Chapter 5. Ions in Solution

CHAPTER 5. IONS IN SOLUTION

5.1 Metal Ions in Solution…………………………………………………………...... 1

5.1.1 Hydration and Hydrolysis of Metal Ions…………………………………… 1

5.1.2 Ionization of Water and Hydration of the Proton…………………………... 4

5.1.3 Polymerization and Precipitation…………………………………………… 5

5.1.4 Structures of Polycations and Polyoxoanions………………………………. 7

5.2 The Concept of Equilibrium Constant…………………………………………. 10

5.2.1 The Solubility Product…………………………………………………….. 10

5.2.2 The Free Energy of Reaction and the Equilibrium Constant……………… 11

5.2.3 Solubility Calculations…………………………………………………….. 14

5.2.4 Solubility of Sparingly Soluble Salts……………………………………… 15

5.2.5 Lattice Energy, Hydration Energy, and Solubility………………………... 17

5.3 Acids and Bases…………………………………………………………………... 18

5.3.1 Acidic and Basic Solutions………………………………………………... 18

5.3.2 Strong Acids and Bases…………………………………………………… 19

5.3.3 Weak Monoprotic Acids and Bases……………………………………….. 23

5.4 Structural Aspects of Acid-Base Strength…………………………………….... 25

5.4.1 Gas Phase Acidity…………………………………………………………. 25

5.4.2 Hydration Effects………………………………………………………….. 28

5.4.3 Strengths of Hydroxyl-Group Acids………………………………………. 29

5.5 Graphical Representations of Ionic Equilibria………………………………… 30

5.5.1 Logarithmic Concentration Diagrams…………………………………….. 30

5.5.2 Distribution Diagrams…………………………………………………….. 34

5.6 The Partial Charge Model and the Reactions of Metal Cations………………. 34

5.6.1 The Acidity of Hydrated Metal Cations…………………………………... 34

5.6.2 The Mean Electronegativity of an Aqueous Solution……………………... 35

5.6.3 Hydrolysis of Metal Cations………………………………………………. 37

5.6.4 Polymerization…………………………………………………………….. 41

5.6.5 Precipitation……………………………………………………………….. 44

5.1. Metal Ions in Solution

5.1.1 Hydration and Hydrolysis of Metal Ions

In the aqueous processing of metals, we are concerned with two major questions: (i) What happens to metal ions in solution? and (ii) What happens to a solid placed in an aqueous environment? Let us for a moment focus our attention on the water molecules which constitute the solvent phase of the aqueous solution. Two hydrogen atoms and an oxygen atom come together to form a water molecule by sharing their outer electrons:

(5.1)

Each pair of shared electrons constitutes a covalent bond. It can be seen from this simplified picture that in a water molecule, the oxygen atom is surrounded by 8 outer electrons, four of which are involved in covalent bonding and 4 of which are unshared. We can add to this picture, the fact that oxygen has a higher affinity than hydrogen for electrons. Thus in a water molecule, the electron cloud is denser around the oxygen nucleus than around the hydrogen nuclei. This effect is acknowledged by ascribing a dipolar structure to the water molecule:

Hd+

(d-) O

Hd+

Thus like a magnet, the water molecule has a positive and a negative pole.

Now let us consider a metal ion immersed in this sea of dipoles. Let us take the simplest case, i.e., the hypothetical situation of a metal ion Mz+ immersed in water with no other ions being present. Through its charge, this ion exerts some influence on the surrounding water molecules. The metal ion is positively charged and by analogy with the well known behavior of magnets, we would expect it to attract the negative pole of a water molecule. This is called an electrostatic interaction:

(5.2)

Depending on the nature of the metal ion, several more water molecules may be attracted towards it in a similar manner. Thus we say that metal ions are hydrated in aqueous solution. We would expect that this interaction will be most intense for the water molecules which are nearest to the central metal ion. These nearest neighbor water molecules constitute the first or inner hydration sphere of the hydrated ion. The hydration number is the number of such nearest neighbor water molecules, and is generally taken to be equal to 6. Thus in aqueous solution, we can represent the dissolved metals ions as M(H2O)6z+, e.g., Ni(H2O)62+, Al(H2O)63+, etc.

