Investigations on metal complexes in solution

In the last few years, the stability constants for several hundred systems of complex ions in aqueous solution have been measured. However, few values for heat and entropy changes in the formation of complexes have been reported, although In several published discussions, the need for such information has been remarked. No full realisation of the fundamentals of complex formation may be achieved without this information.
The majority of known heats of formation of complexes have not been measured by direct colorimetry but derived from the variation of stability with temperature, by the thermodynamic relationships,
RT ln K° =  - ΔF° = - ΔH° - TΔS°
d ln K° =  - ΔH°
dT       RT
As more data are produced, it is becoming increasingly obvious that little reliance may be attached to the results found by this method.
As illustration, the results obtained by Independent workers for the formation of the two well defined complexes of Cu2+ with ethylenediamine range from a value of 30% less than the calorimetric value to one 40% in excess of the calorimetric value.
Although it was realised that the method could not yield results with accuracy approaching that of calorimetry, it was felt that they would still be of value if the errors did not exceed &pm; 10%. Two of the most accurate and reliable methods of measuring stability constants, viz. the determination of solubilities and the Bjerrum potentiometric method using a glass electrode, were therefore employed at a series of temperatures to find heats of formation of some metal ammines.
The solubilities of silver bromate and iodate in solutions of pyridine and 2:6-lutidine were measured at 0°C, 25°C, and 40°C, and from the calculated stability constants, the heats of formation of the silver ammines were derived. They were found to be ~ 15% lower than the calorimetric values.
The system copper-ethylenediamine was reinvestigated, by the glass electrode method. Stability constants were measured at 20°, 25°, 30°, and 40°C. The derived heats of formation were found to be ~ 14% greater than the calorimetric values in this case.
Considerable care was taken to minimise activity effects, to avoid irregularities in the behaviour of the glass electrode, to exclude carbon dioxide from solution and to reduce other experimental errors as far as possible.
To see whether more accurate results could be obtained for another system, heats of formation were derived for complexes formed by Ni2+ and ethylenediamine; here the value for the tris-complex was found to be almost 50% larger than the calorimetric value.
A critical examination of the theoretical assumptions made in the calculation of heat changes from pH measurements leads to the conclusion that there must be experimental errors, as yet undetermined. Although values of Δ H calculated from the temperature coefficients of stability constants are unreliable, (due, principally, to the small temperature range over which it is possible to make stability measurements), measurements of free energy changes by the glass electrode method differ little from the standard free energy changes. When combined with heats of formation measured calorimetrically, the resulting entropy changes do not differ from standard quantities by more than &pm; 2 e.u.
Heats of formation were measured directly in a twin micro-calorimeter, in each vessel of which was mounted an all-glass hypodermic syringe actuated by an external micrometer screw-gauge. Overall heats of formation were measured by observing the heat given out when a small known weight of concentrated metal solution was injected into a large volume of amine solution containing excess ligand.
Several different types of metal ammine systems were studied by calorlmetry in conjunction with glass electrode measurements in aqueous solutions of ionic strength 0.10 at 25°C. In the discussion of results, emphasis is laid upon the fact that the interacting ions and molecules are surrounded by sheaths of water molecules. The complete or partial destruction of such sheaths involve changes in energy and entropy which must be taken into account when interpreting the observed overall heat and entropy changes.
Silver Ammines
The increase of polarity of the nitrogen atoms in the series of methyl-substituted pyridines, pyridine <3-picoline <2-picoline ~4-picoline <2:6-lutidine is shown by the increasing heats of reaction with hydrogen ion, and corresponding increases in the free energy. Entropy changes are small and nearly the same value for each base (~ + 6 e.u.).
With silver-ion, the stabilities of the bis-complexes are found to increase in the above order. pKAH (a meaeure of the affinity of a base for hydrogen ion) varies linearly with log β2 ( a measure of the affinity of a base for Ag+). However, the heats of formation of Ag(2-picoline)+2 and Ag(2:6-lutidine)+2 are found to be smaller than the heat of formation of the less stable complex Ag(pyridine)+2 . It is suggested that this is due to the fact that the 2-methyl groups interact with the hydration sheath of the silver ion. Some of the heat resulting from the formation of the metal-ligand bonds will be absorbed in the "melting" of hydration sheath. The released solvent partlcles cause an increase in the entropy of the system. The entropies of formation of the two complexes containing 2-methyl groups are more positive than the entropy of formation of Ag(pyridlne)+2.
The lowering in the heat terms due to hydration is compensated by the increase in the entropy terms, so that stability constants do constitute a more reliable measure of metal-ligand bond strength than do heats of reaction in aqueous solution
Complexes of Diamines
The same compensation effect is shown by the trisethylenediamine complexes of Zn2+ and Cd2+. Zn2+, which is more highly hydrated than Cd2+ (as shown by its more negative entropy of solution) forms the more stable complex. However, the heat of formation of its tris-complex (-15.52 K.cal/g.ion) is smaller than that of the tris-complex of Cd2+ (-19.74K.cal./g.ion), although there can be little doubt that Zn2+ forms the stronger metal-ligand bonds.
The destruction of the larger water sheath around the zinc ion in the formation of its tris-complex results in the entropy change being more positive for Zn2+ (+2.6 e.u.) than for Cd2+ (-16.9 e.u,).
Five- and Six-Member Rings
Both heat and free energy changes are larger for l:3-diaminopropane than for ethylenediamine in the reactions with hydrogen ion. However, complexes of the divalent transition-metal a with l:3-diaminopropane are found to be less stable than those with ethylenediamine. This is an example of the general phenomenon that chelate complexes containing six-member rings are less stable than comparable chelates containing five-member rings. The lower stability of six-member rings has previously been generally attributed to an entropy effect. The present measurements show that for copper complexes, at least, it is the heat term and not the entropy term which changes with size of ring.
Complexes of l:l0-Phenanthroline
Heats of formation of the tris-phenanthroline complexes of Fe2+, Ni2+, Zn2+ and Cd2+, were determined calorimetrically. The values taken in conjunction with free energy measurements show that the ferrous complex has an abnormally large negative entropy of formation compared with the tris-complexes of the other three cations. The abnormally high stability and the diamagnetism of the ferrous tris-complex have been attributed to "inner type" 3d24s4p3 bonding, and it is suggested that this bonding could cause a high charge density upon the periphery of the complex with an attendant partial "freezing" of solvent particles around it. This hypothesis also accounts satisfactorily for some recently published figures for the entropies of activation in the racemisation of the complex ions Fe(phenan)2+3 and N1(phenan)2+3.