Entropy of formation

The enthalpy of combustion of isoxazole was only determined several years ago (78MI41615). For isoxazole, AH°c (298.15 K) =-(1649.85 0.50) kJ mol , from which the entropy of formation in the gas phase was derived as AH tig) = 78.50 0.54 kJ moF. The enthalpies of combustion of 3-amino-5-methylisoxazole and 5-amino-3,4-dimethyl-isoxazole have also been determined (73MI41606). 

Entropy of Formation The ideal gas standard entropy of formation (AS°298) of a chemical compound is the increment of entropy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard state definea as the existing phase at a temperature of 298.15 K and one atmosphere (101.325 kPa). Thus ... 

Corresponding to the integral heat and entropy of formation of the solution are the partial molar heats A//, and entropies AS, of solution of the components where... 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

TABLE III. Integral Excess Entropies of Formation of Concentrated Solutions a... 

Standard Free Energies, Enthalpies, and Entropies of Formation of Palladium and Nickel Hydrides ... 

The constant of equilibrium of the whole reaction may be formulated as product of the constants of elementary steps, because the same heat and entropy of formation is expected for every single step. 

The entropy of formation is calculated from 5° values obtained from Third Law measurements (Chapter 4) or calculated from statistical thermodynamics (Chapter 10). The combination of AfS with Af// gives AfG. For example, for the reaction at 298.15 K... 

Entropy of formation, solution, and dehydration, halides and halo-... 

The entropy of formation of the Hg/solution interface has been determined for a number of solvents.81,108,291-294,304 It is positive for all... 

The Hg/dimethyl formamide (DMF) interface has been studied by capacitance measurements10,120,294,301,310 in the presence of various tetraalkylammonium and alkali metal perchlorates in the range of temperatures -15 to 40°C. The specific adsorption of (C2H5)4NC104 was found to be negligible.108,109 The properties of the inner layer were analyzed on the basis of a three-state model. The temperature coefficient of the inner-layer potential drop has been found to be negative at Easo, with a minimum at -5.5 fiC cm-2. Thus the entropy of formation of the interface has a maximum at this charge. These data cannot be described... 

The entropy of formation of the interface was calculated from the temperature coefficient of the interfacial tension.304 The entropy of formation has been found to increase with the nature of the electrolyte in the same sequence as the single cation entropy in DMSO.108, 09,329 The entropy of formation showed a maximum at negative charges. The difference in AS between the maximum and the value at ff=ocan be taken as a measure of the specific ordering of the solvent at the electrode/solution interface. Data 108,109304314 have shown that A(AS) decreases in the sequence NMF > DMSO > DMF > H90 > PC > MeOH. 

This expression corresponds to the Arrhenius equation (14.1) and basically provides the possibihty of calculating the preexponential factor (a calculation of is, in fact, not easy). It also shows that in the Arrhenius equation it will be more correct to use the parameter AG rather than A//. However, since AGt = Aff TASt, it follows that the preexponential factor of Eq. (14.4) will contain an additional factor exp(ASi/R) reflecting the entropy of formation of the transition state when the enthalpy is used in this equation. 

Standard enthalpies of formation, A / , and standard entropies of formation, at... 

The entropy of formation of an ideal solution at a given temperature can be obtained from the following equation... 

The variation of the entropy of formation of an ideal solution with composition is shown inFigure3.10. It is again a characteristic ofan ideal solution that the partial (ASA,ld, A. Sg1, ld) and the integral molar (ASM,ld) entropies of its formation are independent of temperature. 

Carell and Olin (58) were the first to derive thermodynamic functions relating to beryllium hydrolysis. They determined the enthalpy and entropy of formation of the species Be2(OH)3+ and Be3(OH)3+. Subsequently, Mesmer and Baes determined the enthalpies for these two species from the temperature variation of the respective equilibrium constants. They also determined a value for the species Be5(OH) + (66). Ishiguro and Ohtaki measured the enthalpies of formation of Be2(OH)3+ and Be3(OH)3+ calorimetrically in solution in water and water/dioxan mixtures (99). The agreement between the values is satisfactory considering the fact that they were obtained with different chemical models and ionic media. 

S°(dimer)/S°(monomer) = 1.52 0.05 J mol-1 K-1 This yields a value of the entropy of formation of the transition state molecule... 

A thorough kinetic and thermodynamic analysis of this model system (small positive or negative enthalpies of formation are canceled by more negative entropies of formation) led Karlin s group to conclude that the stability of dioxygen binding is driven by favorable enthalpies, but unfavorable reaction entropies preclude observation of Cu2-02 at room temperatures.412... 

Figure 8.2 Plot of free energy vs. temperature for two species (molecules or LC phases) with different entropies of formation.

Referring to the plot of G vs. T for the isotropic and nematic fluids, a uni-molecular isomerization process would show the same characteristics if one of the isomers had a higher entropy of formation than the other. In the molecular case, however, the equilibrium constant at a given temperature would derive from the free energies on a per molecule basis, while for the phases this free energy is per collective volume of molecules. The similarities to a molecular isomerization, however, are more important than the differences for the purposes of this discussion. The transition from isotropic fluid to nematic LC can be considered a temperature-driven, or thermotropic, isomerization. 

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