Antoine equation, vapor pressure described

Theoretically based correlations (or semitheoretical extensions of them), rooted in thermodynamics or other fundamentals are ordinarily preferred. However, rigorous theoretical understanding of real systems is far from complete, and purely empirical correlations typically have strict limits on apphcabihty. Many correlations result from curve-fitting the desired parameter to an appropriate independent variable. Some fitting exercises are rooted in theory, eg, Antoine s equation for vapor pressure others can be described as being semitheoretical. These distinctions usually do not refer to adherence to the observations of natural systems, but rather to the agreement in form to mathematical models of idealized systems. The advent of readily available computers has revolutionized the development and use of correlation techniques (see Chemometrics Computer technology Dimensional analysis). 

The Antoine equation is the most commonly used empirical equation for describing the vapor pressure of a liquid as a function of temperature. 

The vapor pressure of a chemical substance increases rapidly with temperature. Many equations have described this temperature dependence so that the vapor pressure can be calculated for a temperature of interest. The Antoine (1888) equation is most familiar. Riddick, Bunger, and Sakano (1996) provide an extensive discussion of many of the empirical equations used to describe the temperature dependence of the vapor pressure. To apply a particular equation to a chemical, the necessary parameters must be available from experimental data. If no such information exists, some method is needed to estimate the parameters. 

One complication with this description is that a species can be present in a liquid mixture, though at the temperature and pressure of the mixture the substance would be a vapor or a solid as a pure component. This is especially troublesome if the compound is below its melting point, so that it is the solid sublimation pressure rather than the vapor pressure that is known, or if the compound is above its critical temperature, so that the vapor pressure is undefined. In the first case one frequently ignores the phase change and extrapolates the liquid vapor pressure from higher temperatures down to the temperature of interest using, for example, the Antoine equation, eqn. (2.3.11). For supercritical components it is best to use an EOS and compute the fugacity of a species in a mixture, as described in Section 2.5. 

The Thermodynamics Research Center at Texas A M University (TRC) has assembled, collected, evaluated and published tables of thermodynamic data for nearly 60 years. These current volumes describing vapor pressures come from those tables and other evaluation projects conducted by TRC and other research groups, and, as of the publication date, represent all known, evaluated data. The volumes contain constants derived from fitting experimental data with the Antoine and extended Antoine vapor pressure equations. The condensed phases can be either liquid or crystal. Thus, these constants provide evaluated vapor pressures which professional thermodynamicists believe represent the data within experimental error. 

A distillation column is separating 100 mol/s of a 30 mol% acetone, 70 mol% methanol mixture at atmospheric pressure. The feed enters as a saturated liquid. The column has a total condenser and a partial reboiler. We desire a distillate with an acetone content of 72 mol%, and a bottoms product with 99.9 mol% methanol. A reflux ratio of 1.25 the minimum will be used. Calculate the number of ideal stages required and the optimum feed location. VLE for this system is described by the modified Raoult s law, with the NRTL equation for calculation of liquid-phase activity coefficients, and the Antoine equation for estimation of the vapor pressures. 

The principal disadvantage of the RKJZ method is the complex temperature dependence of and Qb. Although Haman et al. (13) provided a generalized correlation for Qat and fib, these quantities are not generalized in the form described here but are generated each time they are needed from liquid densities and vapor pressures. Various sources of liquid density and vapor pressure are used versions of the Riedel correlations (14,15) API 44 Antoine equations (16) petroleum fraction correlations and curve fits of experimental information. 

In addition to marking the phase boundary, line FC expresses the relationship between saturation pressure and temperature. The saturation pressure generally increases quickly with temperature up to the critical point. There is no vapor-liquid transition above the critical point therefore, the relationship between saturation pressure and temperature exists only below the critical point. The saturation pressure of pure component is an important physical property and a required parameter in many calculations of phase equilibria. Several equations have been developed to describe the mathematical relationship between saturation pressure and temperature. One of the most widely used is the Antoine equation ... 

A prerequisite for applying estimation techniques is the knowledge of the compound s boiling point (r, ) and for solids also of the melting point The methods described by Grain (1990), Lyman (1985) and Altschuh, Briiggemann and Karcher (1993) are of general applicability and they are not restricted to particular chemical classes. In Table 4.4, model 1 is derived from the Antoine equation, which describes the temperature dependence of vapour pressure model 2 is based on the Watson correlation, which describes the temperature dependence of the heat of vaporization model 3 constitutes an extension of 2. These three models additionally use a class-specific constant (Kp) as input, which is assumed to describe the polarity of the compounds (Table 4.5). 

VLE data, the results of two thermodynamic consistency tests, and the parameters of different -models, such as the Wilson, NRTL, and UNIQUAC equation. Additionally, the parameters of the Margules [28] and van Laar [29] equation are listed. Furthermore, the calculated results for the different models are given. For the model which shows the lowest mean deviation in vapor phase mole fraction the results are additionally shown in graphical form together with the experimental data and the calculated activity coefficients at infinite dilution. In the appendix of the data compilation the reader will find the additionally required pure component data, such as the molar volumes for the Wilson equation, the relative van der Waals properties for the UNIQUAC equation, and the parameters of the dimerization constants for carboxylic acids. Usually, the Antoine parameter A is adjusted to A to start from the vapor pressure data given by the authors, and to use the -model parameters only to describe the deviation from Raoult s law. Since in this data compilation only VLE data up to 5000 mm Hg are presented, ideal vapor phase behavior is assumed when fitting the parameters. For systems with carboxylic acids the association model is used to describe the deviation from ideal vapor phase behavior. 

P8.14 The vapor pressures of liquid anthracene and phenanthrene can be described by the Antoine equation using the Antoine parameters given below. Calculate the vapor-liquid-solid equilibrium (VLSE) along the solid-liquid saturation curve assuming ideal mixture behavior in the liquid phase. Melting points and heats of fusion of both components are given in example P8.1 above. Compare the vapor-liquid separation factors to those of an isothermal VLE data set at 220 "C (calculate assuming ideal liquid mixture behavior). 

In Eq. 8.5, the vapor pressure at wet bulb temperature can be calculated from the Antoine equation, while the solvents concentration (Pout) in the drying gas can be determined in the thermodynamic step described previously. For example, fast evaporation and low drying times can be imposed by manipulating Pout and droplet size (tfo) and used to promote the production of smooth spherical particles. 

When the data are plotted on linear coordinates (see Figure 2.5), a nonlinear dependence of vapor pressure on temperature is obtained. Vapor-pressure data often can be described by the Antoine equation ... 

Equations for the description of the temperature dependence of selected properties of methanol are given here, where T is temperature in K The vapor pressure P (Pa) of methanol in a limited temperature range can be described accurately by the Antoine equation [22] ... 

Parameter values for an expression describing the vapor pressure of all components involved, such as the Antoine equation, are available. 

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