The Entropy of Melting

The Entropy of Melting.—When wc look at the entropies of melting, in Table XVI-1, we see that there is a certain amount of regularity in the table. For most of the metals, the entropy of fusion is 

From the relation (3.2), and the observed change of volume on melting, we can compute the change of entropy. In Table XVI-2 we give values of volume of the solid per mole (extrapolated from room temperature to the melting point by use of the thermal expansion), volume of the liquid 

Molecular volumes of the solid are calculated from observed densities at room temperature (as tabulated in Landolt s Tables), extrapolated to the melting point by using the thermal expansion. For the ionic ciystals, data on densities of liquids and solids are taken from Lorenz and Heiz, Z anory. allgem Chem., 145, 88 (1025). 

Using Stirling s formula, N = (.N/e)N approximately, the expression (3.3) becomes 

In the expression (3.5) let us put a = 0.04, the value which we roughly estimated from the latent heat. Then calculation gives us at once 

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This relationship does not include the correction recommended by Yalkowsky (19) for including differences between solid and liquid compounds because Yalkowsky s work was not available at the beginning of the study. Yalkowsky showed that solids and liquids do not fit well into the same correlation unless the solid solubilities are corrected for the entropy of melting. The error introduced by not including the correction is not significant for this screening analysis. 

In addition to the melting point of the P phase and the a/P allotropic transfonnation temperature in Fig. 6.1(b), there is a fluther intersection between the Gibbs energy of a and liquid phases. This corresponds to the metastable melting point of the a phase. A linear model will then dictate that the entropy of melting for a is defined by the entropies of melting and transformation at the two other critical points (Ardell 1963),... 

The phenomenon of melting point also involves the entropy of melting, which has a much smaller value for a symmetrical molecule (such as methane, with a symmetry number of 12) than with an asymmetrical molecule (such as CH2CIF, with a symmetry number of 1). When we introduce the fourth parameter of the entropy of rotational symmetry given by R In(cr), the regression results is... 

When groups are inserted into the main chain, its regularity is disturbed and chain mobility increases (reduction of the enthalpy of melting as well as increase of the entropy of melting). Thus, polymers are formed that can be further processed from solution or in bulk. 

The conducting ion sublattice in FICs is generally considered molten . The molten sublattice model for fast ion conduction was first proposed by Strock (1936) on the basis of structural and thermodynamic data for Agl. In most FICs, the entropy of the phase transition to the FIC state is larger than the entropy of melting. For example, in Agl the entropy of the transition at 420 K from the -form to the a-form (FIC state) is 14.7 J deg mol , whereas the entropy of melting at 861 K is only 11 J deg mol . ... 

The heat of melting and the entropy of melting can be calculated, from the depression of the crystalline melting point by the plasticizer. The high melting point of the polycarbonate is due essentially to a low entropy of fusion, undoubtedly caused by the high rigidity of the polycarbonate chain. 

Combining Equation (13) with the averaged values for expansional and positional entropy results in the following expression for the entropy of melting 0/K mol) for rigid... 

For the elements and small, roughly spherical molecules, the entropy of melting is primarily due to expansional and positional entropy. This is because no rotational entropy is gained upon melting and there is no internal entropy contribution. Using Equation (19), with a o value of 100 ... 

The hole model for molecular liquids was elaborated by Furth [12], who supposed that the free volume of a liquid is not distributed uniformly between its molecules like in crystals, but is concentrated like some holes which can disappear in one place and appear in another place. These holes are in permanent motion, so that the situation is different from the jumps of the holes in a crystal. The appearance and disappearance of the holes in a liquid are a result of the fluctuations connected with thermal movements. These holes in liquids have no definite shape and size they can increase or decrease spontaneously. Furth [12] tried to calculate a large number of properties of the liquids viscosity, compressibility, thermal expansion, thermal conductivity, but the results were not successful. However, Furth obtained a precise result of the calculation of the volume change by melting and the entropy of melting. 

If the entropy of melting, Aj m, is not known experimentally, an approximation for rigid organic molecules of 13.5cal/degmol can be made. " If the temperature of interest is 298 K then Eq. (2) becomes... 

The melting point is assumed to be 2400 K as estimated by Douglas and Victor (1 ) and Schick et al. (5). Prom the estimated melting point, 2400 K, and an estimated 2.5 cal g-atom for the entropy of melting, the heat of melting was calculated. 

This entropy is larger than the corresponding value for WOCl (cr) (2). In both cases the entropies of the condensed phases are derived from gas phase values using 2nd law analysis of sublimation and vaporization data. The entropy of melting for WOCl is an order of magnitude larger than that of WOF. This suggests some inconsistency in the data for WOCl since all values for W0P (cr, if g) appear internally reasonable. 

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