A fundamentally important matter in teaching inorganic chemistry is to convince students that the changes of various properties of elements, their compounds and more complex systems (where solubility may be important) are strongly related to the position of these elements in the periodic table. Vastness of our contemporary knowledge about various properties of substances impels a teacher of inorganic chemistry to point rather on evolutional transition of selected features in groups of compounds moving through the periodic table than to concentrate on details. Therefore it seems to be essential to present some directions of the selected property alterations within the periodic table and to explain some peculiarities that sometimes occur.
This presentation concentrates on several examples of metallic and salt–water solubilites [1–8] which were critically evaluated by this co-author within the framework of the IUPAC Solubility and Equilibrium Data Subcommittee (previously Solubility Data Commission V. 8). The author is convinced that the examples presented in this paper are not fortuitous and one may find many other groups of inorganic systems where solubility levels would change through the periodic table in a very similar manner.
Solubility of elements in liquid mercury (Hg)
Although Hg and its compounds are now consequently isolated from our environment one should remember that the knowledge about amalgams was fundamentally important to the progress in electrochemistry and the fundamentals of metallurgy. Nowadays applications of Hg are quite limited but still important; without a knowledge of Hg properties  we are not effectively able to protect the nature from its contamination.
The experimental data related to solubility of metals in liquid Hg were compiled and evaluated in volume 25 of the Solubility Data Series (SDS)  and supplemented by data of some non-metallic elements in . The values at 298 K were ordered according to their atomic numbers and are presented in Fig. 1. The data marked with open circles or triangles denote that an intermetallic compound of a metal with Hg is the solute, filled circles or triangles denote that a pure element (or a solid element saturated with Hg) is the equilibrium phase. The inverted triangles denote a detection limit of an analytical technique used in the determination. The corresponding equilibrium solid phases may be easily deduced from the equilibrium phase diagrams of the binary Hg-element systems. The most contemporary and complete form of such diagrams is presented in . Inspection of these diagrams indicates certain evolutional changes of their shapes moving through groups of elements in the periodic table.
Although the course of lines shown in Fig. 1 appears complex, however, after careful examination, some periodically formed maxima and minima can be identified. The solubility changes within the periods are frequently drastic (for example: going from Nb to In) while the changes within the groups of the periodic table are moderate (for example: the Cu–Ag–Au triad). The well-soluble metals in Fig. 1, grouped in the upper portion of the graph, are all the easy-melting metals. The high melting point metals and non-metals are grouped in the lower part of the Fig. 1.
Certain characteristic chemical properties of some elements are reflected in Fig. 1. The low solubility position of H indicates that this individualistic element does not fit with the well-soluble alkali metals group. The relatively easy-melting Mn has a comparatively higher solubility in Hg than the neighboring transition metals. A formation of solid intermetallic compounds between Hg and a metal (for example: Ti, Mn, Ni, Cu) makes their solubility relatively higher than of non-interacting metals (for example: V, Cr, Fe, Co). The majority of lanthanides and actinides reveals similar solubility levels; the exceptions observed for Eu and Yb are connected with the fact that these metals are also bivalent and then exhibit similarity to the alkaline earth metal group. Similarly, the relatively small decrease of Ce solubility might be connected with the fact that Ce can be also four-valent and then approaches the properties of four-valent Th.
Graphical interpolations and extrapolations of the determined solubilities to the adjacent positions of elements leads to a simple prediction of experimentally unknown solubilities. For example, such values could be proposed for: B – 10–12, Sc – 10–3, Y – 10–3, Pm 1 × 10–2, Hf – 10–6, Ac – 10–3, Pa – 2 × 10–3, Np – 6 × 10–3 or Am – 10–2 mol % at 298 K.
It has been previously shown  that analogous dependences, to these presented in Fig. 1, are observed for metals dissolved in liquid Ga, In, Sn, Pb or Bi when the solute metals are arrayed according to their atomic numbers. Therefore, the outlined solubility trends in Hg have the same general character for other metallic systems. The explanation of this observation is straightforward from the thermodynamic point of view. Plots of the atomic volumes, temperatures of melting or boiling, the energies of melting, boiling or sublimation as well as the hardness of the elements (presented in  and handbooks of inorganic chemistry, for example, in ), when ordered according to the atomic number, resemble a reflection of the plot shown in the Fig. 1. This means that the cohesion energies within the elements dominate the energetics of the dissolution process and the solvation effects are explicitly smaller in such systems.