In addition to the attractive Mz+-Od- interaction noted above, we must recognize that a repulsive Mz+-Hd+ interaction also exists. In fact, we may go so far as to say that the hydration of a metal ion really involves two simultaneous processes: (a) attraction of the negative pole of the water molecule to the positively charged metal ion, and (b) repulsion of the positive pole of the water molecule by the positive charge on the metal ion. These two processes, in competition, can cause a splitting of the bound water molecule:

Hd+ Hd+ Hd+

M2+ + O M2+ O M2+ O

Hd+ Hd+ Hd+

Mz+ ß (OH)- + H+ (5.3)

The term hydrolysis describes processes such as Equation 5.3 in which the O-H bonds of water are broken. The resulting OH--containing product is termed a hydroxo metal complex. It is conventional practice to express the formation of a hydroxo complex as indicated in Equation 5.4.

Mz+ + H2O = MOH(z-1)+ + H+ (5.4)

However, in view of our previous treatment of hydration, we can also write:

M(H2O)6z+ + H2O = M(H2O)5(OH)+ + H3O+ (5.5)

The hydrolysis process may not necessarily stop with the splitting of one water molecule; it may involve the other water molecules in the inner hydration sphere. Thus we speak of successive or stepwise hydrolysis:

M(H2O)62+ = M(H2O)5(OH)+ + H+

M(H2O)5(OH)+ = M(H2O)4(OH)2o + H+

M(H2O)4(OH)2o = M(H2O)3(OH)3- + H+

M(H2O)3(OH)3- = M(H2O)2(OH)42- + H+ etc. (5.6)

5.1.2 Ionization of Water and Hydration of the Proton

A similar electrostatic process involving only water molecules, leads to the ionization of water and the hydration of the proton. The ionization of water may be viewed in terms of the transfer of a proton from a water molecule to a second water molecule, yielding a hydrated hydrogen ion and a hydroxyl ion:

H O H O H O

O + H H O H H O H H

H H H

H2O + H2O = H3O+ + OH- (5.7)

The species H3O+ is called the oxonium ion and it may be further hydrated to give the trihydrated oxonium ion, H3O(H2O)3+:

H H

H O H

O H H O

H H

In the above structure the dashed lines are used to emphasize the fact that the O-H bonds between the surrounding water molecules and the oxonium protons are weaker than those within the oxonium ion. The weaker bonds represent hydrogen bonds.

It is common practice to express the ionization of water without explicitly indicating the hydration of the proton:

H2O = H+ + OH- (5.8)

However there are situations where it is necessary to invoke the hydrated nature of the proton.

5.1.3 Polymerization and Precipitation

The hydrolysis products encountered above may react further with each other to give polymeric species:

M(H2O)5(OH)2+ + M(H2O)5(OH)2+ = [(H2O)4M-(OH)2-M(H2O)4]4+ + 2H2O (5.9)

For example, Fe(H2O)5OH2+ can undergo the following dimerization reaction:

Fe(H2O)5OH2+ + Fe(H2O)5OH2+ =

[(H2O)4 Fe Fe(H2O)4]4+ + 2H2O (5.10)

In other words, the two OH groups form bridges between the two nuclei, i.e., the two Fe3+ ions. These polynuclear species can in turn become hydrolyzed:

OH OH

[(H2O)4Fe Fe(H2O)4]4+ = [(OH)(H2O)3Fe Fe(H2O)3(OH)]2+ + 2H+ (5.11)

OH OH

The presence of this new hydrolyzed species can then lead to more polymerization:

OH OH

[(OH)(H2O)3Fe Fe(H2O)3(OH)]2+ + [(OH)(H2O)3Fe Fe(H2O)3(OH)]2+

OH OH

OH OH OH

= [(OH) (H2O)3Fe Fe(H2O)2 (H2O)2Fe Fe(H2O)3(OH)]4+ + 2H2O (5.12)

OH OH OH

Hydrolysis-polymerization reactions can proceed until finally the resulting polymers become too large to remain soluble, i.e., they achieve colloidal dimensions. When this stage is reached, we say we have precipitated a solid. In this hypothetical system consisting of only one type of metal ion in water (i.e., in the absence of anions or other metals ions), each polymerization reaction involves the elimination of water and therefore ultimately we would expect metal hydroxides to be formed.

EXAMPLE 5.1 Hydrolysis reactions

For each of the polynuclear hydroxo species below, write down the corresponding chemical equation that describes its formation via interaction of Mz+ and H2O.

(a) Be6(OH)84+ (b) Zr4(OH)88+ (c) Mg4(OH)44+ (d) Co2OH3+

Solution

(a) 6Be2+ + 8H2O = Be6(OH)84+ + 8H+

(b) 4Zr4+ + 8H2O = Zr4(OH)88+ = 8H+

(d) 2Co2+ + H2O = Co2OH3+ + H+

5.1.4 Structures of Polycations and Polyoxoanions

The species of interest here are those in which metal ions are linked by hydroxyl (M-OH-M) and/or oxo (M-O-M) bridges. In the case of complexes based on M(II), M(III), and M(IV) atoms, the hydroxyl bridge is used almost exclusively. Table 5.1 presents a summary of the structural information on these species. (see Baes and Messmer, p. 420). It can be seen that symmetrical structures are preferred. In these structures, up to six cations are organized into groups of two, three, four, or six and the coordination number of the hydroxyl ion may be 2 or 3. The structure of the square-planar M4(OH)8(H2O)16 complex is illustrated in Figure 5.1a (B&M, p. 157). Adjacent metal cations are linked by a double bridge of hydroxyls. Each metal ion is eight-coordinate - through the oxygens of four hydroxyls and four water molecules. The M6(OH)84+ and M6(OH)126+ structures are illustrated respectively in Figures 5.1b and 5.1c. (See Baes & Mesmer, p.378) In addition to the species listed in Table 5.1, Al(III) forms the complex Al13O4(OH)247+. This species (Figure 5.1d; see Baes and Mesmer, p.118) consists of a central AlO45- tetrahedron surrounded by twelve AlO6 octahedra; the octahedra are linked by shared edges.

In the case of the M(V) and M(VI) atoms, O2- bridges are prominent. The elements which form these polyoxoanions come predominantly from the left-side of the d-block: V(V), Nb(V), Ta(V), Cr(VI), Mo(VI), and W(VI). Table 5.2 shows that the polymerization ranges from dimers to 19-mers. The typical structure consists of MO6 octahedra linked at the corners or edges, as illustrated in Figure 5.2 (Huheey).

Table 5.1 Polynuclear hydroxo complexes (Baes and Mesmer, p. 420)

Species / Cation (source) / Probable structure
·= Mz+, o = OH-
M2OH3+ / Be2+, Mn2+, Co2+, Ni2+,
Zn2+, Cd2+, Hg2+, Pb2+
M2(OH2(2z-2)+ / Cu2+, Sn2+, UO22+, NpO22+, PuO22+, VO2+,
Al3+ Sc3+, Ln3+, Ti3+, Cr3+
Th4+
M3(OH)33+ / Be2+, Hg2+
M3(OH)4(3z-4)+ / Sn2+, Pb2+
Al3+, Cr3+, Fe3+, In3+
M3(OH)5(3z-5)+ / UO22+, NpO22+, PuO22+
Sc3+, Y3+, Ln3+
M4(OH)44+ / Mg2+, Co2+, Ni2+, Cd2+
Pb2+
M4(OH)88+ / Zr4+, Th4+ / M4 square with eight OH- ions, one centered over and under each edge.
M6(OH)84+ / Be2+, Pb2+ / M6 octahedron with eight OH- ions centered on faces.
M6(OH)126+ / Bi3+ / M6 octahedron with 12 OH- ions centered along edges.

