Factors affecting the solubility of ionic compounds

Computational and Theoretical Chemistry 1069 (2015) 132–137

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Factors affecting the solubility of ionic compounds Michael O. Hurst, Ryan C. Fortenberry ⇑ Georgia Southern University, Department of Chemistry, Statesboro, GA 30460, USA

a r t i c l e

i n f o

Article history: Received 29 April 2015 Received in revised form 5 July 2015 Accepted 5 July 2015 Available online 22 July 2015 Keywords: Anions Cations Solubility rules Ionic compounds

a b s t r a c t In order to provide a more robust understanding for the general solubility rules provided in most chemistry introductions, the charge densities for common ionic cations and anions are computed via quantum chemical methods. It is shown that low charge densities on either the cation or, especially, the anion promote solubility. The lowest anion charge densities produced correspond to chlorate, perchlorate, and acetate which are known always to be soluble for the analyzed cations. Silver has the lowest charge density of the cations examined, but is rarely soluble, only with these three singly-charged polyatomic anions and the related nitrate anion. The silver chloride bond is 8 kcal/mol stronger than silver chlorate and 12 kcal/mol stronger than silver nitrate. Sodium chloride is 6 kcal/mol weaker than silver chlorate with potassium chlorate 8 kcal/mol weaker. Hence, silver monomer salts are shown here to produce high bond energies to atomic anions showcasing why charge density alone cannot explain aqueous solubility, even though it is a good marker in a general sense. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction The solubility of ionic compounds is one of their most basic physical properties. It is understood theoretically that ionic crystals in a saturated solution are in equilibrium with the hydrated ions [1]. This equilibrium is pushed toward increased solubility by decreases in lattice energy and by decreases in the energy of hydration of the ions. The competition of the two factors leads to complexities in predicting the solubility of an ionic compound. Empirical tables predicting the solubility of ionic compounds have been developed and are regularly published in introductory-level collegiate chemistry textbooks [2]. However, explaining the solubility of any given individual compound has proven very difficult [3]. Instruction of chemistry concepts to entry-level students is sometimes a mix of half-truths and gross approximations built as such in order to get students thinking in the proper manner but without overwhelming them with details. For instance, quantum chemists will say that the delineations between covalent, ionic, hydrogen, etc. bonding are really just a continuum of electron probabilities, and even this is a poor definition [4,5]. However, these classifications are taught to students, and errors creep into their consciousness as to how molecules behave. Recently, Devarajan and coworkers [6] raised question as to whether deeper descriptions of chemical bonding need to be put into the ⇑ Corresponding author. E-mail address: [email protected] (R.C. Fortenberry). http://dx.doi.org/10.1016/j.comptc.2015.07.019 2210-271X/Ó 2015 Elsevier B.V. All rights reserved.

traditional pedagogy of chemical bonds and bonding. Their conclusions appear to suggest that more complete concepts need to be used for instruction, especially for hydrogen–halide bonds, so that more competent students are created. As a result, the specter of pedagogical depth is raised in many of the basic tenants of chemical instruction. Aqueous ionic solubility is another such example, and is actually intimately tied to the idea of the chemical bond [3]. There exist several explanations within general chemistry texts or online discussion boards as to why certain ionic compounds are soluble in water and why others are not in contradiction to the general solubility rules. Work by Osuna and coworkers [7] indicates that stepwise explicit microsolvation leads to favorable charge separations for the constituent atoms in alkali-halide diatomics. As a result, the standard ions are favored for bond cleavage in water, whereas the neutral atoms are favored as dissociated products in the gas phase. However, there lacks a systematic analysis of more fundamental properties such as the molecular volume and the intimately related charge density property even though such phenomena are known to permeate the underlying chemical physics of solvation [1,3,4]. In order to develop simple theoretical explanations for ionic solubility, this work produces the volumes for a number of typical ions from quantum chemical computations. From this, the charge densities of these ions are determined and compared to the solubilities of several ionic compounds. Additionally, bond energies are computed for several exceptions to these trends in order to provide a more complete picture.

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identical at 3:406  10 24 cm3 giving identical charge densities for this +2 atom of 94,094 C/cm3. The additional functions in the DZP basis apparently do not add any further inclusion of the electron cloud and, hence, volume in this case. This is true for many of the cations since most are atomic and strongly valence making them well-defined by their localized electron clouds. Sodium, calcium, and aluminum are strong exceptions to this where the DZP basis set produces significantly smaller volumes (by a factor of 2 even ranging up to 4). As a result, only comparisons within basis sets should be and will be made. DZP is used for the quantitative comparisons made in the rest of this work since it is available for all included atoms.