The solubilities of metals in Hg and the other metallic solvents may be predicted using various models outlined in . The best theoretical approach, according to the experience of this author , is the cellular model proposed by Miedema et al. [14, 15].
Solubility of intermetallic compounds in liquid Hg
Although this phenomenon was essential to the fundamentals of metallurgy its frequent investigation in the 20th century was additionally stimulated by the importance of formation of intermetallics during the stripping analysis with Hg electrodes. The solubility of alloys in Hg may be also a critical factor in the construction of various technical devices using Hg. Thus the equilibrium between an alloy or a defined intermetallic compound and Hg may be approached from both sides: supersaturation – when amalgams of two (or more) metals are mixed and an intermetallic compound is subsequently precipitated and undersaturation – when beforehand made alloys (or defined intermetallics) are introduced into Hg for a partial dissolution.
It was observed for many systems that intermetallics precipitated in Hg are essentially the most stable intermetallics being formed in the binary systems . Moreover, Hg was very seldom found as a third component of an equilibrium solid phase formed. As it was shown for the majority of cases in the SDS volume 51 devoted to such systems , that the corresponding equilibria are described by the well known quantity of the solubility product but very rarely by the equilibrium constant of a well soluble intermetallic compound. Thus for a solid M′xM″y intermetallic compound, being in equilibrium with its saturated solution of the component metals in Hg, one may write:
thus for PtZn2 formed in Hg (after mixing Pt and Zn amalgams), one should write:
This is the very obvious analogy between the expression for equilibrium of an intermetallic compound in Hg and the well-known expression for the equilibrium of salt solutions in polar solvents.
The thermodynamic stability of an intermetallic compound in Hg depends on the energy of formation of such a compound in the binary system (which is most frequently the dominant contribution) and the dissolution energies of the component metals in Hg. The stability of intermetallics in binary systems (as well as in Hg) depend on the electron structures of component atoms, the difference of their electronegativities and the ratio of their atomic radii; all these parameters are strictly related to the positions of the metals in the periodic table.
Solubility of elements in liquid alkali metals (Li–Cs)
The liquid alkali metals are known as the most effective coolants for high temperature sources of energy (nuclear and chemical reactors, sun heat, space activity). They are also used in the construction of high energy electrochemical cells, as thermionic and magnetohydrodynamic converters, as well as in the extractive metallurgy of some precious metals from their ores or wastes. Due to the high importance of knowledge about the corrosion resistance of constructional metals used in liquid alkali metal media, a great experimental effort was made in the last century to measure the solubilities of the majority of elements in liquid alkali metals. The data, collected from popular journals and spread over many rare reports, were evaluated and the best values were selected in SDS volumes 63, 64 and 75 [3, 4].
As for the solubility data in Hg solvent, one may plot the evaluated experimental results for the elements according to their increasing atomic numbers. Figure 2 presents such data for liquid Na at 873 K. For Li, K, Rb or Cs (as the solvents) the plots are qualitatively similar but fewer experimental values are available.
The trends in Fig. 2 resemble those in Fig. 1. Thus the easy-melting metals occur in the upper portion of the figure whereas the high-melting metals and inactive gases (N2 and noble gases) are located in the lower part of the graph. The solubilities change significantly within the periods (for example: from Li to N or from K to V) and are similar within the groups (for example: V–Nb–Ta or F–Cl–Br–I rows) of the periodic table. Again Mn displays a relatively higher solubility than other transition metals. Lanthanides and actinides are probably all hardly soluble at a similar concentration level; however, this has not been fully established in the experiments so far. Some peculiarities are observed, for example: N is well-soluble in Li, due to the formation of stable Li3N. In contrast, Na3N is not formed in Na and gaseous N2 solute then displays the distinctly lower solubility in liquid Na. A similar situation occurs in the case of C dissolved in either Li or Na.
