Entropy variation with temperature

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. 

A spectrophotometric study of an aqueous solution of silver(II) containing nitric acid and an excess of 2,2 -bipyridine was consistent with the existence of only two complexes related by the equilibrium shown in equation (30). At 25 °C, for this equilibrium was determined as 3.3 0.5 x 10 3. From the variation with temperature the enthalpy and entropy for the reaction were calculated to be 11.5 2.6 kJ mol 1 and -9 10 J K-1 mol-1 respectively.528... 

Variation of Entropy, S with Temperature, T at Constant Pressure (dP = 0)... 

Since A<5max showed no significant variation with temperature and pressure, enthalpy AH and entropy AS of reaction could be easily determined by variable-temperature single-point analyses and the volume of reaction AV by variable-pressure H-NMR studies. 

From this it can be seen that the entropy and enthalpy of a cell reaction can be obtained from the cell potential and its variation with temperature. 

At first, we observe that no data are provided about the molar heat capacities of the components or about their variations with temperature. Consequently, we assume that the standard enthalpies and entropies do not vary with temperature between two state changes. 

Fig. 7.6. Variations with temperature of the two rate constants observed for refolding of staphylococcal nuclease. Activation entropy for the slower process was 33 eu, and for the faster one 58 eu (from Epstein et aU 1971a).

The enthalpy of fomiation is obtained from enthalpies of combustion, usually made at 298.15 K while the standard entropy at 298.15 K is derived by integration of the heat capacity as a function of temperature from T = 0 K to 298.15 K according to equation (B 1.27.16). The Gibbs-FIehiiholtz relation gives the variation of the Gibbs energy with temperature... 

The variation of Cp for crystalline thiazole between 145 and 175°K reveals a marked inflection that has been attributed to a gain in molecular freedom within the crystal lattice. The heat capacity of the liquid phase varies nearly linearly with temperature to 310°K, at which temperature it rises more rapidly. This thermal behavior, which is not uncommon for nitrogen compounds, has been attributed to weak intermolecular association. The remarkable agreement of the third-law ideal-gas entropy at... 

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,... 

Figure 7.9. Variation of (a) the Gibbs energy, (b) ttie enthalpy and (c) the entropy with temperature (scaled to the nearest-nei bour interaction energy J ) for the complex structure A15. Comparison between BWG CVM in the tetrahedron approximation ( ) and the Monte Carlo method (—) (Turchi and Finel 1992).

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