(1832 C/cm3), and chlorate (1986 C/cm3). Table 2 shows that each of these anions are soluble in water no matter the cation with which it is associated. Interestingly, nitrate salts are also all soluble in water even though its charge density is significantly greater at 6963 C/cm3. On the opposite end of the spectrum for the anions, fluoride, oxide, sulfite, carbonate, and phosphate are all insoluble except for a few cases that are consistent across this set. The first two anions from these (fluoride and oxide) have the highest charge densities for any of the anions examined at 8148 C/cm3 and 11,277 C/cm3, respectively. However, the last three have charge densities of less than 4100 C/cm3. The cations that allow for solvation in these anions are lithium, sodium, potassium, ammonium, rubidium, and cesium, all group I elements save for ammonium. The charge densities calculated for these counter ions are all among the lowest for this class at less than 9000 C/cm3 save for sodium. However, the alkali metals decrease in charge density going down the periodic table as a result of the same charge being distributed over progressively larger volumes. The charge densities of the cations are all significantly greater as a set than the charge densities of the anions partly since the anions are molecular and the cations are mostly atomic. The notable exception is sodium with a significantly high charge density at 29,437 C/cm3. Zinc has the highest charge density at over 94,000 C/cm3 with aluminum closely behind at 91,160 C/cm3, and zinc and aluminum are soluble with the same counter anions. Counter to the argument that high charge density leads to insoluble compounds, zinc and aluminum are soluble with those anions with the lowest charge density anions of chloride, bromide, iodide, chlorate, acetate, perchlorate, and sulfate. Each of the anions have charge densities of less than 3400 C/cm3. Carbonate is not soluble with zinc or aluminum, but its charge density is just above this threshold at 3873 C/cm3. Interestingly, nitrate forms a soluble salt with all of the cations even though its charge density is 6963 C/cm3. Chloride, bromide, and iodide are also soluble with most counter anions except with silver (I), mercury I, and lead II. The anions fall in the mid-range of computed charge densities, but the cations are toward the lower end of the scale for their grouping of charge densities with silver having the lowest charge density of 3783 C/cm3 in the class. This is less than the largest alkali metal, cesium (4439 C/cm3), as well as even the lone molecular cation ammonium (5130 C/cm3). As a result, the overall trend holds. The lower the charge density, the more likely a compound is to be soluble in water. A more precise statement follows from the presented results is that if either the cation or, especially, the anion portion has an extremely low charge density, the salt will be soluble in water most of the time. The notable exception for the anions is nitrate. It has a medium charge density but its nature simply makes it soluble regardless of the counter ion. While this is an exception, it makes it own rule. Silver, on the other hand, does not follow this trend with its low charge density and reluctance to solvate. Sodium has a middle charge density at 29,437 C/cm3, but its salts are always soluble. These exceptions and break downs in the theory that charge density is directly tied to aqueous solubility show that such a model is good but incomplete. More must be taking place.

3.1. Charge density

3.2. Covalent bonding character

Weak water shells are associated with low charge density. Tight water shells are associated with high charge density. Therefore, low charge density typically is an indication of solubility whereas high charge density (and the resulting tight water shells) are believed to correlate to a lack of solubility. In large part, comparison of Tables 1 and 2 bears this out. The three lowest charge densities reported in Table 1 are perchlorate (1809 C/cm3), acetate

Silver has the lowest charge density of any cation. It should produce soluble products. Yet, only nitrate and the dominant low charge density chlorate, acetate, and perchlorate polyatomic anions from our set can bring about solvation with silver. Chloride has a medium charge density for the anions at 5428 C/cm3. Silver chloride is insoluble. As any chef or cook can testify, sodium chloride is highly soluble even though sodium’s

