Molar entropy of fusion

C14-0050. Table lists molar enthalpies of fusion of several substances. Calculate the molar entropy of fusion at its normal melting point for each of the following (a) argon (b) methane (c) ethanol and (d) mercury. 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

Substituting this for the molar entropy of fusion in Equation 2.21, and rearranging, gives... 

The molar differential heat capacity at the melting point has proved to be negligible only for benzene and rigid, polyaromatic hydrocarbons, and a compilation of literature data indicates that ACpon the average is 80% of the molar entropy of fusion (Neau and Flynn, 1990). Although the Lrst assumption has been applied in many studies, the second assumption has gained favor in recent pharmaceutical literature (Subrahmanyam et al., 1992 Claramonte et al., 1993 Yu et al., 1994). 

Calculate the molar entropies of fusion and vaporization for benzene. Having a molecular weight of 78.1, benzene melts at 5.5°C with a heat of fusion of 2350 cal/(g mol). Its normal boding point is 80.1°C, and its heat of vaporization at that temperature is 94.1 cal/g. 

In other words, the melting point of a solid, T p, is equal to molar enthalpy of fusion, AHf s, divided by molar entropy of fusion, ASfus-Boiling takes place when the drive toward disorder overcomes the tendency to lose energy. Condensation, shown in Figure 18, takes place when the tendency to lose energy overcomes the drive to increase disorder. In other words, when AH p > TASyap, the liquid state is favored. The gas state is preferred when AHy p < TASyap. 

Tetraphenylgermane, (CgH5)4Ge, has a melting point of 232.5°C, and its enthalpy increases by 106.7 J g during fusion. Calculate the molar enthalpy of fusion and molar entropy of fusion of tetraphenylgermane. 

What would be the molar entropy of fusion of tristearate in its most stable form Try to derive this value in two completely different ways. 

Here, the temperature coefficient corresponds to the negative molar entropy of the substance (compare Sect. 9.3). Subsequently, the difference Sap Sa s can be summarized as the molar entropy of fusion AjusSa of the pure solvent (at the freezing point) (compare Sect. 11.5) ... 

Here is the solubility of a dmg in water on the molar scale (M at 25 °C log s = 1.74 + logxssat for poorly soluble solutes, see above). The first term in Eq. (1.25) assumes that the dmg molecule has a molar cohesive energy similar to that of 1-octanol, so that the logarithm of the activity coefficient of the dmg in water should be equal to P°w, the logarithm of the distribution ratio between 1-octanol and water. This, in turn, can be related to the constitution and stmcture of the dmg (Hansch and Leo 1979). The second term, involving the molar entropy of fusion of the dmg molecule, is taken as zero for liquid solutes (at 25 °C) but non-zero for crystalline drugs. In summary, Eq. (1.25) predicted the aqueous solubility of 167 dmg and related organic solutes with a correlation coefficient of 0.994 and a standard deviation of 0.24 in log s. 

Flexible molecules have an additional, size-dependent entropy contribution that can also be derived from the molar entropy of fusion. Figure 5.123 shows the melting temperatures and entropies of melting of the homologous series of normal paraffins... 

Calculate the molar entropies of fusion and vaporization for water at its normal melting point and boiling point. The molar enthalpies of vaporization and fusion of water are given in Tables 7.7 and 7.8, respectively. 

As was discovered by Joseph Black, the heat absorbed, the latent heat, converts the solid to a liquid at the fixed temperature. Generally this change happens at a fixed pressure, hence we may equate Ag to AH, the enthalpy change associated with melting. The enthalpy associated with the conversion of one mole of the solid to liquid is called the molar enthalpy of fusion AHfus-The corresponding change in entropy, the molar entropy of fusion A5fus can now be written as... 

Calculate the molar entropy of fusion for linear polyethylene from the following data equilibrium enthalpy of fusion Ah° = 293 J and the equilibrium melting point TJ, = 415-418 K (different values have been reported). 

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