Bedded Down– The rmodynamic Stability

A system in the process of achieving thermodynamic stability can be recognized readily in many cases. For example, addition of ammonia to a solution containing Cu2+aq causes a rapid change in colour. This is a signal that a new complex species is forming, and it is apparent from the observation that new complexes between Cu(II) and ammonia form to a great extent, even for low concentrations of ammonia– evidently, the Cu(II)–ammonia complex is more stable than the Cu(II)–water complex. We have discussed some of the reasons for this type of outcome in Chapter 3. Now, we need to understand the pro cesses involved, so that we can quantify such qualitative observations. One important point arising from earlier discussion was that the amount of a complex species existing cannot be predicted simply from the ratio of added ligand to solvent molecules, because ligand preferences override purely statistical aspects. Establishing the actual composition in solution experimentally and expressing it in terms of some general parameter is thus important. The process we are seeing in the copper (II)–ammonia solution is a ligand substitution process where one ligand is replacing another. In general we can represent this for reaction in aqueous solution with a neutral monodentate ligand at this stage, by Equation (5.1):

Since we have written this reaction as an equilibrium, it is possible to write an equilibrium constant for this reaction (5.2) namely:

in which the sets of square brackets in this case refer to concentration of the species. In fact thermodynamics tells us that the equilibrium constant above should be written in terms of activities (a) not concentrations. The relationship between these two is (5.3):

where S is the activity coefficient, which has a value yS = 1 in extremely dilute solutions but for practical solutions has a value of less than 1, caused by the influence of other solute species present on the behaviour of a particular solute molecule. Because activities are difficult to determine and vary with concentration and composition of the solution it is convenient to work with concentrations by assuming that yS = 1 (pure water has this value itself). It is then important to quote the experimental conditions when reporting equilibrium constants as the value will change with conditions. Fortunately the size of the change with conditions usually met where concentrations of complexes may vary between 0.001 and 0.1M, are not large in the context of what we seek to determine. Of more concern is devising processes that permit accurate determination of the concentrations of species present, which is not a trivial task by any means. Because water has a concentration of approximately 55M it varies by only trivial amounts for reactions of dilute species. As a result, it is convenient, and traditional, to leave out the solvent term and usually also to ignore coordinated water molecules. We shall adopt this representation henceforth– but do not assume we are dealing with ‘bare’ metal ions! This reduces Equation (5.1) to Equation (5.4):

and thus Equation (5.2) to Equation (5.5):

The equilibrium constant K in this case is called the formation constant or stability constant, since it is measuring formation of a metal complex, and defining its thermodynamic stability. Experimentally, because we measure K values under non-ideal (in a thermodynamic sense) conditions the term 'constant' here is not absolutely correct, as discussed above. Remember that it is defined only under the particular experimental conditions employed in reality, although it is fairly true to say that the value varies in only a limited way across the range of conditions that we are most likely to apply.

There is also a direct relationship between the stability constant and the free energy (AG°. in kJ mol-1) of a reaction, expressed in terms of the relationship (5.6):

ΔG= -2.303 RT log10 K                  (5.6)

where R is the gas constant and T the temperature in Kelvin. This means that the higher is K the more negative is the free energy of the reaction. We feel this usually as a release of heat on complexation, because of the relationship between free energy and reaction enthalpy

(ΔH0) and reaction entropy (ΔS0) namely (5.7):

ΔG0 = ΔH0−T · S0                         (5.7)

Examination of Equation (5.5) shows that a large value of K means a high concentration of MLn+ relative to M n+ and L; in other words, a large K means a strong preference for complex formation. The size of K with metal complexes is usually so large that we tend to report log10 K values, for ease of use; obviously it's simply easier to refer to a (log) K of 7.5 rather than a K of 3.16 x 107.

In this discussion, we shall also meet another closely related type of stability constant, the overall stability constant (B), which represents the stability for a set of sequential complexation steps, rather than for an individual component step. It allows us to represent, for example the stability constant for an overall reaction M + nL forming ML rather than just for a single ligand addition step such as M + L forming ML. As for K the larger is B. the more thermodynamically stable is the assembly. The overall stability constant is dealt with more fully in Section 5.1.3.

You may already be familiar with another form of equilibrium constant, the acid dissociation constant (Ka), which is so named because it describes the dissociation of the acid HX to its ions (Equation 5.8):

This is, in effect, an instability constant, since it describes a break-up rather than a formation process; the equation for the constant is inverted relative to the form met for the stability constant of interest here. However, expressing it as pKa = -log K, makes it similar to a complex formation or stability constant expressed simply as log K. We shall focus here on complex formation constants.

In the above discussion, we have tended to use a neutral ligand L in discussion, as this avoids dealing with charge variation in equations. This does not imply that the outcome is in any real way different for a neutral or anionic ligand; the same forms of equations apply. Whereas we can perhaps conceive more easily how an anionic ligand X- may be attracted to and form a coordinate bond with a metal cation recall that neutral ligands will display polarity as a result of different atoms in bonds. As a consequence a H-N bond, for example, may be considered as δ+H-Nδ- entity and it is the negative end of the dipole (or in effect, the lone pair) that attaches to the metal cation. As a consequence, one might anticipate that more polar neutral ligands will make better ligands. Most heteroatoms in molecules that act as efficient ligands to metal ions carry substantial partial negative charge.

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مواضيع ذات صلة

Host–Guest Molecular Assemblies

Encapsulation Compounds

Compounds of Polydentate Ligands

Sophisticated Shapes

Isomer Preferences

Constitutional (Structural) Isomerism

Isomerism– Real 3D Effects

Chameleon Complexes

Moulding a Relationship - Ligand Influences

Metallic Genetics– Metal Ion Influences

Higher Coordination Numbers (ML7 to ML9)

Six Coordination (ML6)