Entropy of complexation

In addition to R, the informational capability of a laboratory, 7, was assessed as the entropy of complex system [2], using the information about analytical resources of the laboratory. 

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

An important factor is the temperature. Firstly, more of the salt is extracted into the organic layer at lower temperature (Sousa et al., 1978). This indicates that for these salts the entropy of complexation has a substantial negative value (Kyba et al., 1978). Secondly, the temperature has an effect on the value of the EDC lower temperatures give rise to higher EDC and d(dG°) values (Table 73). The available data on the effect of temperature hardly allow a quantitative... 

In contrast to stability constants, there are very few data for enthalpies and entropies of complex formation for hydroxypyranonate and hydroxypyridinonate complexes. Early studies on zinc-maltolate (190) and first-row transition metal(II) complexes of kojate (191) gave estimates of enthalpies and entropies of formation from temperature variation of stability constants, though as accurate stability constant measurements are only possible over a rather short temperature range the Aff and AS values obtained cannot be of high precision. 

The nature of the medium may also have a strong influence on the complexation process via specific or non specific solvation effects on both the complexed and uncomplexed states. The solvent plays a very important role both on enthalpy and entropy of complexation. Stability and selectivity result from a subtle balance between solvation (of both L and S) and complexation (i.e. "solvation of S by L). 

Enthalpies and entropies of complexation have been measured for complexes of 12,13 (105), 135) and 29, 30 (127) Cation exchange rates have been determined for complexes of ligands 15 (137,138) and 30 (106, 127). 

The enthalpy and entropy of complex formation between Zn11 and picolinate and dipicolinate anions in aqueous solution have been determined by calorimetry and from formation constant data. The greater stability of the dipicolinate complex compared to the picolinate complex reflects an entropy effect, and Ais actually less favourable. These anions are well known to have a low basicity to H+ compared to their complexing ability to metals. In the present case, this probably reflects the coplanarity of the carboxylate anions and the pyridine ring, so that the oxygen atoms are in a favourable position to coordinate.800... 

As to Eq. (7), it is to be remembered that AG, in a general case is a function of p. Therefore, the experimental dependencies of p on concentration, chain length of oligomer and temperature may be employed to find thermodynamic parameters only for a fixed value of p, e.g., for p = 0.5 using Eqs. (8 a- b). These equations have been taken by various authors to calculate the enthalpy and entropy of complex formation between simple synthetic oligomers and polymers 28). In a number of cases the correspondence between the values of complex formation enthalpy thus obtained and determined, either by calorimetry or by potentiometric titration 26), has been found satisfactory although it is obvious that in a general case these values do not necessarily coincide. 

Calix[4]pyrroles are versatile ligands to the extent that the composition of the anion receptor complex is solvent dependent. This chapter has been concerned with the affinity of calix[4]pyrrole for the fluoride anion. It was therefore considered of relevant to focus attention on the steps required for the derivation of reliable thermodynamic data. It is indeed the ratio between stability constants which defines quantitatively the selectivity factor. Thus, representative examples are given to demonstrate selectivity in terms of anion, receptor and solvent. The key role played by solvation in the complexation of these receptors with the fluoride anion is unambiguously demonstrated in the variations observed in the stability constants, enthalpies and entropies of complexation of these systems in the various solvents (Table 2). One convenient measure to assess solvation is through the thermodynamics of transfer of product and reactants from one... 

Relaxation of complicated ligands may occur as a step in both pathways. Diebler and Eigen 461 indicated the ways in which such mechanisms could be analysed using fast reaction methods. Several studies of Ln(III) complex formation and of the formation of Ln(III) mixed complexes have been analysed. Generally the dissociative mechanism is considered to dominate and we are then concerned with the water exchange rate. Several studies have shown that the rate decreases from La(III) to Lu(III) but there seems to be a minimum rate around Tm(III). This is also seen in the rate of rotation of ligands on the surface of the ions, Fig. 7. There may be a small crystal field term, or another contribution to a tetrad -like effect from the 4f electron core. However in the hydrate the precise relationship between the inner and outer sphere water may also be important as we saw when we discussed the heat and entropy of complex ion formation. 

For review, see also MacDiarmid (269). S(29Si) and 5(31P), Chemical shift in ppm AH, enthalpy of complex formation inkcal/mol A5, entropy of complex formation in cal/mol degree Py, pyridine NMI, [Pg.283]

The data assembled in Table 4 indicate that the apparently simple size dependence of the recognition is no longer valid when the enthalpies and entropies of complexation are considered. For the smallest hosts 40 and 45, enthalpy strongly favors chloroform over methylene chloride, although the latter is the preferred... 

Correlations with heat of mixing have the inherent disadvantage that the heat depends upon AH of complex formation through the equilibrium constant of complex formation. Thus the entropy of complex... 

Thus, it is seen that the effect described by Schwarzenbach has precise thermodynamic meaning—the change in the entropy of translation that accompanies metal chelate ring formation. The entropy effects estimated by Schwarzenbach, up to 2.0 log K units, agree quite well with the value obtained with the thermodynamic approximation. Experimentally, one would expect wide deviations from this value (7.9 entropy units per chelate ring) because of the variations in solvation and internal entropies of complexes and ligands that occur in the displacement reaction. 

The AG term can be determined from knowledge of the enthalpy and entropy of complex formation, AH and AS , using the usual equation ... 

A second caveat concerns the dependence of the numerical values of the free energies and entropies of complexation on the concentration scale used. AH" must be calculated by applying the van t Hoff equation to or values, the complexation constants on the mole fraction or molal concentration scales, respectively. If one uses Kc (molar concentration), enthalpies mnst be corrected for the thermal expansion of the solvent. 

The thermodynamic stability constant k which represents the free energy of complex formation (AF° = — RT In k ) can be subdivided into heat and entropy terms (AF° = AH° — TAS°). The entropy of complex formation has been discussed elsewhere (Cobble, 1953 Schwarzenbach, 1954 Williams, 1954). The factors involved include (1) the size and geometry of metal ions and ligand molecules 2) the change in the number of molecules in the system on complex formation as they affect translational freedom (3) restrictions on the freedom of rings imposed by chelation and other restrictions of internal rotation and (4) the entropy of hydration for the water molecules displaced by ligands. 

Fiq. 10. Entropy of complexation (AS°) for Cu, Zn, and Cd complexes of ammonia, ethylenediamine (En), and ethylenediamine tetra-acetate (EDTA). 

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