Graphical prediction of the solubilities in liquid alkali metals by interpolation and extrapolation of the experimental data, as proposed for Hg solvent, is generally acceptable but not at the end of periods due to the abrupt changes of the solubility between noble gases and alkali metals as solutes. One should be especially careful with any prediction of the solubilities for these systems using even the most rational model of Miedema et al. . The solution chemistry in the case of transition metals dissolved in liquid alkali metals is quite complex and the presence of impurities in either a metal solute or a metal solvent may elevate the solubilities by several orders of magnitude . For example, if very pure Mo saturates very pure Li and a small amount of N is introduced then the apparent solubility of Mo will markedly increase due to the formation of better-soluble Li3MoN3. Then the sum of the dissolved metallic Mo and of Li3MoN3 complex in Li is experimentally determined. The latter salt-like compound exists in a dissociated ionic-like form in liquid Li. Generally, the higher N content in the system the higher is the solubility of many transition metals dissolved in Li. Therefore, an inspection of the corresponding phase diagrams of the binary Li-element systems to establish the equilibrium solid phase  is not rational in the case of the transition, lanthanide and actinide metals forming ternary azides.
An analogous situation would be when (for example) one dissolves Cr in liquid Na, K, Rb or Cs which contain traces of O. In such conditions a part of Cr is dissolved in the metallic form but a greater part is in the form of NaCrO2, KCrO2, RbCrO2 or Cs5CrO4, respectively, the salts being more soluble than the metallic Cr. Thus a definition of the saturating solute in such systems is quite complex. Beside the critical contamination of N in Li or the impurities of O in Na, K, Rb, or Cs, the presence of C or H in either the alkali or solute metals may influence the saturating concentrations of transition metals. Therefore, the constructors of technical devices used with liquid alkali metals must base in their decisions on carefully determined experimental values of the solubilities but not on their predicted values. The simultaneous presence of several non-metallic impurities makes the systems still more complicated . The ultra-purification of alkali metals from non-metallic impurities is as problematic as the removal of water traces from some non-aqueous solvents. The formation of soluble ternary azides in Li and ternary oxides in the other alkali metals is analogous to the formation of metal complexes which elevate the solubility of salts in polar solvents .
There is another phenomenon characteristic of these metallic systems which recalls the partitioning of a solute between two immiscible liquids. If one introduces a pure Zr sample into liquid K containing traces of O then after some time the system will reach an equilibrium and a part of the O will be present in the solid Zr phase and a part of the O will remain in the liquid K . The ratio of O contents (mol fraction) in these two practically immiscible phases is constant (Kp) and depends on temperature.
This phenomenon is a general feature of many transition metals and is important in the purification process for alkali metals.
It has been observed for several systems that precipitation of some chemical and intermetallic compounds occurred in when two or more elements were introduced into alkali metals , however, no corresponding solubility products (as for Hg solvent) have been determined so far.
Solubility of halates (ClO3–, BrO3–, IO3–) in water
Many halate salts are popular oxidizers used in the chemical industry. They are frequently applied in paper or match production, and in analytical chemistry. Solubility data of typical metal halates has been collected in various volumes of the SDS [5, 20–22]. Selected results at 298 K are plotted against the increasing atomic numbers of the metals forming chlorates (Fig. 3), bromates (Fig. 4) and iodates (Fig. 5). The richest collection of the data is shown for iodates and the at least complete set is for chlorates because the synthesis and purification of some salts is difficult or there was simply no interest in their investigation.
One may easily observe in Figs. 3–5 that the solubility changes may be assigned to the positions of metals in the periodic table. Although, the ionic nature of these salt systems is completely different from the metallic systems discussed above, a partial likeness between Figs. 1 or 2 and Fig. 5 may be noticed. The solubility of the halates of Li is always high and the solubility of subsequent alkali metals decreases gradually moving from Na to Cs. This is somewhat unusual phenomenon if one compares it with the unsmooth solubility trends observed, for example, for alkali metal perchlorates and trifluoromethanesulfonates . Chlorates and bromates of the bivalent cations are frequently more soluble than the salts of monovalent ones, however the opposite tendency is observed for iodates. The solubilities of majority of the transition metal salts change very smoothly stepping from one metal to a neighboring one. The solubilities of Ti(IO3)4, Zr(IO3)4 and Hf(IO3)4 are low and at the relatively similar level. The solubilities of lanthanide bromates and iodates change very smoothly, which allows for a quite precise prediction of the experimentally unknown solubilities of Ce(BrO3)3, Pm(BrO3)3, Ho(BrO3)3, Tm(BrO3)3 and Pm(IO3)3 at 298 K.