Table 5.2 Polyoxoanions

M2 / M3 / M4 / M6 / M7 / M10 / M12 / M19
V(V) / V2O74- / V3O93- / V4O124- / V10O286-
Nb(V) / Nb6O198-
Ta(V) / Ta6O198-
Cr(VI) / Cr2O72-
Mo(VI) / Mo7O246- / Mo19O594-
W(VI) / W6O192- / W12O4110-

See B&M under the various metal ions, Huheey, pp.755-764, SAL, pp.164-165)

(a) (b)

Figure 5.1 Structures of polycations: (a) M4(OH)8(H2O)168+ , (b) M6(OH)84+

Figure 5.2 Evolution of the structures of polyoxoanions. (Huheey, p. 757)

5.2 The Concept of Equilibrium Constant

5.2.1 The Solubility Product

We learned from our hypothetical metal ion-water system above that successive polymerization-hydrolysis reactions can result in the precipitation of a solid. When a solid, let us say a metal hydroxide, M(OH)2(s), is placed in an aqueous solution, it will dissolve according to a reaction such as:

M(OH)2(s) = M2+ + 2OH- (5.13)

Actually, in view of the hydration of metal ions, it is more appropriate to write

M(OH)2 (s) + 6H2O = M(H2O)62+ + 2OH- (5.14)

We would also expect further reactions to occur in the aqueous solution, e.g., hydrolysis, and polymerization. As more and more solid dissolves, these aqueous phase interactions also increase in extent until finally, the reverse process, i.e., precipitation, starts.

Thus, in effect, the dissolution process can be considered, ideally, in terms of a reversible reaction in which the forward reaction will be dissolution and the reverse reaction, precipitation. The criterion which is used to determine which of these two reactions predominates under a given set of conditions, are called the solubility product. The concentration solubility product for the metal hydroxide reaction (Equation 5.13) is defined as:

Kso = [M2+] [OH-]2 (5.15)

where Kso is the solubility product constant and the square brackets represent concentration. The solid M(OH)2 will precipitate out of solution when the product [M2+] [OH-]2 exceeds the value of Kso. Alternatively, it is sometimes more convenient to write the dissolution reaction in terms of the hydrogen ion:

M(OH)2(s) + 2H+ = M2+ + 2H2O (5.16)

In this case, the solubility equilibrium is described by

*Kso = [M2+]/[H+]2 (5.17)

5.2.2 The Free Energy of Reaction and the Equilibrium Constant

Consider a general reaction,

aA + bB = cC + dD (5.18)

For any arbitrary conditions (i.e., for a system not necessarily at equilibrium), the free energy is given by

DG = DGo + RTln Q (5.19)

where DGo is the standard Gibbs free energy of the reaction and Q is the reaction quotient and is given by

Q = {C}c{D}d/{A}a{B}b (5.20)

where the symbol { } denotes activity.

At equilibrium, DG = 0, and the equilibrium value of Q (i.e., Qeq) is termed the equilibrium constant, K:

K = {C}{D}/{A}{B} (5.21)

It follows therefore that

DGo = -RT 1n Qeq = -RT 1n K (5.22)

Application of Equation 5.22 to Equation 5.19 gives:

DG = RT (1n Q - 1n K) (5.23)

When DG = 0, equilibrium has been attained and ln Qeq = 1n K

DG < 0, reactants form products simultaneously and ln Q < ln K

DG > 0, conversion of reactants to products is impossible; however the reverse reaction is spontaneous and 1n Q > 1n K

The standard Gibbs free energy of reaction is a function of the standard free energies of formation (DGof) of the reactants and products associated with the reaction. That is, for the general reaction described by Equation 5.18, the standard Gibbs free energy (DGo) is given by: