Determination of Phase Equilibria and Construction of Comprehensive

Article pubs.acs.org/jced

Determination of Phase Equilibria and Construction of Comprehensive Phase Diagram for the Quinary Na, K//Cl, SO4, B4O7− H2O System at 25 °C 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, 7340003, Dushanbe, Tajikistan ABSTRACT: Phase equilibria in quinary Na, K//Cl, SO4, B4O7− H2O system at 25 °C were investigated by means of translation method. Five invariant points, 16 monovaraint curves, and 18 divariant fields have been determined in the system on quinary composition. A comprehensive phase equilibria diagram for the system was constructed on the basis of obtained data. The diagram was fragmented into divariant cocrystallization fields and trivariant volumes of two different solid phases and individual equilibrium solid phases, respectively. The comparison of obtained results with available experimental data was deliberated.

1. INTRODUCTION

2. METHODOLOGY 2.1. Determination of Phase Equilibria Using Translation Method. The data on n-component subsystems are used for the prediction of phase equilibria in (n + 1)component overall systems by means of translation method. Initially, the invariant points in the overall system are determined, which renders the generation of other (curves, fields) geometrical figures on this level. This operation takes place in accordance with the Gibbs’ phase rule and stems from compatibility principle7 of physicochemical analysis. The method, which is well described in available literature, involves three techniques.5,6 In prediction of phase equilibria and construction of comprehensive phase diagram for title quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C, the only “through translation technique”5,6 will be required. The term comprehensive is used to emphasize the involvement of every entity of the multicomponent systems. 2.2. The Quaternary Phase Equilibria in Quinary Na, K//Cl, SO4, B4O7−H2O System at 25 °C. The quinary Na, K//Cl, SO4, B4O7−H2O system involves five quaternary subsystems: Na, K//Cl, B4O7−H2O; Na, κ//SO4, B4O7− H2O; Na, K// Cl, SO4−H2O; NaCl−Na2SO4−Na2B4O7−H2O, and KCl−K2SO4−K2B4O7−H2O. Three of the latter quaternary subsystems have been studied experimentally.9 We have predicted the phase equilibria in two other quaternary Na,

Utilization of complicated water−salt systems requires systematic chemical investigations.1 These investigations are expected to be derived from the known principles that lead to more comprehensive knowledge along with solutions to existing problems. In this respect, phase equilibria knowledge and phase diagrams can play important roles. Quinary water−salt systems are investigated with respect to an equilibrium solid phase that reduces the complexity by eliminating two components in the relevant system.2 Even though this elimination produces a part of the phase equilibria data in the system, it does not provide clarity of the system. The title quinary Na, K//Cl, SO4, B4O7−H2O system, which involves industrially valuable content, is a part of the composition of salt lake brines.3 Recently, the Na2B4O7· 10H2 O saturated part of the system was investigated experimentally at 25 °C by Sang et al.4 The authors have measured the solubility and densities of the system saturated with Na2B4O7·10H2O phase and constructed a dry-salt diagram for the latter part. The aim of this work is to comprehensively study the phase equilibria in the quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C using the translation method of prediction of phase equilibria and construction of closed phase diagrams for multicomponent systems.5,6 The applied method is derived from the compatibility principle7 of physicochemical analysis and produces schematic phase equilibria diagrams.8 © 2017 American Chemical Society

Received: August 19, 2016 Accepted: December 28, 2016 Published: January 11, 2017 698

DOI: 10.1021/acs.jced.6b00739 J. Chem. Eng. Data 2017, 62, 698−703

Journal of Chemical & Engineering Data

Article

K//SO4, B4O7−H2O and KCl−K2SO4−K2B4O7−H2O subsystems by means of translation method on the basis of relevant ternary data.10 Equilibrium solid phases at the quaternary invariant points of the listed subsystems are compiled in Table 1.

component subsystems and every thick and dotted arrow curve belongs to the overall (n + 1)-component systems throughout the diagrams and fragmentation segments of this work. The transition phase diagram in Figure 2 is obtained as the common crystallization fields in quaternary diagrams in Figure