Solubility of three-valent rare earth metal halides (F–, Cl–, Br–, I–)
The applications of these compounds has been increased considerably in the last two decades. These halides are used for the production of light emitters (with no Hg use), important alloys and compounds of rare earth metals, in nuclear fuel reprocessing, as materials for various kinds of spectroscopy and lasers, as catalysts for organic reactions and polymerizations, as dyes for ceramics, glass and ink, as corrosion protectors, as solid electrolytes for batteries, as well as medical agents (in tomography).
The solubility data for these compounds were evaluated in SDS volumes 87, 94 and 100 [6–8] and their selected values are graphically presented in Figs. 6 and 7. The saturating concentrations are known with varying precision (chlorides better than 1 %, bromides and iodides a few %, and fluorides about 10 %).
The solubilities of rare earth metal fluorides (Fig. 6) are quite low whereas the solubilities of the other halides (Fig. 7) are high. Saturation is hard to establish in all these systems due to the very slow approach to equilibrium. Additionally, the bromides and the iodides are difficult to purify.
Concerning the fluorides, the equilibrium solid phases are in the form of hydrates with about 0.5–1.0 molecule of water per salt molecule; the hydration number increases with the atomic number of the rare earth metal ion. The dependence of solubility concentrations, shown for the fluorides in Fig. 6, is reasonably smooth (the steps between the values are due to 10 % experimental precision of the solubility) and allows for a safe prediction of PmF3 solubility in water as the mean of the solubilities of NdF3 and SmF3.
In the case of chlorides (circles in Fig. 7) one should differentiate between the isostructural heptahydrates (for the La–Pr sub-group) and the hexahydrates (for the Nd–Lu sub-group) equilibrium solid phases. The appropriate information may be found by inspecting the corresponding salt-water partial phase diagrams ; the shapes of these diagrams change evolutionally within rare earth metal series . Smooth solubility changes are also observed for each sub-group of the rare earth metals: the parabola-like dependences both for the La–Pr and for the Nd–Lu sub-groups of the chlorides. A prediction of PmCl3 solubility from interpolation of the results for NdCl3 and SmCl3 seems to be well supported.
A more complicated run is evidenced for the solubility of the iodides (squares in Fig. 7). Phase diagrams for these salt-water systems are unknown. The distinctly deviant solubility determined for EuI3 is most probably due to the partial reduction of EuI3 to EuI2. On the other hand the solubility decrease between TmI3 and YbI3 may be explained because solid nonahydrates are the equilibrium phases for the sub-group of La–Tm and octahydrates for the sub-group of Yb–Lu of iodides. Nevertheless, one may roughly predict the solubility level for PmI3.
Probably due to experimental difficulties, the solubility results for the bromides appear to be very scattered (triangles in Fig. 7). Only a partial phase diagram is known for the LaBr3–H2O system which is an analogue to the phase diagram of the LaCl3–H2O system. However, composition of the equilibrium solid phases at 300 K are known for the other LnBr3–H2O systems. By analogy to the chlorides, the bromides of the La–Pr sub-group form solid heptahydrates while the bromides of the Nd-Yb sub-group form hexahydrates. In this situation, one should expect smooth change in the solubilities of the bromides as precisely established for the chlorides (Fig. 7). Because various thermodynamic parameters determined for the rare earth chlorides and bromides are similar , the solubilities of the bromides of the Nd-Yb sub-group should form a parabola-like curve being parallel to that of the chlorides. On the basis of such an assumption, it was possible to predict the solubilities of these bromides , which are probably more reliable than the casual experimental results.
