Fusion, entropy equilibria

Sm - Sc) = A/fm-c/Tg > 0 is the fusion entropy. If the equilibrium pressure between the crystalline phase and the melt under the given temperature is known to be Pe, then... 

Entropy of fusion kJK-i mol (of CH2 Macroscopic ideal crystal, from heat of fusion and equilibrium melting temperature 9.9 X 10 (66-70)... 

Once the enthalpy of fusion is known, because solid and liquid are at equilibrium at the melting point, the entropy of the molten component at 7) is also known through... 

Fig. 1. Schematic thermal analysis results on fusion and devitrification (top and bottom curves, respectively). The area under the peak in the top curve represents the heat of fusion Hf and can be used to calculate the entropy of fusion ASf = AHf/Tm in case of equilibrium melting. The increase in heat capacity ACP at Tg is related to the number of motifs that gain mobility...

By calculating the enthalpy of the reaction and assuming no significant entropy change, the AH (based on heats of formation and heats of fusion) of Equation 3 is approximately +5.2 kcal/mole and of Equation 4 is approximately +10.5 kcal/mole. While both reactions are not favored thermodynamically, at high temperatures (i.e., 375°C), these reactions will establish an equilibrium where significant amounts of KOH and/or K+ and OH" may exist. 

The concept of melting point may be put on a more quantitative basis. The process of melting is a thermal one and is characterized by the collapse of molecular units in a crystal to a disordered array. Energy is required to rupture the crystal lattice so that the heat of fusion, A/7fus, is positive. In addition, the solid-liquid transition involves an increase of randomness and the entropy of fusion, ASfts, is also positive. Melting point is the temperature of fusion (7 ) at which solid and liquid phases are in equilibrium. Therefore,... 

The melting point is defined as the temperature at which the liquid is in equilibrium with the solid so that the difference in Gibbs free energy between the two phases is zero. The entropy of fusion can then be expressed as. 

DSC analysis represents a superior method of thermal analysis, in that the area under a DSC peak is directly proportional to the heat absorbed or evolved by the thermal event, and integration of these peak areas yields the enthalpy of reaction (in units of calor-ies/gram or Joules/gram). Even though conclusions reached on the basis of enthalpies of fusion are possibly compromised by their omission of the entropy contribution, an indication of the thermodynamic trends inherent in the system is often possible. For instance, the same polymorphic form of moricizine hydrochloride was deduced on the basis of thermal analysis and equilibrium solubility measurements. On the other hand, auranofin represents a compound for which one anhydrous polymorphic form is predicted to be the most stable by virtue of its melting point and heat of fusion but for which solubility measurements demonstrate that the other polymorph was in fact the thermodynamically stable form. ... 

Let us first consider the ice-water equilibrium. For the ice water transition, AH is the molar heat of fusion (see Table 11.8), and T is the melting point. The entropy change is therefore... 

Answer At the melting point, the system is at equilibrium. Therefore AG = 0 and the entropy of fusion is given by... 

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