Table 1. Equilibrium Solid Phases at Quaternary Invariant Points in the Na, K//Cl, SO4, B4O7−H2O System at 25 °C (Also the Equilibrium Solid Phases at the Quinary Monovariant Curves Generated from the Points) point

composition

Na, K//Cl, B4O7−H2O E41

NB10 + NC + KC E42 NB10 + KC + KB4 NaCl−Na2SO4− Na2B4O7−H2O E411 NS + S10 + NB10 E412 NS + NC + NB10

points

composition

Na, K//SO4, B4O7− H2O E44 KS + KB4 + NB10 E45 NB10 + KS + GS NB10 + S10 + E46 GS KCl−K2SO4− K2B4O7−H2O E43 KC + KS + KB4

points

composition

Na, K// Cl, SO4− H2O E47 KS + KC + GS E48 GS + KC + NC E49 NC + NS + GS GS + NS + E410 S10

There are eight solid phases in equilibrium at 25 °C of the Na, K//Cl, SO4, B4O7−H2O system: NaCl (NC), KCl (KC), 3K2SO4·Na2SO4 (GS), Na2B4O7·10H2O (NB10), K2B4O7· 4H2O (KB4), K2SO4 (KS), Na2SO4 (NS), and Na2SO4· 10H2O (S10). In Table 1 and thereafter, the capital letter “E” represents an invariant point whose subscript shows the serial number of point whereas superscript shows the complexity of relevant system. The quaternary schematic phase equilibria diagrams arranged on an unfolded prism in Figure 1 were constructed according to the data in Table 1. Every thin solid curve belongs to n-

Figure 2. Transition phase equilibria (phase complex) diagram of the Na, K//Cl, SO4, B4O7−H2O system at 25 °C.

1 are combined. The KCl segment of the diagram in Figure 2 completes the surface of prism that reflects the quaternary composition of quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C. 2.3. Determination of Quinary Invariant Points. The combination of the quinary monovariant curves generated from the transformation of quaternary points produce five quinary

Figure 1. Set of phase diagrams of quaternary subsystems of the quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C. 699



Article

invariant points in the system. The combining quaternary points vary from each other by one solid phase and are located in different subsystems. Three of the quinary points in eqs 1−3 are generated by means of translation of two quaternary points and two more points in eqs 4 and 5 are generated by means of translation of three quaternary points to the overall quinary composition. E14 + E84 → E15 = NC + NB10 + KC + GS

(1)

4 E 94 + E12 → E52 = NC + NB10 + NS + GS

(2)

E54 + E 74 → E55 = NB10 + KS + GS + KC

(3)

4 4 E64 + E10 + E11 → E53 = S10 + GS + NS + NB10

(4)

E 24 + E34 + E44 → E54 = KB4 + KC + KS + NB10

(5)

2.4. Determination of Quinary Monovariant Curves. In order to determine the curves in the overall (n + 1)-component composition, the extension of invariant points of n-component subsystems to the overall composition is considered first. The transformation and extension of quaternary invariant points to the quinary composition generate 12 quinary monovariant curves with the relevant identical equilibrium solid phases in Table 1. However, the equilibrium solid phases at the quinary monovariant curves extending between the determined quinary invariant points are shown in eqs 6−9. As the curves in eqs 6−9 extend between the points that vary by one equilibrium solid phase, the extending curves involve the shared solid phases by the two points. E15 − E52 = NB10, GS, NC

(6)

E15 − E55 = NB10, GS, KC

(7)

E52 − E53 = NS, GS, NB10

(8)

E54 − E55 = KC, KS, NB10

(9)

Figure 3. Reciprocal arrangement of determined quinary points and curves in the Na, K//Cl, SO4, B4O7−H2O system at 25 °C.

Figure 4. Schematic phase equilibria (phase complex) diagram of the quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C.

