Enthalpy and entropy of fusion

If the enthalpy and entropy of fusion-are assumed to be independent of temperature, Eq. (17) with Eq. (18) to obtain... 

Let us now consider the effect of a difference between the heat capacity of pure liquid i and pure solid i on the enthalpy and entropy of fusion and subsequently on the phase diagram. This effect is easily taken into consideration by using eqs. (1.24) and (1.54). Ais now given as... 

The melting points of a series of poly (a-olefin) crystals were studied. All of the polymers were isotactic and had chains substituents of different bulkiness. The results are listed below. Use Eq. (2.12) to derive a relationship between the melting point, T, and the enthalpy and entropy of fusion. A/// and A5/, respectively. Use this relationship, plus what you know about polymer crystallinity and structure from Chapter 1, to rationalize the trend in melting point. 

Danusso, F., G. Moraglio and E. Flores Enthalpy and entropy of fusion of isotactic polypropylene. Atti Accad. Naz. Lincei Rend. 25, 420—527 (1958). 

A pronounced minimum in the freezing curve be occurs at approximately 0.3 K. As we have discussed earlier for 4He, this leads to the conclusion that Afus-Sm = AfUSi/m = 0 at the pressure minimum, in this case, 2.98 MPa. Below 0.3 K, the liquid has a lower entropy than the solid, and both the enthalpy and entropy of fusion are negative. It is an interesting exercise to start with liquid 3He at 7 = 0.1 K and p = 3 MPa and heat it isobarically. At about 0.6 K, the liquid solidifies with the absorption of heat. Heating the solid to 0.65 K causes it to melt, again with the absorption of heat ... 

The enthalpies of fusion that have been derived from the enthalpy increment equations for the solid and liquid phase are listed in table 13 and the derived entropies of fusion are plotted in fig. 29. It can be seen that the enthalpies and entropies of fusion for ErF3 to LuF3 are significantly lower than those of the other lanthanide trifluorides. Because these four compounds... 

It is possible to determine C quantitatively using Hildebrand s theory of microsolutes. An example of the accuracy that can be achieved is provided by the calculation of the solubilities of a series of p-aminobenzoate esters in hexane (17,18). Michaels, et al. (19) used this approach to estimate the solubility of steroids in various polymers. The solubilities of seven steroids in six polymers were calculated from the steroid melting points, heats of fusion, and solubility parameters. Equation 8 was derived, where Jjj is the maximum steady state flux, h is the membrane thickness, x is the product of V, the molar volume of the liquid drug, and the square of the difference in the solubility parameters of the drug and polymer, p is the steroid density, T is melting point (°K), T is the temperature of the environment, R is the gas constant, and AH and ASf are the enthalpy and entropy of fusion, respectively. 

On the left-hand side of Equation (23) the 1 bar enthalpy and entropy of fusion are both temperature dependent, but because of the opposite signs in the equation their temperature dependence tend to cancel one another (Wood and Fraser, 1976, p. 29). This means that AG° can generally be calculated reasonably accurately over a wide temperature range with fixed values of enthalpy (A//f) and entropy (A5 ). However, the volume of fusion ATf is, because of the compressibility of the liquid, rather pressure dependent. Assuming that the pressure dependence is linear. Equation (23) yields... 

Like water, almost all substances can be in the three common states of matter. Table 5 lists the molar enthalpies and entropies of fusion and vaporization for some elements and compounds. Because intermolecular forces are not significant in the gaseous state, most substances have similar values for molar entropy of vaporization, ASy p-... 

Table 5 Molar Enthalpies and Entropies of Fusion and Vaporization... 

The enthalpy and entropy of fusion, and the melting temperature may all be measured through the use of differential scanning calorimetry (DSC), and therefore equations (18) and (20) provide a simple way to predict the solubility of a solute in an ideal solution. 

Monoclinic selenium is metastable and its enthalpy of formation and entropy are needed as auxiliary data for some evaluations. They were derived from a thermodynamic cycle involving the enthalpy and entropy of fusion at the melting point 413 K, the selected data for trigonal and liquid selenium, and the heat capacity of monoclinic selenium. The selected enthalpy of fusion is that in [81GAU/SHU] ... 

The magnitudes of the enthalpies and entropies of fusion determine the temperature of melting (Table 10-4). The entropy of fusion can be further separated into the contribution from the conformational change on melting, A Sc, and the contribution resulting from the change in volume, a/P) iS Vm, where a is the cubic expression coefficient and is the compressibility... 

The vaporization enthalpies and entropies of fusion must also be considered in the polymerization of gaseous monomer to condensed crystalline polymer. Thus, the enthalpies of polymerization depend on the state of the materials in the same way as do the polymerization entropies, that is, gc > gc> gg> Ic,... 

Assuming the enthalpy and entropy of fusion to be temperature independent, and since at equilibrium... 

H20(/) at -10.0°C (a) assuming that the enthalpy and entropy of fusion are constant over the temperature range and (b) assuming that the heat capacities are constant over the temperature range, but that the enthalpy and entropy of fusion are not. 

In practice, heat capacity measurements are usually made from about 10 K. Values of C, below the lowest temperature of the measurements are obtained by extrapolation. For organic compounds with melting temperatures below the highest temperature of the Cj, measurements, values for the enthalpy and entropy of fusion are obtained in the course of the measurements and it is usual to calculate the equilibrium temperature (Tm) in the... 

The change of the reference state has been made assuming that the enthalpies and entropies of fusion or of allotropic transformation do not vary with temperature. These values have been taken from Hultgren et al. (1973b) for the rare earths and from Getting et al. (1976) for the actinides. This choice was motivated by the fact that many authors have used these values to calculate the changes of the reference state (see for example Chiotti et al. 1981). 

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