Entropy, of fusion

The entropy of fusion, AfhjTf, like the entropy of vaporization, exhibits some interesting regularities. 

For elements the entropy of fusion lies in the region of R, as shown in table 14.4, while for compounds it appears to depend very largely on the molecular shape. 

Molecules which are roughly spherical have values of AfS which are approximately the same as for the elements, as is shown in table 14.5, while for straight chain molecules the entropy of fusion increases steadily with the chain length. Thus, in table 14.6, we see that for methane the entropy of fusion corresponds to its spherical shape, while for ethane which is a long ellipsoid the value is over twice as great. Similarly for 72.-octane which melts at 216 °K, Afh is 4,930 cal./mole so that AfS = 22-8 cal./deg. mole. while its isomer hexamethylethane which is nearly spherical melts at 377 °K with Afh —1,700 cal./mole, and an entropy of fusion of only 4 5 cal./deg. mole. There are many other examples of this kind of behaviour. The interpretation of the small entropy of fusion of spherical molecules is related to the fact that these compounds acquire free rotation while still in the solid state.f 

In general, however, rotation and translation of the molecules are degrees of freedom which are acquired simultaneously on fusion, although sometimes only translational freedom is acquired. This happens, for example, in the case of very long molecules where rotation is prevented by steric factors (anisotropic liquids), and also when the intermolecular forces are powerful and anisotropic as for associated liquids. In these instances the freedom of rotation is achieved progressively as the temperature is raised above the melting point. This is in contrast to spherical molecules which, because of their shape and the symmetry of their force fields, begin to rotate freely in the solid state. 

We must however notice that abnormally low values of the entropy of fusion are also encountered with some non-spherical molecules, table 14.7 indicates that some substances classed as associated appear to acquire rotational degrees of freedom before melting. 

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Further information on the effect of polymer structure on melting points has been obtained by considering the heats and entropies of fusion. The relationship between free energy change AF with change in heat content A// and entropy change A5 at constant temperature is given by the equation... 

Where is the melting point Af/n, the heat of fusion AS , the entropy of fusion... 

The entropy term is a measure of the degree of freedom of the molecules and thus a measure of its flexibility. Measurement of the heats and entropies of fusion has provided interesting information on the relative importance of various factors... 

In Chapter 4 it was argued that the melting point (T ) could be related to the heat of fusion (A//) and entropy of fusion (AS) by the expression... 

It is reasonable to consider that in an ester group the in-chain ether link —C—O—C— increases the chain flexibility compared with a polymethylene chain to decrease the heat of fusion. At the same time there will be some increase in interchain attraction via the carbonyl group which will decrease the entropy of fusion. Since these two effects almost cancel each other out there is almost no change in melting point with change in ester group concentration. 

It is believed that this difference, which is typical of many polymers, is due to the higher entropy of fusion of the w-linked polymers. 

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

A smaller increase in entropy occurs when solids melt than when liquids vaporize, because a liquid is only slightly more disordered than a solid (Fig. 7.5). By applying the same argument used for vaporization to the standard entropy of fusion of a substance at its melting (or freezing) point, we obtain... 

Here, AHfu° is the standard enthalpy of fusion and T, is the melting point. All entropies of fusion are positive, and so they are normally reported without their positive sign. 

Self-Tfst 7.8A Calculate the standard entropy of fusion of mercury at its freezing point (see Table 6.3). 

SOLUTION The enthalpy of fusion is 6.01 kj-mol 1 and the entropy of fusion is 22.0 J-K 1 -mol. These values are almost independent of temperature over the temperature range considered. 

According to Trouton s rule, the entropy of vaporization of an organic liquid is a constant of approximately 85 J-mol 1 -K 1. The relationship between entropy of fusion, enthalpy of fusion, and melting point is given by... 

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. 

In Table XXXV are given the heats and entropies of fusion (AaSu = I Hu/T where is in °K) for various polymers. The melting... 

Table XXXV.—Heats and Entropies of Fusion of Polymers...

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