2. Computational details Gaussian09 [8] can compute molecular and molar volumes as part of its standard release and is the computational program utilized herein for this purpose. B3LYP [9,10] geometry optimizations (for polyatomic systems) and single-point energy computations (for atoms) are computed with the typical 6-31G basis set [11] where available (p-block atoms and d-block atoms above period six) as well as the DZP basis set [12–14] for all systems. The cations and anions chosen are fairly common ones discussed in most general chemistry texts. The computed molar volume is divided by Avogadro’s number to arrive at the ionic volume. Dividing this number by the Coulomb-converted charge for a given ion produces the charge density in C/cm3. Besides the charge density, the bond energy is also explored as a consideration in the solvation of these ions. The bond energy is simply determined from the energy sum of the dissociated ionic products minus that of the actual molecular monomeric compound. The bond energy is then used to obtain information about the bonding nature and covalent character of these bonds. Several ionic compounds are used as examples with the bond energies used to explain some of the exceptions in the standard ionic solubility tables and the general trends of charge density. 3. Results and discussion Table 1 lists the B3LYP/6-31G and B3LYP/DZP molar volume, ionic (molecular or atomic) volume, and charge density. Anionic species are given in the top of Table 1 with the cations in the bottom. Those cations without data entries in the 6-31G half do not have available and comparable basis set constructions available for use. The magnesium B3LYP/DZP computations failed to convergence after several attempts. Even though the DZP basis set has been well-used and has largely fallen out of vogue of late, its simplicity makes it available for use across the periodic table especially for density functional computations of period six atoms. The two basis sets are largely consistent for the same systems as one would expect for two double-zeta basis sets. The DZP basis is larger; zinc, for instance, has 43 DZP basis functions while the 6-31G basis set contains 36. As a result, the total electronic energies differ: 1778.3023143 Eh and 1778.1070143 Eh , respectively. Interestingly for this example, the ionic volumes are

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Table 1 B3LYP/6-31G and DZP molecular volumes and charge densities. Molecule

6-31G

DZP 3

Molar volume (cm /mol)

3

Ionic volume (cm )

3

Charge density (C/cm )

Molar volume (cm3/mol)

Ionic volume (cm3)

Charge density (C/cm3)

