Entropy favourable changes

The process shown in Figure 7.5 is certainly a favourable change. Yet no exchange of energy is involved. The condition that influences this change is called entropy. It is an important condition in all physical and chemical changes. 

What does entropy have to do with favourable chemical changes and equilibrium systems All favourable changes involve an increase in the total amount of entropy. Recall the endothermic reaction in Figure 7.4. 

Now recall the reaction between mercury and oxygen. It favours the formation of HgO below about 400°C, but the decomposition of HgO above 400°C. This reaction highlights the importance of temperature to favourable change. Enthalpy, entropy, and temperature are linked in a concept called free energy. 

As you know from Chapter 7, a change is favoured when AG is negative. When a salt dissolves, the entropy of the system always increases, because ions in solution are more disordered than ions in a solid crystal. An increase in entropy favours the formation of a solution because the term -TAS is negative. Most solids dissolve to a greater extent at higher solution temperatures, because the term -TAS becomes more negative. 

The driving force for the spin crossover is the change in the Gibbs energy the enthalpy-unfavourable high-spin state becomes entropy-favoured above Tc. An opposite transition from the high-spin to a low-spin state with rising temperature has not been reported so far. 

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 . ... 

There is also an entropy term associated with the desolvation of the ligands. This is much more difficult to assess, and may make for either favourable or unfavourable contributions to the overall entropy changes. 

The reaction favours the formation of ozone with a significant equilibrium constant. Appendix C also lists the enthalpies of formation and the standard enthalpy of the reaction ArH° can be calculated. The answer for the enthalpy calculation is ArH° = —106.47 kJ mol, showing this to be an exothermic reaction, liberating heat. The entropy change at 298 K can also be calculated because ArG° = ArH° — T ArS°, so ArS° = 25.4 Jmol-1 K-1, indicating an increase in the entropy of the reaction as it proceeds by creating one molecule from two. 

The solubility of solids in liquids is an important process for the analyst, who frequently uses dissolution as a primary step in an analysis or uses precipitation as a separation procedure. The dissolution of a solid in a liquid is favoured by the entropy change as explained by the principle of maximum disorder discussed earlier. However it is necessary to supply energy in order to break up the lattice and for ionic solids this may be several hundred kilojoules per mole. Even so many of these compounds are soluble in water. After break up of the lattice the solute species are dispersed within the solvent, requiring further energy and producing some weakening of the solvent-solvent interactions. 

As seen in Table 2, A//yS = 9.42 kcal mol-1 and AAxS = 13.9 e.u., and so the free energy of transition state stabilization (approximately 5 kcal mol-1) results from a favourable enthalpy change, partly offset by an unfavourable entropy change. A similar situation pertains to binding of the substrate also (Table 2). Thus, the similarity between transition state binding and substrate binding, pointed out above from the correlation of p/fTS with pKs, is evident in thermodynamic parameters as well. 

For soft cations, such as Ag+ and Pb2+, covalent contributions are much more important, and consequently the observed order of complex stabilities is quite different from that for alkali cations NH > O > S for Pb2+ and NH, S > O for Ag+. Dissection of the overall effect into enthalpy and entropy contributions (Table 15) reveals the complicated nature of the heteroatom effect. For K+ and Ba2+, the more favourable entropy contribution for N and S ligands is more than offset by the unfavourable change in enthalpy of binding. 

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. 

What conditions determine whether or not a change is favourable How are different conditions related to equilibrium, where forward and reverse changes occur at the same rate The answers to these questions are linked to two important concepts in thermodynamics enthalpy and entropy. 

O O Write a short paragraph, or use a graphic organizer, to show the relationship among the following concepts favourable chemical change, temperature, enthalpy, entropy, free energy. 

Based on the change in enthalpy, you would expect that water would always freeze. Use the concepts of entropy and free energy to explain why this phase change is favourable only below 0°C. 

In Chapter 7, you learned that three factors—change in enthalpy (AH), change in entropy (AS), and temperature (T)—determine whether or not a change is favoured. The same three factors are important for determining how much of a salt will dissolve in a certain volume of water. These factors are combined in the following equation, where AG is the change in free energy of the system. 

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