Thermodynamic properties of condensed phases

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

Thus AC and BC can be chosen as thermodynamic components of the solid solution whose chemical potentials are independent of the C to A + atom ratio. Relying on the relative insensitivity of the thermodynamic properties of condensed phases to the pressure P, we neglect this pressure dependence in... 

The theoretical calculation of the thermodynamic properties of condensed phases is still in an early stage of development and only the simplest models can be treated quantitatively. For solids the simplest useful theory, that of Debye, assumes that the distribution of vibration frequencies among the atoms in the solid is the same as that of the frequencies of vibration of a continuous medium. The errors introduced by this hypothesis are difficult to estimate. Some progress has, however, been made recently in the direct evaluation of the thermodynamic properties of crystal lattices without having to liken them to continuous media.f... 

At the point C the two liquid layers become identical, and this is called the critical solution point or con-solute point. If the total applied pressure is varied, both the critical temperature and composition of the critical mixture alter and we obtain a critical solution line. As an example of this we give in table 16. If the dependence of the critical solution temperature on pressure for the system cyclohexane -f aniline. An increase of pressure raises the critical solution temperature, and the mutual solubility of the two substances is decreased. We saw earlier that the applied pressure had only a small effect on the thermodynamic properties of condensed phases, and we notice in this case that an increase of pressure of 250 atm. alters the critical temperature by only 1.6 °C. 

In addition to the determination of thermodynamic data for homogeneous and heterogeneous equilibria of the type Eqs. (8-11), important thermodynamic properties of condensed phases can be evaluated from gas phase studies. 

Thermodynamic properties of condensed phases can be evaluated from gas phase data. They show for example a small tendency to immiscibility for the solid solution of the NaBr-Nal system (Miller and Hilpert [532]) as observed for the KCl-KBr system (Miller and Skudlarski [534]). In contrast to this, the Gibbs energy of the melt of the Nal-Dylj system for Nal > 0.53 at 1000 K indicates a tendency to compoimd formation (Hilpert et al. [530]). 

Reactions are often carried out at pressures in the neighbourhood of 101.325 kPa, and in this pressure region the thermodynamic properties of condensed phases (i.e. liquids and solids) do not change very rapidly with small changes in pressure. As a result, it is usual to adopt the following standard states when recording thermodynamic quantities ... 

This chapter introduces additional central concepts of thermodynamics and gives an overview of the formal methods that are used to describe single-component systems. The thermodynamic relationships between different phases of a single-component system are described and the basics of phase transitions and phase diagrams are discussed. Formal mathematical descriptions of the properties of ideal and real gases are given in the second part of the chapter, while the last part is devoted to the thermodynamic description of condensed phases. 

Potential energy surfaces of weakly bound dimers and trimers are the key quantities needed to compute transition frequencies in the high resolution spectra, (differential and integral) scattering cross sections or rate coefficients describing collisional processes between the molecules, or some thermodynamic properties needed to derive equations of state for condensed phases. However, some other quantities governed by weak intermolecular forces are needed to describe intensities in the spectra or, more generally, infrared and Raman spectra of unbound (collisional complexes) of two molecules, and dielectric and refractive properties of condensed phases. These are the interaction-induced (or collision-induced) dipole moments and polarizabilities. 

MCM-41 material synthesized in 1992 by the Mobil Oil Company [1, 2] is up to now the first model mesoporous material as a consequence of its well defined porosity, composed of an hexagonal structure of cylindrical mesopores (whose diameter can be monitored in the range 20 - 100 A). MCM-41 samples are very suited to analyze the capillary condensation phenomenon. In particular the phase diagram of the confined capillary phase can be determined. Such a "capillary phase diagram" is characterized by the capillary critical temperature Tcc and the capillary triple point temperature T. Recent studies of the thermodynamic properties of confined phases (Ar, N2, O2, C2H4 and CO2) in MCM-41 have pointed out that their critical temperatures T are strongly displaced to-... 

