Equilibria Involving Complex Ions

Suppose you want to find the solubility of AgCl in a solution of aqueous ammonia of given concentration. This problem involves the solubility equilibrium for AgCl, in addition to the complex-ion equilibrium. As silver chloride dissolves to give ions, the Ag ion reacts with NH3 to give the complex ion Ag(NH3)2. The eqniUbria are... 

In Section 16-6, we describe how metal cations in aqueous solution can form bonds to anions or neutral molecules that have lone pairs of electrons. This leads to formation of complex ions and to chemical equilibria involving complexation. The complexation equilibrium between Ag and NH3 is an example ... 

This equilibrium may be used to define an extraction constant (Kex) in the usual way. It should be noted that under some conditions, especially when larger ions are involved, a second equilibrium involving complexation of a further molecule of (non-deprotonated) ligand may also be present. 

As has been suggested in the previous section, explanations of solvent effects on the basis of the macroscopic physical properties of the solvent are not very successful. The alternative approach is to make use of the microscopic or chemical properties of the solvent and to consider the detailed interaction of solvent molecules with their own kind and with solute molecules. If a configuration in which one or more solvent molecules interacts with a solute molecule has a particularly low free energy, it is feasible to describe at least that part of the solute-solvent interaction as the formation of a molecular complex and to speak of an equilibrium between solvated and non-solvated molecules. Such a stabilization of a particular solute by solvation will shift any equilibrium involving that solute. For example, in the case of formation of carbonium ions from triphenylcarbinol, the equilibrium is shifted in favor of the carbonium ion by an acidic solvent that reacts with hydroxide ion and with water. The carbonium ion concentration in sulfuric acid is greater than it is in methanol-... 

One of the objectives of this paper will be to show some specific examples of these effects in electrolysis and illustrate the substantial need for a better understanding of the thermodynamics of the solution chemistry involved in electrodics. Some of these needs are more obvious and have been indicated previously ( 3) and include such items as AG°, Kg0 and Cp data on the systems of interest. However, much more extensive information is necessary on adsorption phenomena, complex ion formation and the equilibrium concentrations of these influential species. This need has always existed but it is even more important now if the current challenges being imposed by energy and materials shortages and environmental control are to be met. 

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ signihcantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable. As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent efifect, due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

Many of these are substantially non-nucleophilic and unlikely to effect the rate or course of the reaction, although this should always be checked. References 29 to 31 relate some problems in the use of some of these buffers. Occasionally, one of the reactants being used in excess may possess buffer capacity and this obviates the necessity for added buffer. The situation will often arise in the study of complex ion-ligand interactions when either reactant may be involved in an acid-base equilibrium. 

Thus, for the conditions where second-order behavior is observed, the chemical circumstances indicate the cerium(IV) oxidation of each chromium complex will involve a rate-determining one-equivalent oxidation of the complex ion (or a species in rapid equilibrium with the complex ion) to an intermediate, followed by the rapid one-equivalent oxidation of the intermediate. Without reference to the role of water coordinated to the chromium, the most obvious mechanism in accord with these specifications is ... 

Two simultaneous equilibria are involved the solubility equilibrium (horizontal equation), and the dissociation of the complex ion (vertical equation). The Ag+ is shared in common with both equilibria. 

A change in the spin state of a metal ion also can accompany a change in coordination number. Again, in some cases conditions may be established in which an equilibrium exists between two complexes with different coordination numbers and different numbers of unpaired electrons. Some of the concepts which are used to describe intramolecular spin equilibria can be extended to the description of these coordination-spin equilibria. Examples include equilibria among four-, five-, and six-coordinate nickel(II) complexes and equilibria involving coordination number changes in iron porphyrin complexes and in heme proteins. 

Hydroxo Complexes. Here, one considers hydroxide vs. chloride vs. fluoride coordination. For the equilibrium involving first complex formation with a metal ion of unspecified charge, we may write Equa-... 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

From Eqn. (14) it follows that with an exothermic reaction - and this is the case for most reactions in reactive absorption processes - decreases with increasing temperature. The electrolyte solution chemistry involves a variety of chemical reactions in the liquid phase, for example, complete dissociation of strong electrolytes, partial dissociation of weak electrolytes, reactions among ionic species, and complex ion formation. These reactions occur very rapidly, and hence, chemical equilibrium conditions are often assumed. Therefore, for electrolyte systems, chemical equilibrium calculations are of special importance. Concentration or activity-based reaction equilibrium constants as functions of temperature can be found in the literature [50]. 

The properties of complex ions will be discussed in more detail in Chapter 20. For now we will just look at the equilibria involving these species. Metal ions add ligands one at a time in steps characterized by equilibrium constants called formation constants, or stability constants. For example, when solutions containing Ag+ ions and NH3 molecules are mixed, the following reactions take place ... 

As with any other chemical reaction, the formation of a metal complex from a metal ion and a set of proligands can be described by an equilibrium constant. In its simplest form, a complexation reaction might involve the reaction of unsolvated metal ions in the gas phase with gas phase proligands to form a complex. In practice it is difficult to study such reactions in the gas phase and complex formation is normally studied in solution, often in water. This introduces the complication that the solvent can also function as a ligand, so that complex formation will involve the displacement of solvent from the metal coordination sphere by the proligand. 

Cobalt(III) hexaammine is quite inert to hydrolysis. In strongly basic media ([OH ] = 0.1 to 2.1 M) the reaction rate increases and [OH ] apparently reaches a limiting value around 1 M, where the reaction becomes independent of [OH ], 3 x 10 s at 61.8°, (i = 2.0 (157). The mechanism of the reaction involves the SnI(CB) pathway. The limiting rate observed at high pH is thought to refiect a pre-equilibrium ion pair formation between the complex ion and OH , rather than the first-order reaction of the fuly deprotonated complex ion. The rate of... 

The second equilibrium involves hydrated 1 ions in equilibrium with E" complexes. In the forward step, an iodide ion donates an electron to the working electrode and is hence oxidized to a I atom. We may speculate that the 1 ion remains outside the double layer and that an electron tunnels through the double layer. However, from many experimental results and molecular dynamic simulations (see Section 4.7.2), it became clear that this is not the case. Instead, a solvated ion penetrates the double layer and becomes chemisorbed as a 1" ion (<5 < 1) on the metal surface, losing about half of its hydration shell [18, 19]. Moreover, there is a local restructuring of the double layer. Here also, the electrochemical reaction does not involve tunneling of an electron through the double layer. 

An example of the effect of temperature on an endothermic reaction is illustrated in Figure 12. The following equation describes an equilibrium that involves the two colored cobalt complex ions. 

Numerous applications of standard electrode potentials have been made in various aspects of electrochemistry and analytical chemistry, as well as in thermodynamics. Some of these applications will be considered here, and others will be mentioned later. Just as standard potentials which cannot be determined directly can be calculated from equilibrium constant and free energy data, so the procedure can be reversed and electrode potentials used for the evaluation, for example, of equilibrium constants which do not permit of direct experimental study. Some of the results are of analjrtical interest, as may be shown by the following illustration. Stannous salts have been employed for the reduction of ferric ions to ferrous ions in acid solution, and it is of interest to know how far this process goes toward completion. Although the solutions undoubtedly contain complex ions, particularly those involving tin, the reaction may be represented, approximately, by... 

Table 17-3 lists formation constants for common EDTA complexes. Note that the constant refers to the equilibrium involving the fully unprotonated species Y" with the metal ion ... 

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