Hence, the total number of quinary curves becomes 16, 12 of which are formed as a result of extension of quaternary points to the quinary level, and 4 of them are the latter ones in eqs 6−9 extending between the points. 2.5. Construction of Total Phase Diagram for the System. Figure 3 shows the reciprocal arrangement of determined geometrical figures, quinary points, and curves in the system. Every point generated by means of triple translation (E53, E54) is linked to one; whereas each of the points generated by means of double translation (E51, E52, E55) of quaternary points is linked to two other quinary points. A comprehensive phase diagram of the system in Figure 4 is obtained as the arrangement of quinary geometrical figures in Figure 3 is superimposed on the transition phase diagram in Figure 2. The diagram in Figure 4 involves every equilibrium solid phase and relevant geometrical figures (point, curve, field, volume) in the Na, K//Cl, SO4, B4O7−H2O system at 25 °C.

and better visualization, it can be fragmented into individual crystallization volumes of equilibrium solid phases and also into divariant cocrystallization fields of two different solid phases. 3.1. Fragmentation of the Diagram into Individual Volumes. There are eight trivariant volumes generated as a result of extension of quaternary divaraint fields of available eight equilibrium solid phases. Figure 5 presents the trivariant crystallization volumes that are extracted for seven of the solid phases from the diagram in Figure 4. The trivariant volume for the Na2B4O7.10H2O phase is shown in Figure 6 along with drysalt diagrams of the system at 25 and 50 °C obtained by Sang et al.4,12 Each of the volumes extracted from the total diagrams of the overall systems visualize the geometrical figures and their reciprocal arrangement in dry-salt diagrams of system saturated with relevant equilibrium solid phases. Similarly, the volumes in Figure 5 and Figure 6 visualize the geometrical figures along with their reciprocal arrangement in relevant dry-salt diagrams of the Na, K//Cl, SO4, B4O7−H2O system at 25 °C. 3.2. Fragmentation of the Diagram into Divariant Cocrystallization Fields. Table 2 presents the equilibrium

3. RESULTS AND DISCUSSION The diagram in Figure 4 shows the quaternary and quinary geometrical figures and their reciprocal arrangement in accordance with main principles of physicochemical analysis7,11 and Gibbs’ phase rule. There are no coordinate axes in the latter diagram hence it is called schematic. For greater clarity 700



Article

Figure 5. Trivariant crystallization volumes of (a) Na2SO4, (b) 3K2SO4·Na2SO4, (c) NaCl, (d) Na2SO4·10H2O, (e) K2B4O7·4H2O, (f) K2SO4, and (g) KCl phases in the Na, K//Cl, SO4, B4O7−H2O system at 25 °C. Every geometrical figure in volumes is saturated with the relevant equilibrium solid phases.

Figure 6. (a) Dry-salt solubility diagram of the quinary Na+, K+/Cl−, SO42−, B4O72−−H2O system at 25 °C saturated with Na2B4O7·10H2O4. (b) Dry-salt solubility diagram of the quinary Na+, K+//Cl−, SO42−, B4O72−−H2O system at 50 °C saturated with Na2B4O7·10H2O12. (c) Trivariant crystallization volume of the Na2B4O7·10H2O phase in the quinary Na+, K+/Cl−, SO42−, B4O72−−H2O system at 25 °C. Every geometrical figure is saturated with Na2B4O7·10H2O.

solid phases and outlines of divariant cocrystallization fields extracted from the diagram in Figure 4. There are 18 fields that are generated as a result of extension of quaternary monovaraint curves to the quinary composition. Each of the equilibrium solid phases participates in the following number of quinary divariant fields in the system Na2B4O7·10H2O, seven; 3K2SO4·Na2SO4, six; KCl, five; NaCl, four; Na2SO4, four; K2SO4, four; K2B4O7·4H2O, three; Na2SO4· 10H2O, three. 3.3. Comparison of Obtained Results with Available Literature Data. The previous experimental study by Sang et al. was devoted on Na2B4O7·10H2O saturated part of the system. The authors have determined 5 quinary invariant points, 11 monovariant curves, and 7 divariant fields each saturated with the Na2B4O7·10H2O phase. The dry-salt

