Sublimation, heat of

S = Heat of sublimation of sodium D = Dissociation energy of chlorine / = Ionization energy of sodium = Electron affinity of chlorine Uq = Lattice energy of sodium chloride AHf = Heat of formation of sodium chloride. 

We have seen that in a metal the atoms are close-packed, i.e. each metal atom is surrounded by a large number of similar atoms (often 12, or 8). The heat required to break up 1 mole of a metal into its constituent atoms is the heat of atomisation or heat of sublimation. Values of this enthalpy vary between about 80 and 800 kJ. for metals in their standard states these values indicate that the bonds between metal atoms can vary from weak to very strong. There is a rough proportionality between the m.p. of a metal and its heat of atomisation. so that the m.p. gives an approximate measure of bond strength. 

Fig. 2.25 The differential heat of adsorption of argon on carbon blacks at 78 K, before and after graphitizalion.. Spheron O, Graphon. , and El denote molar heat of sublimation and of evaporation respectively.

Most of the water is sublimated from the frozen mass by heating the product under reduced pressure. The operating conditions must be such that the product remains in a soHd state while sublimation is taking place. The completion of sublimation can be observed by an increase in product temperature. This increase occurs when the energy being introduced is no longer consumed by the latent heat of sublimation, but is absorbed by the product instead. 

Consequently, the development of chain length of the polymer is restricted and the average molecular weight tends to be low. PhthaUc anhydride has a tendency to sublime. Its heat of sublimation is 598 J /g (143 cal/g), and the heat of vaporization is 365 J/g (87.2 cal/g). Therefore, care must be taken to prevent its loss (see later discussions on Production Processes). 

AH ammonium haUdes exhibit high vapor pressures at elevated temperatures, and thus, sublime readily. The vapor formed on sublimation consists not of discrete ammonium haUde molecules, but is composed primarily of equal volumes of ammonia and hydrogen haUde. The vapor densities are essentiaHy half that expected for the vaporous ammonium haUdes. Vapor pressures at various temperatures are given in Table 2 (11). Latent heats of sublimation, assuming complete dissociation of vapors and including heats of dissociation are 165.7, 184.1, and 176.6 kJ /mol (39.6, 44.0, and 42.2... 

Finally, it is to be expected that the evaporation coefficient of a very stable compound, such as alumina, which has a large heat of sublimation resulting from the decomposition into the elements, will be low. Since the heat of evaporation must be drawn from the surface, in die case of a substance widr a low thermal conductivity such as an oxide, the resultant cooling of the surface may lead to a temperature gradient in and immediately below the surface. This will lower die evaporation rate compared to that which is calculated from the apparent, bulk, temperature of the evaporating sample as observed by optical pyromeuy, and thus lead to an apparently low free surface vaporization coefficient. This is probably die case in the evaporation of alumina in a vacuum. 

The relationship of the surface energy to the heat of sublimation can be readily seen in these data. An empirical equation for this relationship has been given by Miedema et al., (1980)... 

Significant progress in the optimization of VDW parameters was associated with the development of the OPLS force field [53]. In those efforts the approach of using Monte Carlo calculations on pure solvents to compute heats of vaporization and molecular volumes and then using that information to refine the VDW parameters was first developed and applied. Subsequently, developers of other force fields have used this same approach for optimization of biomolecular force fields [20,21]. Van der Waals parameters may also be optimized based on calculated heats of sublimation of crystals [68], as has been done for the optimization of some of the VDW parameters in the nucleic acid bases [18]. Alternative approaches to optimizing VDW parameters have been based primarily on the use of QM data. Quantum mechanical data contains detailed information on the electron distribution around a molecule, which, in principle, should be useful for the optimization of VDW... 

At best, van der Waals interactions are weak and individually contribute 0.4 to 4.0 kj/mol of stabilization energy. ITowever, the sum of many such interactions within a macromolecule or between macromolecules can be substantial. For example, model studies of heats of sublimation show that each methylene group in a crystalline hydrocarbon accounts for 8 k[, and each C—IT group in a benzene crystal contributes 7 k[ of van der Waals energy per mole. Calculations indicate that the attractive van der Waals energy between the enzyme lysozyme and a sugar substrate that it binds is about 60 k[/mol. 

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