Vapor pressure, corresponding-state

To calculate the fugacity of a pure vapor from corresponding states that, at the conditions of the mixture, exists only as a liquid, we will use Eq. 7.8-1 with f- T, P) equal to the total pressure, if the pressure is low enough, or... 

PRESSURE, CRITICAL - Vapor pressure corresponding to the substance s critical state at which the liquid and vapor have identicai properties. 

First, it is shown that liquids can flow cavitation-free through pressure regions that are significantly less than saturation vapor pressure corresponding to free-stream liquid temperature. For this condition, the liquid is locally in a thermodynamically metastable state of superheat, and as such, the flowing liquid can be expected to sustain these unusually low pressures only for relatively short periods of time. The maximum decrement of local pressure relative to stream vapor pressure that existed at, or just prior to, incipient cavitation is called, for engineering purposes herein, eflfective liquid tension. Effective tension may be viewed as a pressure difference tending to rupture, or cavitate, the liquid. 

Corresponding states have been used in other equations. For example, the Peng-Robinson equation is a modified RedHch-Kwong equation formulated to better correlate vapor—Hquid equiHbrium (VLE) vapor pressure data. This equation, however, is not useful in reduced form because it is specifically designed to calculate accurate pressure data. Reduced equations generally presuppose knowledge of the pressure. 

Three Parameter Models. Most fluids deviate from the predicted corresponding states values. Thus the acentric factor, CO, was introduced to account for asymmetry in molecular stmcture (79). The acentric factor is defined as the deviation of reduced vapor pressure from 0.1, measured at a reduced temperature of 0.7. In equation form this becomes ... 

For pure organic vapors, the Lydersen et al. corresponding states method is the most accurate technique for predicting compressibility factors and, hence, vapor densities. Critical temperature, critical pressure, and critical compressibility factor defined by Eq. (2-21) are used as input parameters. Figure 2-37 is used to predict the compressibihty factor at = 0.27, and the result is corrected to the Z of the desired fluid using Eq. (2-83). 

The partial pressure of water vapor in air cannot be higher than the vapor pressure of saturated water ft (T) corresponding to air temperature T. If it were higher, condensation of water vapor would occur until the equilibrium state corresponding to the saturated vapor pressure was achieved. 

Clinch, J. M., andH. B. Karplus, 1964, An Analytical Study of the Propagation of Pressure Waves in Liquid Hydrogen-Vapor Mixtures, Report IITRI-N-6054-6, IIT Research Inst., NASA-CR-54015. (3) Cobb, C. B., and E. L. Park, Jr., 1969, Nucleate Boiling—A Maximum Heat Flux Correlation for Corresponding States Liquids, Chem. Eng. Prog. Symp. Ser. 65(92) 188—193. (4)... 

When the standard states for the solid and liquid species correspond to the pure species at 1 atm pressure or at a low equilibrium vapor pressure of the condensed phase, the activities of the pure species at equilibrium are taken as unity at all moderate pressures. Consequently, the gas phase composition at equilibrium will not be... 

This is known as the Clausius-Clapeyron equation. It is a state relationship that allows the determination of the saturation condition p = p(T) at which the vapor and liquid are in equilibrium at a pressure corresponding to a given temperature. 

TABLE II. Corresponding-States Vapor Pressures and Surface Tensions for Molten Alkali Halides... 

Note that the diagram has three general areas corresponding to the three states of matter solid, liquid, and gas. The line from A to C represents the change in vapor pressure of the solid with temperature for the sublimation (going directly from a solid to a gas without first becoming a liquid) equilibrium. The A to... 

It is important to point out here, in an early chapter, that the Born-Oppenheimer approximation leads to several of the major applications of isotope effect theory. For example the measurement of isotope effects on vapor pressures of isotopomers leads to an understanding of the differences in the isotope independent force fields of liquids (or solids) and the corresponding vapor molecules with which they are in equilibrium through use of statistical mechanical theories which involve vibrational motions on isotope independent potential functions. Similarly, when one goes on to the consideration of isotope effects on rate constants, one can obtain information about the isotope independent force constants which characterize the transition state, and how they compare with those of the reactants. 

Fig. 13.1 Reduced vapor pressure and molar density vs. reciprocal reduced temperature for HoO, CH4, H2, and 4He. In each case, were simple corresponding states theory adequate, all data would lie on a single master curve. Using extended CS the curves are fit to acceptable precision, (a) (top) = reduced vapor pressures, (b) (bottom) = reduced liquid molar densities... 

Figure 13.1a shows reduced vapor pressures and Fig. 13.1b reduced liquid molar densities for the parent isotopomers of the reference compounds. Such data can be fit to acceptable precision with an extended four parameter CS model, for example using a modified Van der Waals equation. In each case the parameters are defined in terms of the three critical properties plus one system specific parameter (e.g. Pitzer acentric factor). Were simple corresponding states theory adequate, the data for all... 

For most of the situations encountered in solvent extraction the gas phase above the two liquid phases is mainly air and the partial (vapor) pressures of the liquids present are low, so that the system is at atmospheric pressure. Under such conditions, the gas phase is practically ideal, and the vapor pressures represent the activities of the corresponding substances in the gas phase (also called their fugacities). Equilibrium between two or more phases means that there is no net transfer of material between them, although there still is a dynamic exchange (cf. Chapter 3). This state is achieved when the chemical potential x as... 

Figure 9,4 (A) Reduced isotherms of N2, CO2, and H2O vapor according to reduced pressure. (B) Comparison between experimental isotherms of H2O and f predicted by principle of corresponding states.

Further information is needed to select the thermodynamically stable state. The equilibrium vapor pressure is psat = 1.529x10 Pa at the given temperature (ref. 9), hence we accept the root v = 1.505298xl0- m /mol corresponding to the gaseous state. (If no experimental value is available for p53 can... 

Evaluating a chemical s activity, a,(phase), in any phase of interest corresponds to contrasting its concentration to whatever concentration would be expected at equilibrium with the reference state. Choosing the pure liquid organic compound as the reference state implies that the chemical s activity is equal to 1 when it occurs at its liquid solubility in water or its pure liquid vapor pressure in air. Since we have... 

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