Entropy estimating temperature effects

Vapour pressure measurements have led to heats of sublimation of octafluoro-naphthalene and decafluorobiphenyl of 79.3 2.4 and 85.2 2.3 kJ mol , respectively, and the enthalpy of fusion and heat capacity of octafluorotoluene have been obtained from adiabatic calorimetry at 10—365 K the last study yields a triple-point temperature of 207.69 K, and the standard entropy of the ideal gas is 462.6 J K mol i at 298.15 K. Adiabatic calorimetry has also been used to obtain the heat capacities of the three tetrafluorobenzenes at 11— 353 K, and the entropies of the liquids at 298.15 K are 256.1,257.3, and 250.4 J mol- for the 1,2,3,4-, 1,2,3,5-, and 1,2,4,5-isomers, respectively 1,2,3-trichlorotrifluorobenzene fcry-stals) has an entropy of 243.3 J mol at 298.15 K. . Liquid densities from 293 to 490 K have been determined for eight polyfluoroarenes (CeFe, CeFsH, 1,2,3,4-F4C H2, CsFsa. l,3.5-F3C6Cl3, CsFs CFa, CeFsMe, and CeFsOH) and densities up to the critical temperatures have been estimated the effects of dissolved... 

It is noteworthy that the value of this substrate is smaller by one order compared to non-cyclic compounds. According to the discussions proposed above, this is considered to be due to its conformation already being fixed to the one that fits to the binding site of the enzyme. This estimation was demonstrated to be true by the examination of the effect of temperature on the kinetic parameters. Arrhenius plots of the rate constants of indane dicarboxylic acid and phenyl-malonic acid showed that the activation entropies of these substrates are —27.6 and —38.5 calmol K , respectively. The smaller activation entropy for the cyclic compound demonstrates that the 5yn-periplanar conformation of the substrate resembles the one of the transition state. 

Reasonably reliable pATbh+ values for the protonation of weak bases or of weakly basic substrates can be obtained via equation (17), together with m slope parameters that can be used to classify basic molecules as to type, and for an estimate of the solvation requirements of the protonated base. Measurements at temperatures other than 25°C can be handled using equation (22), and enthalpies and entropies for the protonation can be obtained. Protonation-dehydration processes are covered by equation (26). Medium effects on the... 

Free energy variations with temperature can also be used to estimate reaction enthalpies. However, few studies devoted to the temperature dependence of adsorption phenomena have been published. In one such study of potassium octyl hydroxamate adsorption on barite, calcite and bastnaesite, it was observed that adsorption increased markedly with temperature, which suggested the enthalpies were endothermic (26). The resulting large positive entropies were attributed to loosening of ordered water structure, both at the mineral surface and in the solvent surrounding octyl hydroxamate ions during the adsorption process, as well as hydrophobic chain association effects. 

We are at a loss to explain the discrepancy in the BF3 enthalpies of interaction with the sulfur donors. Steric effects may be operative, but this is far from the whole story for the BCI3 interaction is much larger than BF3 with these donors. Furthermore, using the tentative ( 113)3 parameters to estimate those of ( 2115)3 , we calculate an enthalpy from E and of 11.1 k.cal mole- for the BF3-P( 2H6)3 adduct compared to a measured value of 9.5 k.cal mole i. The authors report much difficulty with the sulfur donor system, but their error estimates could not possibly account for the difference between our calculated and the observed result. The behavior of ( 2115)35 compared to ( 2115)3 is clearly inconsistent with the behavior of these two donors toward ( 2H5)sAl where both enthalpies are correctly predicted with our parameters. It may be that the BF3-( 2115)25 system has an even lower equilibrium constant than reported and is completely dissociated over the temperature range studied. (This would require a very different entropy if the — AH predicted by E and were correct.) A slight impurity (reported to be less than 0.1%) or decomposition product could interact appreciably with BF3 and changing pressure contributions from this adduct with temperature could be attributed incorrectly to the sulfur donor adduct. The actual BF3-sulfur donor adduct would then be a very common example of an adduct which cannot be studied by the vapor pressure technique because it is completely dissociated at the temperatures at which one of the components has appreciable vapor pressure. We have examined the reaction of BF3 ( 2Hs) 2O with large excess of ( H2) 4S in dichloroethane solution at 25 ° and have found the equilibrium constant to be too low to be measured calorimetrically. 

