Predictions with vapor pressure data

EXAMPLE 12-4 Making Predictions with Vapor Pressure Data... 

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

Equations 14.17 and 14.18 are very simple, but the accuracy of the predictions depends greatly on the realistic estimation of Ca, which varies with time during the operation of the SVE system. For the start of the SVE project and considering that the free organic phase, NAPL, is present in the subsurface, a hrst approximation is to calculate Ca from the vapor pressure data of the contaminants (equation 2 in Table 14.3 or Equation 14.1). The actual concentration, however, will be lower than this value for two main reasons (1) the extracted airstream does not pass only through the contaminated zone and (2) limitations on mass transfer exist. An effectiveness factor q should be considered to take into account the effect of these phenomena on removal rates. The value of this factor can be determined by comparing the calculated concentration with data obtained from the preliminary pilot tests at the site ... 

Predict the vapor pressure of heavy water D20 and of normal water at 25°C, using data in Appendix 2A. How do these values compare with each other ... 

It is very satisfying and useful that the COSMO-RS model—in contrast to empirical group contribution models—is able to access the gas phase in addition to the liquid state. This allows for the prediction of vapor pressures and solvation free energies. Also, the large amount of accurate, temperature-dependent vapor pressure data can be used for the parameterization of COSMO-RS. On the other hand, the fundamental difference between the liquid state and gas phase limits the accuracy of vapor pressure prediction, while accurate, pure compound vapor pressure data are available for most chemical compounds. Therefore, it is preferable to use experimental vapor pressures in combination with calculated activity coefficients for vapor-liquid equilibria predictions in most practical applications. 

VL(L) E measurements for binaries involving water with alcohol and acid have been done, as described elsewhere [2]. Figure 8.6 presents experimental vapor pressure data for 2-ethylhexyl laurate. The normal boiling point (nbp) is 607.6 K, close to the prediction by Gani s method. On the other hand, the prediction of the whole saturation curve by Riedel s method (noted estimation in Figure 8.6) is in large error at lower pressures. This fact can affect the accuracy of chemical equilibrium calculation, but fortunately the errors compensate each other [2]. 

We particularly welcome estimation methods that incorporate available experimental data, such as melting point. Engineers engage in a number of steps to quantify their confidence in an estimation method and to improve the accuracy of the prediction when working with new molecules. As shown in Table 2, a new molecule with the structure has a molecular weight of 163.606, a measured normal boiling point (T ) of 237.6 C, and a few vapor pressure data. Using an estimation method... 

Equation 1.14 incorporates the definition of the acentric factor and may also be used to predict the vapor pressure, once the acentric factor has been determined. Another route for calculating the vapor pressure is via an equation of state, as described below. In the Soave equation, co is used in formulating the temperature dependency of the parameter a, which may be considered as a function of both P and co. The function fl(P,co) was determined with the objective of fitting vapor pressures calculated by the equation of state to experimental pure component vapor pressure data. 

This equation (Peng and Robinson, 1976) was developed with the goal of overcoming some of the deficiencies of the Soave equation, namely its inaccuracy in the critical region and in predicting liquid densities. The equation is similar to the Soave equation in that it is cubic in the volume, expresses its parameters in terms of the critical temperature, critical pressure, and acentric factor, and is based on correlating pure-component vapor pressure data. The equation is written as... 

A number of studies have explored ways in which partial vapor pressures may be obtained using TGA data, thereby allowing both prediction of vapor pressure under a range of circumstances and calculation of the constants associated with the approaches described previously. In particular, Price and Hawkins (12) have argued that the rate of mass loss for vaporization and sublimation within a TGA should be a zero-order process, and hence should be constant for any given temperature, subject to the important condition that the available surface area also remains constant. This means that the value of v from Equation 6.4 should be easily calculated from the TGA data. If one performs this experiment for materials with known vapor pressure and temperature relationships (the authors used discs of acetamide, benzoic acid, benzophenone, and phenanthrene), then the constant k for the given set of TGA experimental conditions may be found. Once this parameter is known, the vapor pressure may be assessed for an unknown material in the same manner. 

Figure 7.5-2 contains experimental vapor pressure versus temperature data for / -butane, together with vapor pressure predictions from (1) the van der Waals equation ... 

