Entropy change complexity

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

On the basis of the values of AS° derived in this way it appears that the chelate effect is usually due to more favourable entropy changes associated with ring formation. However, the objection can be made that and /3l-l as just defined have different dimensions and so are not directly comparable. It has been suggested that to surmount this objection concentrations should be expressed in the dimensionless unit mole fraction instead of the more usual mol dm. Since the concentration of pure water at 25°C is approximately 55.5 moldm , the value of concentration expressed in mole fractions = cone in moldm /55.5 Thus, while is thereby increased by the factor (55.5), /3l-l is increased by the factor (55.5) so that the derived values of AG° and AS° will be quite different. The effect of this change in units is shown in Table 19.1 for the Cd complexes of L = methylamine and L-L = ethylenediamine. It appears that the entropy advantage of the chelate, and with it the chelate effect itself, virtually disappears when mole fractions replace moldm . ... 

Quite similar equations can be formulated for AG and AH by use of the partition function f of the activated complex. It follows from equations (6) and (7) that AEp can only be evaluated if the partition functions and AEz are available from spectroscopic data or heat capacity measurements. However, if AG = AH, the entropy change AS equals zero, and if AEz also equal to zero, either AG or AH can then be identified with the potential energy change. If... 

Regardless of the relative importance of polar and nonpolar interactions in stabilizing the cyclohexaamylose-DFP inclusion complex, the results derived for this system cannot, with any confidence, be extrapolated to the chiral analogs. DFP is peculiar in the sense that the dissociation constant of the cyclohexaamylose-DFP complex exceeds the dissociation constants of related cyclohexaamylose-substrate inclusion complexes by an order of magnitude. This is probably a direct result of the unfavorable entropy change associated with the formation of the DFP complex. Thus, worthwhile speculation about the attractive forces that lead to enantiomeric specificity must await the measurement of thermodynamic parameters for the chiral substrates. 

Lu, N. Kofke, D. A. Woolf, T. B., Staging is more important than perturbation method for computation of enthalpy and entropy changes in complex systems, J. Phys. Chem. B 2003,107, 5598-5611... 

Thus, the steric factor may be explained with the help of entropy change. When two molecules come together to produce the activated complex, the total translational degrees of freedom are reduced (from 6 to 3) and rotational degrees of freedom also diminish. This is compensated by an increase in vibrational degrees of freedom. But the definite orientation in forming the activated complex necessarily reduced the entropy, i.e. AS is negative. This decrease in entropy is small when reaction takes place between simple atoms. The calculated value of kbT/h corresponds to collision frequency... 

It may prove possible to apply titration calorimetry data in one further direction. If AG can be estimated for SAL-goethite complexation and reaction enthalpies can be obtained under equilibrium conditions, then an entropy change for this reaction can also be derived. This can only be done, however, if the adsorption reaction can be shown to be reversible. Since this has not been proven as yet in our systems, such thermodynamic extensions of titration calorimetry can only be speculative at this time. 

As noted in table 11.1, the ability of THFTCA to separate LJO from trivalent lanthanide ions is mainly of enthalpic origin. Reaction 11.33 has a considerably more unfavorable enthalpic contribution than reaction 11.32. The complexation is, however, predominantly entropy driven because the T ArS° term dominates the ArH° contribution for all systems. The large positive entropy changes observed for reactions 11.32 and 11.33 result from the release of water molecules coordinated to the metal on complexation with the tridentate THFTCA2- ligand. Note that a negative entropy contribution would be expected if these reactions were truly 2 particle = 1 particle reactions [226]. 

The second important solvent effect on Lewis acid-Lewis base equilibria concerns the interactions with the Lewis base. Since water is also a good electron-pair acceptor129, Lewis-type interactions are competitive. This often seriously hampers the efficiency of Lewis acid catalysis in water. Thirdly, the intermolecular association of a solvent affects the Lewis acid-base equilibrium242. Upon complexation, one or more solvent molecules that were initially coordinated to the Lewis acid or the Lewis base are liberated into the bulk liquid phase, which is an entropically favourable process. This effect is more pronounced in aprotic than in protic solvents which usually have higher cohesive energy densities. The unfavourable entropy changes in protic solvents are somewhat counterbalanced by the formation of new hydrogen bonds in the bulk liquid. 

Since the equilibrium is largely in favour of the octadiene, kj > k, and hence these Arrhenius parameters must be very close to the values for the forward reaction. The normal value for the A factor is to be expected in this case since the reactant has a rigid structure with no possibility of free internal rotations, and hence there is httle entropy change on going to the transition complex. 

The entropy change between reactant and activated complex might not be zero. Thus, if the reactant had some rotational and/or translational... 

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