Condensation condensed phase equilibria

Gas and condensed phase equilibrium the Clausius-Clapeyron equation... 

In our consideration of phase equilibria at constant pressure, we imagined the overall system confined by a piston. However, when we talk about constant-pressure systems, we usually mean that the pressure is maintained by an inert gas (e.g., the atmosphere).2 In some situations, much higher constant pressures of inert gases are applied to systems. If we take a gas-condensed phase equilibrium and apply an inert gas pressure to both phases, we get, from Eqs. (31) and (33),... 

Condensed-phase equilibria are treated by Eq. (40), the Clapeyron equation. The most important type of condensed-phase equilibrium is that between solid and liquid. For melting, Ais always positive, because the solid is the lowest-energy (and enthalpy) arrangement of molecules. The direction of change of the melting temperature with pressure,... 

There is no low temperature heat capacity data reported in the literature for T < 298 K. In order to have the 3rd law results of the equilibrium data agree with the combustion data, an entropy value of the order of 13-14 cal K mol would be necessary. At this point, however, the 3rd law drifts would be all positive. S (298.15 K) 10.2 cal K mol would lead to a more satisfying variation in the 3rd law drifts for the condensed phase equilibrium data but an intermediate value S (298.15 K)... 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

In this brief review of dynamics in condensed phases, we have considered dense systems in various situations. First, we considered systems in equilibrium and gave an overview of how the space-time correlations, arising from the themial fluctuations of slowly varying physical variables like density, can be computed and experimentally probed. We also considered capillary waves in an inliomogeneous system with a planar interface for two cases an equilibrium system and a NESS system under a small temperature gradient. 

The treatment of equilibrium solvation effects in condensed-phase kmetics on the basis of TST has a long history and the literature on this topic is extensive. As the basic ideas can be found m most physical chemistry textbooks and excellent reviews and monographs on more advanced aspects are available (see, for example, the recent review article by Tnihlar et al [6] and references therein), the following presentation will be brief and far from providing a complete picture. 

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). 

The Clapeyron equation expresses the dynamic equilibrium existing between the vapor and the condensed phase of a pure substance ... 

The equilibrium between a compressed gas and a liquid is outside the scope of this review, since such a system has, in general, two mixed phases and not one mixed and one pure phase. This loss of simplicity makes the statistical interpretation of the behavior of such systems very difficult. However, it is probable that liquid mercury does not dissolve appreciable amounts of propane and butane so that these systems may be treated here as equilibria between a pure condensed phase and a gaseous mixture. Jepson, Richardson, and Rowlinson39 have measured the concentration of... 

Letp be the ordinary equilibrium pressure in a system composed of a condensed phase and its vapour, and let, r, Y be the specific volumes of these phases, respectively, under a pressure p. We now assume that these values are altered to p r Y, when the condensed phase alone is exposed to a pressure P + p. 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

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... 

Fugacity, like other thermodynamics properties, is a defined quantity that does not need to have physical significance, but it is nice that it does relate to physical quantities. Under some conditions, it becomes (within experimental error) the equilibrium gas pressure (vapor pressure) above a condensed phase. It is this property that makes fugacity especially useful. We will now define fugacity, see how to calculate it, and see how it is related to vapor pressure. We will then define a related quantity known as the activity and describe the properties of fugacity and activity, especially in solution. 

Alternate expressions can also be written for equilibrium constants in condensed phase reactions. For example, for the reaction... 

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. 

Vapor pressures and vapor compositions in equilibrium with a hypostoichiometric plutonium dioxide condensed phase have been calculated for the temperature range 1500 I H 4000 K. Thermodynamic functions for the condensed phase and for each of the gaseous species were combined with an oxygen-potential model, which we extended from the solid into the liquid region to obtain the partial pressures of O2, 0, Pu, PuO and Pu02 as functions of temperature and of condensed phase composition. The calculated oxygen pressures increase rapidly as stoichiometry is approached. At least part of this increase is a consequence of the exclusion of Pu +... 

One of the most Important thermophysical properties of reactor fuel In reactor safety analysis Is vapor pressure, for which data are needed for temperatures above 3000 K. We have recently completed an analysis of the vapor pressure and vapor composition In equilibrium with the hypostolchiometric uranium dioxide condensed phase (1 ), and we present here a similar analysis for the plutonium/oxygen (Pu/0) system. 

General. The methods we have used to calculate the vapor pressures and vapor compositions at high temperatures are the same as those used previously (1-2) for the U/0 system. The total pressure, p(total), In equilibrium with a Pu02 x condensed phase Is... 

Table III. Ionization Potentials (IP) of the Molecules and Atoms In Equilibrium with a Plutonium Dioxide Condensed Phase (1 eV molecule- - - 23.06 kcal mol- =...

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