11.843

1:966  10

23

Hydroxide

16.385

2:721  10

23

5889

16.385

2:721  10

23

5889

Chloride

30.815

5:117  10

23

3131

17.778

2:952  10

23

5428

Nitrate

32.157

5:339  10

23

6001

27.718

4:602  10

23

6963

Bromide

34.133

5:667  10

23

2827

29.013

4:817  10

23

3326

Iodide

41.812

6:943  10

23

2307

30.198

5:014  10

23

3195

Chlorate

64.000

1:063  10

22

1508

48.592

8:068  10

23

1986

Acetate

48.839

8:109  10

23

1976

52.676

8:746  10

23

1832

Perchlorate

50.963

8:462  10

23

1893

53.333

8:855  10

23

1809

Oxide

17.713

2:941  10

23

10,895

17.113

2:841  10

23

11,277 5242

Fluoride

8148

Sulfide

36.812

6:112  10

23

5243

36.812

6:112  10

23

Sulfite

51.274

8:514  10

23

3764

47.330

7:859  10

23

4077

Carbonate

38.807

6:444  10

23

4973

49.830

8:274  10

23

3873

Sulfate

53.904

8:950  10

23

3580

60.477

1:004  10

22

3191

Phosphate

59.313

9:848  10

23

4881

65.557

1:089  10

22

4416

Ammonium

19.347

3:212  10

23

4988

18.810

3:123  10

23

5130

6.555

1:088  10

23

14,721

3.278

5:443  10

24

29,437

10.818

1:796  10

23

8930

Sodium Potassium Rubidium Cesium Magnesium Calcium

2.570

4:267  10

24

75,092

19.861

3:298  10

23

9717

Strontium Barium Iron II Iron III Nickel II

5.385

10.818

1:796  10

23

8920

24.486

4:066  10

23

7882

43.478

7:219  10

23

4439

11.916

1:979  10

23

16,196

9.574

1:590  10

23

20,157

30.882

5:128  10

23

6249

23

13,438

8:941  10

24

35,838

14.361

2:385  10

7.181

1:192  10

23

26,875

14.361

2:385  10

23

20,157

10.407

1:728  10

23

18,544

3.469

5:760  10

24

55,632 18,205

Cobalt II

8.834

1:467  10

23

21,846

10.601

1:760  10

23

Cobalt III

5.301

8:802  10

24

36,406

5.301

8:802  10

24

54,609

Copper I

3.590

5:961  10

24

53,757

7.181

1:192  10

23

13,437

Copper II

3.590

5:961  10

24

53,757

25.132

4:173  10

23

7679

25.509

4:236  10

23

3783

2.051

3:406  10

24

94,094

Mercury I

33.226

5:517  10

23

5808

Mercury II

14.581

2:421  10

23

13,235

2.117

3:515  10

24

91,160

17.032

2:828  10

23

11,331

Silver Zinc

Aluminum

2.051

8.466

3:406  10

1:406  10

24

23

94,094

22,796

Lead II

charge density is nearly eight times greater than that of silver. Potassium chloride also has similar properties as sodium chloride. The model is clearly lacking for the description of the silver salts in particular, and the sharing of electrons between atoms is a sensible avenue to explore as a part of explaining this phenomenon. While for ionic compounds a full lattice energy may provide the needed insights, it is hypothesized herein the necessary trends can be produced from stoichiometrically basic monomers as a first-order approximation. Table 3 lists the B3LYP/DZP computed absolute and relative bond strengths for the salt molecular monomers of silver, sodium, and potassium coupled to nitrate, chlorate, and chloride. Nitrate and chlorate are chosen for analysis since they are soluble with any counter ion, but they have such different charge densities, again, 6963 C/cm3 and 1986 C/cm3, respectively. Sodium and potassium are chosen for the same reason but from the cation perspective. The optimized geometries for these nine systems is given in Table 4 with the atom numbering and visual depictions of these systems in a generic sense shown in Figs. 1–3. It is interesting to note that the silver and sodium salt monomers are very similar to one another while the potassium molecules differ quite noticeably from the other two when combined with each anion.

An immediate observation for the absolute bonding energies (Table 3) of these systems treated as gas-phase monomers is the consistency for the bond strength of a given cation. The sodium chloride bond strength is the weakest of the sodium set at 140.8 kcal/mol, but the other two sodium salt X-anion bond energies are both within 6.0 kcal/mol of the sodium chloride bond strength. Interestingly, this is strong enough for the ‘‘covalent’’ and isolated sodium chloride and potassium chloride monomeric molecules to exist in nature; there were detected in the interstellar medium via radio astronomy in 1987 [15]. Potassium gives bond strengths between 118.6 kcal/mol and 126.8 kcal/mol. Even silver-containing monomers are within 12.3 kcal/mol stretching from 164.5 kcal/mol to 176.7 kcal/mol which is surprising for anions of such varying charge densities. In every case presented herein, sodium has a larger bond strength than its larger alkali metal family member, potassium. Interestingly, sodium chlorate (and silver chlorate, actually) prefers a C s geometry while potassium chlorate optimizes to a full C 3v structure interacting with the chlorine and the oxygen atoms. These differences between sodium and potassium are almost certainly due to the smaller size and charge density of sodium compared to potassium in much the same way that silicon has

Ammonium Lithium Sodium Potassium Rubidium Cesium Magnesium Calcium Strontium Barium Iron II Iron III Nickel II Cobalt II Cobalt III Copper I Copper II Silver Zinc Mercury I Mercury II Aluminum Lead II

Fluoride

Hydroxide

Chloride

Nitrate

Bromide

Iodide

Chlorate

Acetate

Perchlorate

Oxide

Sulfide

Sulfite

Carbonate

Sulfate

Phosphate

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Insoluble Soluble Soluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Insoluble Soluble Soluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Insoluble Soluble Soluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Soluble Soluble Insoluble

Soluble Soluble Soluble Soluble Soluble Soluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble Insoluble

M.O. Hurst, R.C. Fortenberry / Computational and Theoretical Chemistry 1069 (2015) 132–137

Table 2 The solubility of various salt combinations.

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M.O. Hurst, R.C. Fortenberry / Computational and Theoretical Chemistry 1069 (2015) 132–137

Table 3 Absolute and relativea covalent bond strengths (in kcal/mol) of representative charge density molecular monomer exceptions. Silver

Sodium

Potassium

Absolute Nitrate Chlorate Chloride

164.5 168.8 176.7

141.8 146.8 140.8

118.6 126.8 118.8

Relative Nitrate Chlorate Chloride

12.3 7.9 0.0

1.0 6.0 0.0

0.2 8.0 0.0

a All relative energies are computed with relation of each cation to the chloride salt.

well-known altered properties (and weaker bond strengths) compared to carbon [16–18]. As a result, it could be said that sodium produces more covalency in its bonds than potassium by around 20 kcal/mol. Silver, however, has even greater bond strength by 22.0 kcal/mol to 35.9 kcal/mol per anion than sodium. Hence, silver has more covalency in its molecular interactions arising from its unique electronic properties. As a result of its covalency, silver should be less likely to create soluble products when conjoined to a given anion even though it has an exceptionally low charge density. Its stronger bonds, even as a monomer, means that energy is required to break the lattice due to the sharing of electrons that silver induces. Computations of silver fluoride further corroborate the argument that silver is more covalent since the bond energy of this salt monomer is 205.8 kcal/mol, which greater still than the already insoluble silver chloride likely due to the exceptionally high fluoride charge density of 8148 C/cm3. Consequently, the bond strength and the charge density of the chloride and fluoride counter anions go hand-in-hand here for the silver salts. This describes why silver is less soluble but not why some silver salts actually are soluble. The relative bond energies in the bottom half of Table 3 tell the more complete story. Comparing within the silver salts, silver chloride has the strongest bond. This decreases for chlorate and continues to do so for silver nitrate. Sodium and potassium show nearly the opposite trend. The chloride salt has the weakest bond, and the chlorate salt has the strongest bond for this set. Hence, a more complete picture as to why some silver salts are insoluble and other silver salts are soluble is emerging. The interactions of the electrons between the cation and anion in these salts are strongly mitigated not by the charge density but by the intrinsic properties

