Inner sphere, entropy

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. 

Often, it is difficult to distinguish definitely between inner sphere and outer sphere complexes in the same system. Based on the preceding discussion of the thermodynamic parameters, AH and AS values can be used, with cation, to obtain insight into the outer vs. inner sphere nature of metal complexes. For inner sphere complexation, the hydration sphere is disrupted more extensively and the net entropy and enthalpy changes are usually positive. In outer sphere complexes, the dehydration sphere is less disrupted. The net enthalpy and entropy changes are negative due to the complexation with its decrease in randomness without a compensatory disruption of the hydration spheres. 

The binding time (Tm = 1 /kex) of water molecules in the inner sphere is assumed to obey the Eyring equation (Eq. (21)), where AS and AH are the entropy and enthalpy of activation for the exchange process, and k2x98 is the exchange rate at 298.15 K. 

The thermodynamic parameters (i.e.) the enthalpy and entropy values showed the formation of inner-sphere chloro complexes in the case of all the lanthanides. The enthalpies for the formation of monobromo complexes of lanthanides are also positive but smaller in magnitude than the corresponding chloro complexes. The complex formation enthalpies follow the sequence A//°(C1) > A//°(Br) > A//°(I) which is unusual for hard metal(III) ions. 

Considering these thermodynamic values, we suggest that fluoride forms inner-sphere complexes like the acetate and sulfate rather than ion pairs like chloride, nitrate, and thiocyanate. Similar to the other inner-sphere complexes, stability is attributed to the positive entropies which have been interpreted in the earlier studies as reflecting the... 

Explain why the stability of inner-sphere complexes is usually favored by a positive entropy of formation of the complex. 

For this type of system, the entropy associated with inner sphere reorganization is negligible [5]. Therefore, the work can be equated to the corresponding change in Gibbs energy, so that... 

Analysis of the entropy changes, indicates essentially 100% inner sphere formation for the Ac, 3 ClPr and ClAc complexes, 50% inner sphere for the CI2AC complexes. However, a study of 139La nmr shifts (18) was interpreted to show only 50% inner sphere character for LaClAc+2 and 20-25% for LaCl2Ac+. In light of this lack of agreement, we have analysed the complexation by another approach which would seem to be more justified than the entropy based estimations. 

J/m/K. The agreement between the nmr estimates and those from equation (1) add weight to the estimates in Table III. In Figure 2 the variation of log i and log 0 as functions of pKa reflect the vital role of ligand basicity in the inner-outer sphere competition. These curves indicate that the cross-over from predominantly outer sphere to predominantly inner sphere occurs near pKa values of 2. However, since the enthalpy and entropy changes for inner sphere complexation are larger than for outer sphere formation, both AH and AS would still be endothermic (characteristic of inner sphere reaction). 

The interpretation was that the entropy term was primarily responsible for the slow reaction in this case, and very approximately, a TAS value at 298.13 K of 20kJ mol compared to the experimental value of 27 kJ moP was obtained. However, it was pointed out that the quantitative interpretation needs to be considered with care, as ASjf is the total transition-state activation entropy and not only the inner-sphere reorganization part [452]. In addition, DFT-based studies have shown the importance of the influence of the second coordination sphere [453]. 

Kgure 4. Mixed aquo-chloro complexes of Zn. The static formation energy of the more hydrated cluster is only 2 kJ/mole more stable. This is less than the cost in entropy associated with the increased hydration at T > 25°C. Hence, in aqueous solutions, ZnCb will have only two inner-sphere water molecules in its solvation sphere. 

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