It has been shown that the solubilities of the selected groups of elements and inorganic compounds are related to their positions in the periodic table. These observations can effectively assist in the solubility evaluation process and in solubility predictions. Solubility and solution chemistry of the selected systems, either metallic or salts in a polar solvent, are ruled by the same physico-chemical relations and open up possibilities for similar kinds of analysis for other systems.
The author is greatly indebted to Dr. J. Stroka for a technical help in preparation of the figures.
Z. Galus, C. Guminski. Solubility Data Series, Metals in Mercury, Vol. 25, C. Hirayama (Ed.), Pergamon Press, Oxford (1986).Google Scholar
C. Guminski, Z. Galus. Solubility Data Series, Intermetallic Compounds in Mercury, Vol. 51, J. G. Osteryoung, M. M. Schreiner (Eds.), Pergamon Press, Oxford (1992).Google Scholar
H. U. Borgstedt, C. Guminski. Solubility Data Series, Metals in Liquid Alkali Metals, Vols. 63–64, Oxford University Press, Oxford (1996).Google Scholar
H. Miyamoto, R. Miyamoto, C. Guminski, M. Salomon. IUPAC-NIST Solubility Data Series, Transition Metals, Lanthanide, Actinide and Ammonium Halates, Vol. 85, J. Phys. Chem. Ref. Data37, 933 (2008).Google Scholar
T. Mioduski, C. Guminski, D. Zeng. IUPAC-NIST Solubility Data Series, Rare Earth Metal Chlorides, Vol. 87, J. Phys. Chem. Ref. Data37, 1765 (2008), 38, 441, 925 (2009).Google Scholar
T. Mioduski, C. Guminski, D. Zeng, H. Voigt. IUPAC-NIST Solubility Data Series, Rare Earth Metal Iodides and Bromides, Vol. 94, J. Phys. Chem. Ref. Data41, 013104-1 (2012), 42, 013101-1 (2013).CrossrefGoogle Scholar
L. F. Kozin, S. C. Hansen. Mercury Handbook, C. Guminski, (Ed.), The Royal Society of Chemistry Publishing, Cambridge (2013).Google Scholar
C. Guminski. Polish J. Chem.78, 1733 (2004).Google Scholar
C. Guminski. Z. Metallk.81, 105 (1990).Google Scholar
L. F. Kozin. Fiziko-Khimiya i Metallurgiya Vysokochistoi Rtuti i eyo Splavov, Chapter 2, pp. 24, Naukova Dumka, Kiev (1992); in Russian.Google Scholar
N. N. Greenwood, A. Earnshaw. Chemistry of Elements, Chapter 2, pp. 20, Elsevier, Oxford (2005).Google Scholar
A. K. Niessen, F. R. DeBoer, R. Boom, P. F. DeChatel, W. C. M. Mattens, A. R. Miedema. Calphad7, 51 (1983).Google Scholar
C. Guminski. Z. Metallk.77, 87 (1986).Google Scholar
H. U. Borgstedt, C. Guminski. Monatsh. Chem. 131, 917 (2000).Google Scholar
C. Guminski, H. U. Borgstedt. Arch. Metall. Mater.49, 529 (2004).Google Scholar
G. T. Hefter. Rev. Inorg. Chem.10, 185 (1989).Google Scholar
H. Miyamoto, M. Salomon, H. L. Clever. Solubility Data Series, Alkaline Earth Metal Halates, Vol. 14, Pergamon Press, Oxford (1983).Google Scholar
H. Miyamoto, M. Salomon. Solubility Data Series, Alkali Metal Halates, Vol. 30, Pergamon Press, Oxford (1987).Google Scholar
H. Miyamoto, E. M. Woolley, M. Salomon. Solubility Data Series, Copper and Silver Halates , Vol. 44, Pergamon Press, Oxford (1990).Google Scholar
G. T. Hefter. Pure Appl. Chem.85, 2077 (2013).Google Scholar
C. Guminski. Arch. Metall. Mater.51, 617 (2006).Google Scholar
C. Guminski, H. Voigt, D. Zeng. Monatsh. Chem.142, 211 (2011).Google Scholar