Complex formation equilibria

CHAPTER 7 COMPLEX FORMATION EQUILIBRIA

7.1. Introduction………………………………………………………………………………... 1

7.2. Speciation and Distribution……………………………………………………………….1

7.2.1 Metal-Ligand Systems…………………………………………………………..….. 1

7.2.2 Speciation and Distribution Diagrams…………………………………………..….. 5

7.2.3 Polynuclear Hydroxo Complexes………………………………………………… 13

7.2.4 Polyprotic Complexes……………………………………………………………... 15

7.3 Speciation and the Solubility of Metal Salts……………………………………………. 20

7.3.1 Complex Formation and Solubility……………………………………………….. 20

7.3.2 Anion Speciation and Solubility…………………………………………………... 21

7.3.3 Metal Ion Speciation and Solubility……………………………………………….. 24

7.1. Introduction

Complexation reactions of a metal ion can be considered in terms of the displacement of anionic water molecules within the hydration sphere by anionic or neutral ligands:

M(H2O)z+6 + L = M(H2O)5Lz+ + H2O (7.1)

where L is a neutral ligand in this case. It can be seen from the above expression that the hydrated metal ion also constitutes a complex, with the water molecules as the ligands. Similarly the hydroxyl ions associated with the hydrolysis products encountered in Chapter 5, are also ligands.

The structural aspects of metal-ligand complexes were treated in Chapter 3. In the present chapter we direct our attention to the quantitative description of the equilibrium reactions involving metal complexes. We shall also consider the reactions of protolyzable species such, as polyprotic acids (HnA) and polyamines (e.g., hydrazine, NH2-NH2). The reactions of interest here include those between aqueous species, as well as reactions between aqueous species and solid compounds.

7.2 Speciation and Distribution

7.2.1 Metal-Ligand Systems

It is convenient to use a short-hand expression where the water molecules are not explicitly indicated:

Mz+ + L = MLz+ (7.2)

This convention is adopted in the rest of our discussion. The following are examples of complexation reactions:

Ag+ + OH- = AgOH(aq) (hydroxo complex) (7.3a)

Ni2+ + 6NH3 = Ni(NH3)2+6 (ammine complex) (7.3b)

Co2+ + 4Cl- = CoCl2-4 (chloro complex) (7.3c)

Au+ + 2CN- = Au(CN)-2 (cyanide complex) (7.3d)

It will be noticed that in the above equations, a variety of ligand numbers is indicated ranging from one hydroxyl ligand for AgOH(aq) to six ammonia ligands for Ni(NH3)2+6 . In general the formation of complexes proceeds in a step-wise manner, with each consecutive reaction governed by its own equilibrium constant:

Mz+ + L = Mz+ K1 (7.4a)

MLz+ + L = MLz+2 K2 (7.4b)

MLz+2 + L = MLz+3 K3, etc (7.4c)

where

Ki = [MLz+i ]/[MLz+i-1 ]L] (7.5)

The constants K1, K2... etc are called stability constants, in recognition of the fact that they provide a measure of the stability of the respective complexes. Thus a large equilibrium constant indicates a highly stable complex. Corresponding to the consecutive stability constants, Ki, are overall stability constants, i, defined as:

Mz+ + L = MLz+ 1 (7.6a)

Mz+ + 2L = MLz+2 2 (7.6b)

Mz+ + 3L = MLz+3 3 (7.6c)

where

i = K1K2...Ki = [MLz+i ]/[Mz+][L]i (7.6)

Table 7.1 provides a collection of selected stability constants for various complexes. Several factors account for the differences in stability constants, among which are (a) properties of the central metal ion (ionic size, ionic charge, electronegativity), (b) properties of the ligand (size, ionic charge, basic character, extent of chelation, steric effects, size of chelate ring).

Table 7.1 Stability constants for selected metal-ligand complexes

Knowledge of the relevant equilibrium or stability constants allows us to calculate the concentrations of all the individual complexes for any given solution conditions; the resulting set of concentrations is called the speciation of the aqueous phase for those particular conditions. Consider a system consisting of a metal ion Mz+ and a ligand L, with overall stability constants i as indicated by Equations 7.4a-c, and 7.6. The concentrations of the various complexes may be written as:

[MLz+]

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