams involve all the Jänecke dry-salt phase diagrams of the systems schematically. The divariant fields of double saturation and trivariant volumes of single saturation were obtained by fragmentation of the diagrams. The extracted volumes reflect the nearby locations of solid phases, their reciprocal arrangement, and crystallization pathways in the N



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Investigation of Phase Equilibria in Quinary WaterâSalt Systems

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Investigation of Phase Equilibria in Quinary WaterâSalt Systems