The conformational entropies of copolymer chains are calculated through utilization of semiempirical potential energy functions and adoption of the RIS model of polymers. It is assumed that the glass transition temperature, Tg, is inversely related to the intramolecular, equilibrium flexibility of a copolymer chain as manifested by its conformational entropy. This approach is applied to the vinyl copolymers of vinyl chloride and vinylidene chloride with methyl acrylate, where the stereoregularity of each copolymer is explicitly considered, and correctly predicts the observed deviations from the Fox relation when they occur. It therefore appears that the sequence distribution - Tg effects observed in many copolymers may have an intramolecular origin in the form of specific molecular interactions between adjacent monomer units, which can be characterized by estimating the resultant conformational entropy. 

The equilibrium constants derived from the 31P NMR spectra at temperatures below coalescence show that there is a considerable predominance of the axial conformer of 2-diphenylphosphinoyltetrahydrothiopyran (Table 26) which contrasts with the equatorial preference in the corresponding cyclohexane derivative. This result indicates a strong anomeric effect, estimated at 2.40 kcal mol-1. The corresponding data for the anancomeric cis and trans 4-/-butyl derivative at chemical equilibration are presented in Table 26. The large difference in AG° at 173 and 323 K is compatible with a significant entropy effect, calculated AS° = +4.8 0.7 cal K.mol-1, with... 

This compound, which is monomeric in the solid state, exists in toluene solution in equilibrium with its dimer (Scheme 2)18 as evident from analyses of variable temperature H, 7Li and 13C NMR. Whereas the monomer is favored at higher temperatures in terms of the entropy effect, the dimer is favored at lower temperatures in terms of electrostatic interactions through which electrons of the germanium negative centers are efficiently stabilized by the two lithium cations. The thermodynamic parameters for this equilibrium were estimated. 

A frequent assumption is that pressure has a negligible effect on liquid-phase properties, and that the properties of a compressed liquid are essentially those of the saturated liquid at the same temperature. Estimate the errors when the enthalpy and entropy of liquid ammonia at 270 K. and 1,500 kPa are assumed equal to the enthalpy and entropy of saturated liquid ammonia at 270 K. For saturated liquid ammonia at 270 K, P" = 381 kPa, V1 = 1.551 x 10 3 m3 kg , and p = 2,095 x 10 3 K . 

The calculations yield S and AS° values of appreciable magnitude, +18 eu (cal moff and +10 eu, respectively, and in contrast to the free energies, calculated S and H quantities depart substantially from the quadratic relationship given by Eq. 112. In the case of small a and also small 7.,s-, one expects, from Eq. 112, the value of S /AS° to be approximately 0.5, whereas the calculations yield a ratio of approximately 2 (the distinction is pronounced even when the sizable estimated statistical uncertainties ( 5 eu) in the calculated entropies is taken account of). For this result to be compatible with Eq. 112, it would require a sizable positive value of /..S, but in fact the simulation results indicated a.s 0. Thus, for reaction 107, as represented by the simulation and model molecular Hamiltonian [36], we infer that near room temperature the separate entropy and enthalpy quantities are not well accounted for by a harmonic model, whereas, due to compensating effects, harmonic behavior is recovered when they are combined in the free-energy quantities. 

Doye and Calvo54 included entropy effects for large Lennard-Jones clusters and used the results in estimating which structures will be dominating as a function of size and temperature of the cluster. Their main results are reproduced in Figure 9. Most interesting may be that the crystal structure is not found before N is well above 100 000. 

---