Pressure, vapor condensed phase

FIGURE A.l. Vapor pressures versus condensed-phase composition for completely miscible binary systems. 

The first criterion is most easily examined. In pure benzene vapor excited at 2536 A or longer wave lengths, both the quantum yield and the observed singlet state lifetime show only a very shallow dependence on benzene pressure above 10 torr. Addition of foreign gases such as hydrocarbons to these experiments also has little (but sometimes finite) effect on fluorescence yields " or lifetimes. Even in the extreme collisional limit of condensed phase at 77°K, the fluorescence yield of 0.2 matches that of the vapor. - (Condensed phase yields drop to about 0.05 at 300°K, but this is probably a special thermal effect somewhat apart from a collision-induced electronic decay. See Section IVC.)... 

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 diazirines are of special interest because of their isomerism with the aliphatic diazo compounds. The diazirines show considerable differences in their properties from the aliphatic diazo compounds, except in their explosive nature. The compounds 3-methyl-3-ethyl-diazirine and 3,3-diethyldiazirine prepared by Paulsen detonated on shock and on heating. Small quantities of 3,3-pentamethylenediazirine (68) can be distilled at normal pressures (bp 109°C). On overheating, explosion followed. 3-n-Propyldiazirine exploded on attempts to distil it a little above room temperature. 3-Methyldiazirine is stable as a gas, but on attempting to condense ca. 100 mg for vapor pressure measurements, it detonated with complete destruction of the apparatus." Diazirine (67) decomposed at once when a sample which had been condensed in dry ice was taken out of the cold trap. Work with the lower molecular weight diazirines in condensed phases should therefore be avoided. 

In general, gas solubilities are measured at constant temperature as a function of pressure. Permanent gases (gases with critical temperatures below room temperature) will not condense to form an additional liquid phase no matter how high the applied pressure. However, condensable gases (those with critical temperatures above room temperature) will condense to form a liquid phase when the vapor pressure is reached. The solubilities of many gases in normal liquids are quite low and can be adequately described at ambient pressure or below by Henry s law. The Henry s law constant is defined as... 

Use the Third Law to calculate the standard entropy, S°nV of quinoline (g) p — 0.101325 MPa) at T= 298,15 K. (You may assume that the effects of pressure on all of the condensed phases are negligible, and that the vapor may be treated as an ideal gas at a pressure of 0.0112 kPa, the vapor pressure of quinoline at 298.15 K.) (c) Statistical mechanical calculations have been performed on this molecule and yield a value for 5 of quinoline gas at 298.15 K of 344 J K l mol 1. Assuming an uncertainty of about 1 j K 1-mol 1 for both your calculation in part (b) and the statistical calculation, discuss the agreement of the calorimetric value with the statistical... 

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. 

Continued compression increases the pressure along the vertical dotted line. The compositions and amounts of the vapor and liquid phases continue to change along the liquid and vapor lines and the relative amounts change as required by the lever rule. When a pressure corresponding to point g is reached, the last drop of vapor condenses. Continued compression to a point such as h simply increases the total pressure exerted by the piston on the liquid. 

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. 

It should be emphasized that a survey of the vapor pressure measurements of plutonium-bearing species above bivariant Pu02-x(s) revealed that in general these measurements suffer from a lack of knowledge of the composition of the condensed phase. 

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. 

In this paper we describe (1) the gas-phase thermodynamic functions (2) the condensed-phase thermodynamic functions (3) the oxygen potential (and the phase boundaries that are consistent with It) and (4) the resulting vapor pressure and composition as functions of temperature and composition of the condensed phase. 

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... 

Another significant comparison between the two systems concerns the partial pressures of the metal dioxide molecules. These pressures are relatively insensitive to the condensed-phase composition and are quite similar in the plutonia and urania systems. Calculated metal dioxide vapor pressures are compared in Table V for 0/M = 1.96. 

Hydroxysulfate compounds, structure 56-57 Hypostoichiometric Pu dioxide condensed phase, vapor pressures and vapor compositions.124-41... 

The vapor pressure of a given phase of a substance is the pressure exerted by its vapor when the vapor is in dynamic equilibrium with the condensed phase. 

A vapor pressure is the pressure exerted by a gas in equilibrium with its condensed phase. When this equilibrium has been reached, the gas is saturated with that particular vapor. Notice in Table 5A that at 25 °C the atmosphere is saturated with water vapor when the partial pressure of H2 O is 23.756 torr. At this pressure, the molecular density of H2 O in the gas phase is sufficient to make the rate of condensation equal to the rate of evaporation. Any attempt to add more water molecules to the gas phase results in condensation to hold the partial pressure of H2 O fixed at 23.756 torr. 

A 7/vap always is 3.10 kJ/mol greater than A fi vap At 298 K (25 °C, room temperature) A /Tvap always is 2.48 kJ/mol greater than A ivap The difference between A vap and A i7vap arises because, in addition to overcoming intermolecular forces in the condensed phase (A E), the escaping vapor must do work, w = A(P V ) — RT as it expands against the constant external pressure of the atmosphere. 

Phase changes are characteristic of all substances. The normal phases displayed by the halogens appear in Section II-L where we also show that a gas liquefies or a liquid freezes at low enough temperatures. Vapor pressure, which results from molecules escaping from a condensed phase into the gas phase, is one of the liquid properties described in Section II-I. Phase changes depends on temperature, pressure, and the magnitudes of intermolecular forces. 

The temperature for conversion between the vapor and a condensed phase depends strongly on pressure. Qualitatively, this is because compressing a gas increases the collision rate and makes condensation more favorable. We describe the quantitative details of this variation in Section 14.5. 

Potential explosion phenomena include vapor cloud explosions (VCEs), confined explosions, condensed-phase explosions, exothermic chemical reactions, boiling liquid expanding vapor explosions (BLEVEs), and pressure-volume (PV) ruptures. Potential fire phenomena include flash fires, pool fires, jet fires, and fireballs. Guidelines for evaluating the characteristics of VCEs, BLEVEs, and flash fires are provided in another CCPS publication (Ref. 5). The basic principles from Reference 5 for evaluating characteristics of these phenomena are briefly summarized in this appendix. In addition, the basic principles for evaluating characteristics of the other explosion and fire phenomena listed above are briefly summarized, and references for detailed evaluation of characteristics are provided. 

Finally, the bubble collapse stops when the pressure inside a bubble (pg) in the right hand side of (1.13) dramatically increases as the density inside a bubble nearly reaches that of a condensed phase (A bubble is almost completely occupied by the van der Waals hard-cores of gas and vapor molecules at that moment). At the same time, the temperature and pressure inside a bubble dramatically increase. 

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