diagrams of the system saturated with the Na2B4O7·10H2O phase at 25 and 50 °C are shown in Figure 6a,b, respectively.4,12 In our view, the diagram in Figure 6a has some defects; three invariant (F1, F3, F4) points and two monovariant (F1−F4, F1− F3) curves do not exist in this diagram, which represents the Na2B4O7·10H2O saturated part of the system. This is due to the location of the point F4 that connects the curve extending from the quaternary point E6 with the curve between the quinary points F1 and F2. A more appropriate connection point of this curve is on the curve extending between the two F3 and F5 quinary points that are saturated with KCl. The trivariant volume in Figure 6c and two quinary divariant fields (16, 18) in Table 2 reflect the above-mentioned case sufficiently. The latter volume shows the structure of the drysalt diagram of the system saturated with Na2B4O7·10H2O at 25 701



Article

Table 2. Equilibrium Solid Phases and Outlines of Quinary Divariant Co-crystallization Fields in the Na, K//Cl, SO4, B4O7− H2O system at 25 °C

°C. It involves 5 points, 11 curves, and 7 fields saturated with the latter phase on the quinary level. The outlines of the divariant fields are presented in Table 2 whereas the equilibrium solid phases of points and curves are presented in eqs 1−9. The dry-salt diagram of the systems saturated with Na2B4O7·10H2O phase at 25 °C is expected to involve the same reciprocal relation of geometrical figures and relevant equilibrium solid phase compositions in the volume in Figure 6c. The field 16 shows the part of system saturated with both K2SO4 and Na2B4O7·10H2O phases; it involves two quinary points (E54, E55) and three quinary curves. Two of curves are generated from the extension of quaternary invariant points whereas the other curve extends between the quinary points. The field 18 shows the field saturated with both Glaserite and Na2B4O7·10H2O phases. It is outlined by four quinary points (E51, E52, E53, E55) and five quinary curves. Two among the quinary curves are generated as a result of extension of quaternary points where the latter two phases are involved, whereas the other three curves extend between quinary points. It can be deduced that the difference between structures of diagrams of the system at 25 °C from 50 °C is that at at 25 °C there is a curve above the E1−F1 curve of diagram at 50 °C; the rest of the quinary curves and points have the same reciprocal relation as 50 °C of the system. The data that was presented by Van’t Hoff and that can only be found in compilations9 today are in good agreement with our findings and support our indicated points above. Van’t hoff has determined two invariant points in the system at 25 °C, where (NaCl + KCl + 3K2SO4·Na2SO4 + Na2B4O7·10H2O) and (NaCl + Na2SO4 + 3K2SO4·Na2SO4 + Na2B4O7·10H2O) solid phases are in equilibrium. The composition of the abovementioned three invariant (F1, F3, F4) points and two

monovariant (F1−F4, F1−F3) curves presented by Sang et al.4 do not comply with the equilibrium solid phase composition of the Van’t Hoff’s latter two quinary points, which correspond to two of the (E51) and (E52) invariant points, found by translation method, respectively. According to these findings, the expected curve that generates from the quaternary point E6 in dry-salt diagram4 of Na, K//Cl, SO4, B4O7−H2O system at 25 °C is modified with a dotted arrow in Figure 7. The curve that extends from the quaternary point E6 connects on a point between F3 and F5. The resulted point on the curve F3−F5 corresponds to our quinary point E55 which is saturated with K2SO4, KCl, Glaserite, and Na2B4O7.10H2O phases.

Figure 7. Expected dry-salt solubility diagram of the quinary Na+, K+/ Cl−, SO42−, B4O72−−H2O system at 25 °C saturated with Na2B4O7· 10H2O. 702