An account of the gaseous species observed by Knudsen effusion mass spectrometry in the eqilibrium vapor of metals, alloys, oxides, halides, and technical systems is given. The fundamentals and recent developments of this method are briefly reported. Dissociation and atomization enthalpies of selected gaseous species are tabulated. Accounts of the equilibrium studies by Knudsen effusion mass spectrometry in order to obtain thermodynamic properties for condensed phases from gas phase data are additionally given for the aforementioned materials. Table 8 shows as an example the enthalpies and Gibbs energies of formation for different solid intermetallic compounds. A special section (Sect. 

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of (1) electronic structure, potential energy surfaces, and force fields (2) vibrational-rotational motion and (3) equilibrium properties of condensed-phase systems and macromolecules. Chemical dynamics includes (1) bimolecular kinetics and the collision theory of reactions and energy transfer (2) unimolecular rate theory and metastable states and (3) condensed-phase and macromolecular aspects of dynamics. 

Up to now, the discussion has been about thermodynamic properties of gaseous and liquid Freon-22. The thermodynamic functions of condensed-phase Freon-22, including the solid, are tabulated in Ref. [3.55] at T = 15-232 K (Table 31). This table also includes the values for entropy, enthalpy, and Gibb s function in the vapor phase at Tnbp- Specifically, - //q)g = 9482.8 cal/ mol at Tnbp- On the other hand, data in [3.41, 3.63] show that =... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

R.C. Oliver et al, USDeptCom, Office Tech-Serv ..AD 265822,(1961) CA 60, 10466 (1969) Metal additives for solid proplnts formulas for calculating specific impulse and other proplnt performance parameters are given. A mathematical treatment of the free-energy minimization procedure for equilibrium compn calcns is provided. The treatment is extended to include ionized species and mixing of condensed phases. Sources and techniques for thermodynamic-property calcns are also discussed... 

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. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

The thermodynamic properties of single-component condensed phases are traditionally given in tabulated form in large data monographs. Separate tables are given for each solid phase as well as for the liquid and for the gas. In recent years analytical representations have been increasingly used to ease the implementation of the data in computations. These polynomial representations typically describe the thermodynamic properties above room temperature (or 200 K) only. 

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. 

Figure 7.4 illustrates the phase diagram of the 4He isotope in the low-temperature condensation region. The thermodynamic properties of 4He are fundamentally distinct from those of the trace isotope 3He, and the two isotopes spontaneously phase-separate near IK. Both isotopes exhibit the spectacular phenomenon of superfluidity, the near-vanishing of viscosity and frictional resistance to flow. The strong dependence on fermionic (3He) or bosonic (4He) character and bizarre hydrodynamic properties are manifestations of the quantum fluid nature of both species. 3He is not discussed further here. 

A computer algorithm has been developed for making multi-component mixture calculations to predict (a) thermodynamic properties of liquid and vapor phases (b) bubble point, dew point, and flash conditions (c) multiple flashes, condensations, compression, and expansion operations and (d) separations by distillation and absorption. 

To be useful, this type of simulator must calculate the thermodynamic properties of multicomponent mixtures in both liquid and vapor phases while predicting bubble and dew points or partial vaporizations or condensations. Using this basic information, the simulator must then make calculations for other processes, such as gas cooling by expansion, gas compression, multiple flashes condensations, and separations by absorption... 

The study of small, homonuclear clusters of atoms Is Important In understanding nucleatlon because such clusters are Intermediates In the formation of bulk condensed phases. The dynamic process of condensation from a gas must Initially Involve the formation of tiny aggregates of the new phase. This can be Illustrated by the reaction sequence A(g)—A2(g)— A3(g)— . . . — A(1). One of the major weak points In the present day understanding of such nucleatlon phenomena Is the unknown thermodynamic properties of clusters. Certainly, the common practice of treating a 2-200 atom cluster as a tiny piece of the bulk with a large surface Is Inexact. There Is a need for precise thermodynamic data on atomic and molecular clusters to better define nucleatlon kinetics. 

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