C2. An equation for Oorg-w in w similar to Eq. f8-131 is easy to derive do it. Conpare the predicted equilibrium in water with the butanol-water equilibrium data given in Problem 8.D2. Comment on the fit. Vapor pressure data are in Perry and Green (1984). Use the data in Table 8-2 for solubility data. 

Vapor pressure data for water are given in Problem 8.D10. This data can be fit to an Antoine equation form with C = 273.16. The vapor pressure of 1-octanol is predicted by the Antoine equation ... 

Perhaps the most successful variation on the RK equation is that proposed by Soave ( ) who expresses the RK constant a by an empirical function of reduced temperature and acentric factor. This empirical function was determined from vapor-pressure data for paraffins and therefore, when Soave s equation is used with reasonable mixing rules and one adjustable binary parameter, it gives good K factors for typical light-hydrogen mixtures however, it predicts poor liquid densities. This illustrates a point known to all workers in the equation-of-state field it is not difficult to represent any one thermodynamic property but it is difficult, with one equation of state, to represent them all. 

In some applications, because of the weak dependence of the b parameter on temperature at low vapor pressures (Panagiotopoulos Kumar 1985), it is held constant also, some investigations (Trebble Bishnoi 1986 Hngdkovsk Cibulka 1990) have shown that varying the b parameter with temperature may lead to thermodynamic inconsistencies in the compressed liquid region at elevated pressures and above the critical temperature, which result in the prediction of negative heat capacities and crossovers in enthalpy isotherms. In these cases equations (8.14) are solved for the unknowns a, V and Fg by fitting to vapor pressure data alone. 

One use of vapor pressure data is in calculations dealing with the collection of gases over liquids, particularly water (Section 6-6). Another use, illustrated in Example 12, is in predicting whether a substance exists solely as a gas (vapor) or as a liquid and vapor in equilibrium. 

An afternate method with approximately the same accuracy as the Rackett method is the COSTALD metnod of Hanldnson and Thomson.The critical temperature, a characteristic volume near the critical volume, and an acentric factor optimized for vapor pressure prediction by the Soave equation of state are required input parameters. The method is detailed in the Technical Data Book ... 

This information allows prediction of X T.E at 323.15 K and at the higher temperatures, 372.8, 397.7, and 422.6 K, for which measured X T.E values are given by Wilsak, et al. (Fluid Phase Equilibria, 28, pp. 13-37 [1986]). Values of In yX and hence of the Margules parameters at the higher temperatures are given by Eq. (4-325) with Cf = 0. The pure-species vapor pressures in all cases are the measured values reported with the data sets. Res lilts of these calculations are displayed in Table 4-1, where the parentheses enclose values from the gamma/ phi approach as reported in the papers cited. 

Example 4.5 2-Propanol (isopropanol) and water form an azeotropic mixture at a particular liquid composition that results in the vapor and liquid compositions being equal. Vapor-liquid equilibrium for 2-propanol-water mixtures can be predicted by the Wilson equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.113. Data for the Wilson equation are given in Table 4.126. Assume the gas constant R = 8.3145 kJ-kmol 1-K 1. Determine the azeotropic composition at 1 atm. 

It is shown that the properties of fully ionized aqueous electrolyte systems can be represented by relatively simple equations over wide ranges of composition. There are only a few systems for which data are available over the full range to fused salt. A simple equation commonly used for nonelectrolytes fits the measured vapor pressure of water reasonably well and further refinements are clearly possible. Over the somewhat more limited composition range up to saturation of typical salts such as NaCl, the equations representing thermodynamic properties with a Debye-Hiickel term plus second and third virial coefficients are very successful and these coefficients are known for nearly 300 electrolytes at room temperature. These same equations effectively predict the properties of mixed electrolytes. A stringent test is offered by the calculation of the solubility relationships of the system Na-K-Mg-Ca-Cl-SO - O and the calculated results of Harvie and Weare show excellent agreement with experiment. 

Passino-Reader, D.R., Hickey, J.P., and Ogilvie, L.M. Toxicity to Daphnia pulexmA QSAR predictions for polycyclic hydrocarbons representative of Great Lakes contaminants. Bull. Environ. Contam. Toxicol, 59(5) 834-840, 1997. Pathare, S., Bhethanabotla, V.R., and Campbell, S.W. Total vapor-pressure measurements for 2-ethoxyethanol with carbon tetrachloride, chloroform, and dichloromethane at 303.15 K, J. Chem. Eng. Data, 49(3) 510-513, 2004. 

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