Article

(6) Tursunbadalov, S.; Soliev, L. Phase equilibria in multicomponent water-salt systems. J. Chem. Eng. Data 2016, 61, 2209−2220. (7) Goroshchenko, Y. G. The Centroid Method for Imaging Multicomponent Systems; Naukova Dumka: Kiev, 1982 [in Russian]. (8) Soliev, L. Schematic phase equilibria diagrams for multicomponent systems. Zh. Neorg. Khim. 1988, 33, 1305−1310. (9) Zdanovskiy, A. B.; Soloveva, E. F.; Lyakhovskaya, E. I.; Shestakov, N. E.; Shleymovich, R. E.; Abutkova, A. B.; Cheromnikh, L. M.; Kulikova, T. A. Handbook of experimental data on solubility of multicomponent water-salt systems; Khimizdat: Saint Petersburg, 2004, Vol. II [in Russian]. (10) Zdanovskiy, A. B.; Soloveva, E. F.; Lyakhovskaya, E. I.; Shestakov, N. E.; Shleymovich, R. E.; Abutkova, A. B.; Cheromnikh, L. M.; Kulikova, T. A. Handbook of experimental data on solubility of multicomponent water-salt systems; Khimizdat: Saint Petersburg, 2003; Vol. I [in Russian]. (11) Anosov, V. Y.; Ozerova, M. I.; Fialkov, Y. Y.. The Principles of Physicochemical Analysis; Nauka: Moscow, 1976 [in Russian]. (12) Sang, S.; Zhang, X.; Zhang, J.-J. Solid liquid equilibria in the Quinary System Na, K//Cl, SO4, B4O7 - H2O at 323K. J. Chem. Eng. Data 2012, 57, 907−910.

We have predicted the phase equilibria in the overall quinary Na, K//Cl,SO4,B4O7−H2O system at 25 °C using the available literature data on three of the quaternary subsystems along with the data obtained by means of translation method for the other two quaternary subsystems. Review of the quaternary data showed no evidence of solid solutions between NaCl and KCl phases at 25 °C; the two quaternary Na, K//Cl, SO4−H2O and Na, K//Cl, B4O7−H2O subsystems that are investigated experimentally9 and that involve NaCl−KCl−H2O ternary subsystem do not involve solid solutions under a wide range of temperatures. Table 3 compiles the quaternary and quinary geometrical figures in the Na, K//Cl, SO4, B4O7−H2O system at 25 °C. Table 3. Total Number of Quaternary and Quinary Geometrical Figures in Na, K//Cl, 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

4. CONCLUSIONS Obtained results considerably broaden the phase equilibria data in quinary Na, K//Cl, SO4, B4O7−H2O system at 25 °C. None of the available solid phases were eliminated from the study; conversely phase equilibria relevant to every equilibrium solid phase were observed. The number of equilibrium solid phases in geometrical figures has been determined. Each of the extracted crystallization volumes reflects the qualitative composition and reciprocal arrangement of the phase complexes in dry-salt diagrams of system saturated with the relevant solid phases.

■

AUTHOR INFORMATION

Corresponding Author

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

Sherali Tursunbadalov: 0000-0002-2642-3111 Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Voigt, W. Chemistry of salts in aqueous solutions: Applications, experiments and theory. Pure Appl. Chem. 2011, 83, 1015−1030. (2) Zhang, Y.; Xu, H.-b.; Liu, C.-l.; Zhang, Y.; Pei, L.-l.; Qing, P.-h.; Hong, J.-h.; Liu, K. Phase Equilibria of Na+, NH4+// SO42−, HCO3−, Cl−−H2O Quinary System. J. Chem. Eng. Data 2013, 58, 2095−2099. (3) Deng, T. Stable and Metastable Phase Equilibria in the Salt-Water Systems, Advances in Crystallization Processes; Mastai, Y., Ed.; InTech: New York, 2012; ttp://www.intechopen.com/books/advances-incrystallization-processes/stable-and-metastable-phase-equilibria-of-thesalt-water-system (accessed Nov. 24, 2016). (4) Sang, S.; Zhang, X.; Zeng, X Solid liquid equilibria in the Quinary Na, K//Cl, SO4, B4O7 - H2O System at 298K. Chin. J. Chem. 2011, 29, 1285−1289. (5) Soliev, L. Prediction of Marine - Type Multicomponent System Phase Equilibria by Means of Translation Method; TGPU: Dushanbe, 2000; Book I [in Russian]. 703


Determination of Phase Equilibria and Construction of Comprehensive

Recommend Documents