Table 4 The B3LYP/DZP optimized geometrical values (in Å and  ) for the examined salt monomers.a Silver

Sodium

Potassium

X–O3/2 O3/2–N N–O1 \X–O3/2–N \O3/2–N–O1 Point group

2.249 1.294 1.215 92.81 122.04 C 2v

2.205 1.291 1.220 91.91 121.72 C 2v

2.588 1.285 1.228 96.21 121.31 C 2v

Chlorate

X–O3/2 O3/2–Cl Cl–O1 \X–O3/2 Cl \O3/2 Cl–O1 O3 Cl–O2 O1 torsion Point group

2.261 1.599 1.513 95.69 109.25 114.41 Cs

2.230 1.588 1.522 91.92 108.15 114.14 Cs

2.775 1.565 1.565 81.82 105.69 111.78 C 3v

Chloride

X–Cl

2.261

2.387

2.789

Nitrate

a

The atom orderings are taken from Figs. 1–3.

X

Fig. 1. The X–NO3 monomer for X = Ag, Na, and K.

X

Fig. 2. The X–ClO3 monomer for X = Ag, Na, and K.

X Fig. 3. The X–Cl monomer for X = Ag, Na, and K.

of the atomic cations themselves. These initial data show that the interaction of the silver cation is intrinsically different from the alkali metals. Silver prefers to make strong bonds to singly-charged atomic anions and has weaker interactions with singly-charged molecular anions. The standard solubility rules and charge density explanations are still quite powerful, but the exceptions appear to be related to the covalency of the bonds in question. While we have not probed the full lattice strength in this study due to computational limitations, especially for the period six atoms, it is clear that the strength of electron sharing between the cation and anion portions of these salts cannot be neglected for a complete picture of solubility to be given. 4. Conclusions In this work, it has been shown that charge density is indeed a good marker of aqueous solubility. The strongest indicators are in the low charge density species. If either the cation or anion portion exhibits a low charge density, the salt is highly likely to be soluble. This is especially true for the very low charge density anions: chlorate, perchlorate, and acetate. Silver and sodium are the strong exceptions to the charge density–solubility relationship for the cation set. Sodium is an alkali metal with a high charge density, but all in this group create soluble products due to their valence shell construction and preferred propensity to donate their single

M.O. Hurst, R.C. Fortenberry / Computational and Theoretical Chemistry 1069 (2015) 132–137

valence s electron. However, sodium is shown here to produce stronger bonds and more covalency than potassium and, presumably, the other group one element atomic cations. Interestingly, sodium salts with larger systems are showing that its high charge density does break its always soluble rule if the counter system is large enough to donate electrons in a delocalized fashion [19]. Silver is singly charged like the alkali metals but has the lowest charge density of any cation analyzed in the present set. Yet, silver is only soluble with the four consistently soluble molecular anions: nitrate, chlorate, perchlorate, and acetate. Comparison of silver to sodium and potassium shows stronger bond energies and, hence, higher levels of covalency in the silver monomers. These bond energies may weaken when explicitly solvated as indicated previously [7]. Even so, the present works suggests that the greatest indicator for the difference between these singly-charged cations is that the sodium and potassium bond strengths to the anions discussed in Table 3 are weakest in the chloride salts where they are strongest for the silver salts. As a result, the atomic electronic structure differences unique to the cations really are what dictate the solubility. For silver, it makes relatively strong bonds to singly-charged atomic anions while the alkali metals do not. Singly-charged molecular anions do not make as strong bonds for silver and probably also the other low charge density, period 5 and 6/group 11–14 cations explaining the charge density/solubility exceptions for mercury I and lead II, as well. Acknowledgements The authors acknowledge Georgia Southern University for providing the necessary funds to perform this research and Jim LoBue of Georgia Southern University for being part of these initial conversations. The figures were generated with the CheMVP program developed at the Center for Computational and Quantum Chemistry at the University of Georgia, and the authors are thankful for the use of this program. References [1] W.G. van der Sluys, The solubility rules: why are all acetates soluble?, J Chem. Educ. 78 (2001) 111–115. [2] T.E. Brown, H.E.H. LeMay, B.E. Bursten, C. Murphy, P. Woodward, M.E. Stoltzfus, Chemistry: The Central Science, 13th ed., Pearson, Upper Saddle River, NJ, 2015.

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