Vapor pressure as function

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

Tabulation of Br2 Vapor Pressure as Function of Br2 Mole Fraction in Br2—Cl Solutions at Room Temperature ... 

Table 3.11.1 Tabulation of Bra vapor pressure as function of Bra mole fraction in Bra-CCl4...

The plots of the total vapor pressure as functions of the mole fraction of A in both the liquid and vapor phases are shown in Figure 9.12(a) and (b), respectively. The combined plot shown in Eigure 9.12(c) is a liquid-vapor phase diagram for an ideal binary solution at a fixed temperature T—often called a pressure-composition diagram. At any pressure and composition above the upper curve (the liquid line) the mixtnre is a liquid. Below the lower curve (the vapor line), the mixture is entirely vapor. The region between the two curves is a region of phase coexistence, that is, both liquid and vapor phases are present in the system. 

Debutanized gasoline cuts from Arabian Light crude. Reid Vapor Pressure as a function of yield, weight %. Aromatics content as a function of yield, volume %. 

Acrylic acid is a moderately strong carboxylic acid. Its dissociation constant is 5.5 x 10. Vapor pressure as a function of temperature is given in Table 4 for acrylic acid and four important esters (4,16—18). The lower esters form a2eotropes both with water and with their corresponding alcohols. 

Va.por Pressure. Vapor pressure is one of the most fundamental properties of steam. Eigure 1 shows the vapor pressure as a function of temperature for temperatures between the melting point of water and the critical point. This line is called the saturation line. Liquid at the saturation line is called saturated Hquid Hquid below the saturation line is called subcooled. Similarly, steam at the saturation line is saturated steam steam at higher temperature is superheated. Properties of the Hquid and vapor converge at the critical point, such that at temperatures above the critical point, there is only one fluid. Along the saturation line, the fraction of the fluid that is vapor is defined by its quaHty, which ranges from 0 to 100% steam. 

The accurate representation of vapor pressure data over a wide temperature range requires an equation of greater complexity. The Wagner equation (eq. 22) expresses the reduced vapor pressure as a function of reduced temperature TIT/... 

Vapor pressure as a function of the temperature is correlated by the Antoine equation ... 

An alternate method for flash point prediction is the method of Gmehling and Rasmussen and depends on the lower flammabihty limit (discussed later). Vapor pressure as a function of temperature is also required. The method is generally not as accurate as the preceding method as flammability limit errors are propagated. The authors have also extended the method to defined mixtures of organics. 

Although Eq. (6.37) is commonly used to represent the vapor pressure as a function of temperature, it is by no means the best equation for the purpose. For many compounds, a more accurate representation of the vapor pressure is given by the Antoine equation,... 

The desorption isotherm describes, under equilibrium conditions, the amount of water absorbed on the product at a given temperature as a function of water vapor pressure, as shown in Fig. 1.96. To approximate the equilibrium at a given temperature in a short time, the pressure during SD should be small compared with the equilibrium vapor pressure,... 

Results for vapor pressure as a function of temperature are presented for major organic chemical compounds. The coefficients are displayed in an easy-to-use table which is especially applicable for rapid engineering usage with the personal computer or hand calculator. The organic chemicals encompass hydrocarbon, oxygen, nitrogen, halogen, silicon, sulfur and other chemical type compounds. 

The Antoine-type equation with extended terms was selected for correlation of vapor pressure as a function of temperature ... 

Any one of Equations (8.14), (8.15), or (8.16) is known as the Clausius-Clapeyron equation and can be used either to obtain AH from known values of the vapor pressure as a function of temperature or to predict vapor pressures of a hquid (or a solid) when the heat of vaporization (or sublimation) and one vapor pressure are known. The same equations also represent the variation in the boiling point of a liquid with changing pressure. 

It can be observed from Figure 4.15 that the predicted fiow rate of siiane increases exponentiaiiy as the anneai temperature is increased, as expected. This is due to the exponentiai increase in Si vapor pressure as a function of temperature, which was previousiy discussed. Simiiariy, caicuiations were performed to determine siiane fiow rates for different process pressures starting from 10 Torr to atmospheric pressure (760 Torr) as a function of anneaiing temperature. The partiai pressure of siiane at 1,600°C was recaicuiated at different pressures and then substituted into our empiricai modei to determine the partiai pressure at different... 

As is indicated by the examples given in Table 4.2, both methods (Eqs. 4-20 and 4-21) provide reasonable estimates of AvapSj(Tb). Such equations, along with the generally applicable integrated Clapeyron expression, establish a highly flexible means of estimating compound vapor pressures as a function of temperature (see Section 4.4 for examples). 

The LCM accurately predicted the vapor pressure of SO and CO2 over sulfite/bisulfite and carbonate/bicarbonate solutions, respectively, for salts of sodium, calcium, and magnesium. Figure 3 plots the LCM predictions of SO2 vapor pressure as a function of theQtotal SO to sodium ratio for a sodium sulfite/bisulfite system at 50 C... 

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