Entropy high temperature

The acid hydrolysis of diaziridines has been investigated kinetic-ally. The reaction is first order and shows a relatively high temperature coefficient. Thus one finds a relatively high activation enthalpy (23-28 kcal) and a positive activation entropy (2-6 eu). The influence of substitution on nitrogen is small. The velocity of the diaziridine hydrolysis depends only in the weakly acid region on the acid concentration. Between pH 7 and 3 the fc-values rise by nearly 10 . For the... 

It is more common to find that AH° and AS° have the same sign (Table 17.2, III and IV). When this happens, the enthalpy and entropy factors oppose each other. AG° changes sign as temperature increases, and the direction of spontaneity reverses. At low temperatures, AH° predominates, and the exothermic reaction, which may be either the forward or the reverse reaction, occurs. As the temperature rises, the quantity TAS° increases in magnitude and eventually exceeds AH°. At high temperatures, the reaction that leads to an increase in entropy occurs. In most cases, 25°C is a low temperature, at least at a pressure of 1 atm. This explains why exothermic reactions are usually spontaneous at room temperature and atmospheric pressure. 

Of course, even in the case of acyclic alkenes reaction enthalpy is not exactly zero, and therefore the product distribution is never completely statistically determined. Table V gives equilibrium data for the metathesis of some lower alkenes, where deviations of the reaction enthalpy from zero are relatively large. In this table the ratio of the contributions of the reaction enthalpy and the reaction entropy to the free enthalpy of the reaction, expressed as AHr/TASr, is given together with the equilibrium distribution. It can be seen that for the metathesis of the lower linear alkenes the equilibrium distribution is determined predominantly by the reaction entropy, whereas in the case of the lower branched alkenes the reaction enthalpy dominates. If the reaction enthalpy deviates substantially from zero, the influence of the temperature on the equilibrium distribution will be considerable, since the high temperature limit will always be a 2 1 1 distribution. Typical examples of the influence of the temperature are given in Tables VI and VII. 

Cyclic monomers with five- and six-membered ring atoms exist in strainless puckered conformations their heats of polymerization are either negative or have small positive values due to the repulsion of eclipsed hydrogen atoms. Because the nthalpy and entropy contributions are comparable, the free energies of polymerization are either positive or may become positive at high temperatures. 

Although reactions in which molecules are cleaved into two or more pieces have favorable entropy effects, many potential cleavages do not take place because of large increases in enthalpy. An example is cleavage of ethane into two methyl radicals. In this case, a bond of 79 kcal mol (330 kJ mol ) is broken, and no new bond is formed to compensate for this enthalpy increase. However, ethane can be cleaved at very high temperatures, which illustrates the principle that entropy becomes more important as the temperature increases, as is obvious from the equation AG = AH — TAS. The enthalpy term is independent of temperature, while the entropy term is directly proportional to the absolute temperature. 

Reactions that have positive AH° and positive A S ° are favored by entropy but dis-favored by enthalpy. Such reactions are spontaneous at high temperature, where the T AS° term dominates A G °, because matter becomes dispersed during the reaction. A reaction is entropy-driven under these conditions. These reactions are nonspontaneous at low temperature, where the A iiT ° term dominates A G °. 

As described in Section 14-1. when AR and ZlS have the same sign, the spontaneous direction of a process depends on T. For a phase change, enthalpy dominates AG at low temperature, and the formation of the more constrained phase is spontaneous, hi contrast, entropy dominates AG at high temperature, and the formation of the less constrained phase is spontaneous. At one characteristic temperature, A G = 0, and the phase change proceeds in both directions at the same rate. The two phases coexist, and the system is in a state of d Tiamic equilibrium. 

At very high temperatures, however, the excited state will also be occupied. Entropy maximization requires that both levels be equally populated. The high-temperature limit of the partition function is... 

At sufficiently high temperatures, the term TS in the Gibbs free energy will dominate and the stable isomer will be that of greater entropy which is in general the HS state. 

The first expression clarifies that entropy of the system increases when it takes up heat. Absorption of heat results in rise of temperature. Increase in entropy per degree rise in temperature is not the same at all temperatures it is more at low temperatures and relatively less at high temperatures. This is shown by the inverse relationship between the entropy change and temperature. The combined expression for the variation of entropy change with quantity of heat and temperature, therefore becomes,... 

For many reactions in which the number of molecules of products equals the number of molecules of reactants => the entropy change is small => AG° will be determined by AH° except at high temperatures. 

However at elevated temperatures (T2 > Tj, Figure 9) the increased entropy (TAS) associated with an open shell structure overcomes the ti —ti enthalpy of dimerisation associated with these distorted Ti-stacked structures and they undergo a solid-solid phase transition (Figure 9) The high temperature phase is typically associated with a Ti-stack of regularly spaced radicals which exhibit longer inter-radical S- S contacts (ca. 3.7 A). This process was first observed by Oakley60 in the DTA radical thiadiazolopyrazine-l,3,2-dithiazolyl 26, and a number of other derivatives have subsequently been identified which exhibit similar behaviour. These are compiled in Table 1. 

The important quantities AH and AS are assumed to be temperature independent. This is often quite a good approximation, but the vibrational component of the entropy, which has been neglected altogether, will become increasingly important at high temperatures. The effects of these factors can cause the major defect type present to change as the temperature increases. Near to the transition temperature a complex equilibrium between both defect types will be present. 

Whereas the latter expression must be solved numerically for low temperatures, the entropy at high temperatures can be derived by a series expansion [4], For the Debye or Einstein models the entropy is essentially given in terms of a single parameter at high temperature ... 

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