Entropy illustrating changes

The effect of the leaving group is illustrated in the comparison of fluoro- and chloro-nitrobenzenes (Table VIII) in their reactions with ethoxide ion (lines 5 and 8) and with piperidine (lines 7 and 9). Rate ratios F Cl are 23 1 (opposing and entropy of activation changes) and 201 1 (E effect), respectively, for the two nucleophiles. For the reasons discussed in Section II, D, 1, a fluorine substituent produces a lower energy of repulsion of the nucleophile and thus facilitates reaction. 

The increase in the entropy of an irreversible process may be illustrated in the following manner. Considering the spontaneous transfer of a quantity of heat 8q from one part of a system at a temperature T, to another part at a temperature 7, then the net change in the entropy of the system as a whole is then ... 

Equation refers to molar quantities. To obtain the total entropy of a sample, we must multiply its molar entropy by n, the number of moles. Example illustrates the calculation of A S for a change in concentration. 

Schematic view of the three phase changes leading from more constrained to less constrained phases, illustrated by the phase changes for water. Each is accompanied by positive enthalpy and entropy changes for the substance.

Usually, activation energies for dissociation are much higher than k T and situations like this, where the apparent activation energy becomes negative for the rate-limiting process, are rare. Nevertheless, the present case illustrates nicely that entropy changes may play an important role and that it is not always the activation energy that dominates the process. 

A further illustration and summary of the entropy and temperature changes involved upon moving between two magnetic fields is shown in Figure 9.2 [13]. 

To determine the entropy change in this irreversible adiabatic process, it is necessary to find a reversible path from a to b. An infinite number of reversible paths are possible, and two are illustrated by the dashed lines in Figure 6.7. 

Figure 6.4. (a) Variation of the entropy of fusion with melting point for different crystal structures (from Saunders el at. 1988) and (b) schematic illustration of the possibility of a change in value and sign for the entropy of transformation if the metastable structure has a low melting point (from Miodownik 1992). 

A more general explanation of the temperature independence of the phase-transition quantities will be illustrated with ASa—although it could be illustrated equally as well with AThe integral entropy change for the phase transition is related to the partial entropy changes by Equation 21 (53). 

The term entropy, which literally means a change within, was first used in 1851 by Rudolf Clausius, one of the formulators of the second law of thermodynamics. A rigorous quantitative definition of entropy involves statistical and probability considerations. However, its nature can be illustrated qualitatively by three simple examples, each demonstrating one aspect of entropy. The key descriptors of entropy are randomness and disorder, manifested in different ways. 

The melting process can be characterized by the entropy change on fusion8. Thermal analysis of fusion is illustrated in Fig. 1. We can break the overall entropy of fusion ASf into the three approximate parts positional, orientational, and conformational entropy of fusion... 

No general rules about the entropy of transitions, as were found for liquid and plastic crystal transitions, can be set up for condis crystals. Two typical examples may illustrate this point. Polytetrafluoroethylene has a relatively small room-temperature transition-entropy on its change to the condis state and a larger transition entropy for final melting. Polyethylene has, in contrast, a higher condis crystal transition entropy than melting entropy (see Sect. 5.3.2). 

---