Sublimation entropy

Metals. Kruglikh, et al. (104) measured saturated vapor pressures of erbium, samarium, and ytterbium by the Knudsen effusion method, and standard (average) sublimation entropies of 18.4, 20.7, and 25.6 cal./(gram atom °K.) were derived. Nesmeyanov, et al. (146) studied the vapor pressure of yttrium by an integral variant of the effusion technique. Similar studies at higher temperatures by Herrick (70) on samarium metal have been interpreted in good accord by both first and second law methods. Ideal gas thermodynamic functions have been derived from 100 °K. to 6000°K. at 100° intervals for both actinide and lanthanide elements by Feber and Herrick (45). 

The other phase boundaries can also be calculated using the chemical potential. For example, the sublimation pressure curve can be described analogously to the boiling pressure curve. We only need the drive Ag,o = /[Pg.309]

AS j can be computed as the difference between the entropy of an ideal gas and the entropy of the crystal at a given temperature and pressure. If the intra- and intermolecular contributions to the entropy of the crystal are considered to be decoupled, such that the change in intramolecular vibrational entropy for transfer from crystal to gas can be taken to be zero, then the sublimation entropy of rigid molecules can be approximated by AS where and are the... 

From these measured properties, thermodynamic state functions (enthalpies of sublimation, entropies, and free-energy functions) have been derived. For several actinides, these properties have been critically reviewed by Hultgren et al. [24] and more recently by Getting, Rand, and Ackermann [14]. The latter compilation includes properties for the metallic state and for ideal gas to 5(XX) K for the elements Th through Cm. Sublimation enthalpies (determined from measured vaporization behavior for Th through Es) and standard entropies (determined from measured heat capacities for Th through Am) of the actinide metals are compiled in Table 17.1. Sublimation enthalpies have been correlated with metal structures and electronic energy levels [27,28]. 

The saturated vapor pressure of a crystal can be determined from the standard free energy of sublimation and is related to volatility. The sublimation entropy is ... 

The sublimation entropy can be calculated as follows (at standard pressure) ... 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

Linear least squares treatments of plots of the logarithm of the vapor pressure versus the reciprocal temperature were performed. The second-law enthalpy and entropy of sublimation at the median temperature are proportioned to the slope and... 

Heats and entropies of sublimation and formation of Pu-intermetallics at median temperature and 298 K. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

Phase changes, which convert a substance from one phase to another, have characteristic thermodynamic properties Any change from a more constrained phase to a less constrained phase increases both the enthalpy and the entropy of the substance. Recall from our description of phase changes in Chapter 11 that enthalpy increases because energy must be provided to overcome the intermolecular forces that hold the molecules in the more constrained phase. Entropy increases because the molecules are more dispersed in the less constrained phase. Thus, when a solid melts or sublimes or a liquid vaporizes, both A H and A S are positive. Figure 14-18 summarizes these features. 

There is an increase in entropy (dispersal of energy) in only the process (c) sublimation of dry ice, C02(s) - C02(g). In the other physical processes, the systems are becoming more ordered and the entropy is decreasing. 

The product of sublimation is a gas, and the precursor is a solid. Clearly, the product has greater entropy than the starting material, so A 5 increases during sublimation. The process is spontaneous because A 5 is positive. 

The printed data output step 4 lists the values for the constants A and B of the general vapor pressure equation and the enthalpy and entropy of vaporization or sublimation. 

The types of values reported in the database standard enthalpies of formation at 298.15 K and 0 K, bond dissociation energies or enthalpies (D) at any temperature, standard enthalpy of phase transition—fusion, vaporization, or sublimation—at 298.15 K, standard entropy at 298.15 K, standard heat capacity at 298.15 K, standard enthalpy differences between T and 298.15 K, proton affinity, ionization energy, appearance energy, and electron affinity. The absence of a check mark indicates that the data are not provided. However, that does not necessarily mean that they cannot be calculated from other quantities tabulated in the database. 

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