Acentric factors. Pitzer

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... 

Pitzers acentric factor = -[1.0 + loglO(PVPc)] Dimensionless ... 

Look up the critical temperature and pressure (Tc and Pc) for the species of interest in Table B.l or elsewhere. Also look up the Pitzer acentric factor, selected compounds, and a more complete list can be found in Reid et al. 

Standard Conditions for Gases Pitzer Acentric Factors Compressibility Charts... 

The Pitzer acentric factor is a property of pure fluids and has been widely tabulated (for example, see Ref. [ ]). It can be estimated in several ways, one of w hich [5] is given in the Nomenclature. 

M Molecular weight, g/g-mole Pc Critical pressure, atm T Temperature, K Tb Normal boiling point, K Tc Critical temperature, K T Dimensionless temperature A Thermal conductivity, cal/(s)(cm)(K) A Dimensionless thermal conductivity M Dipole moment, debyes M Dimensionless dipole moment p Density, g/cm p Dimensionless density 0) Pitzer acentric factor, dimensionless k Boltzmann s constant... 

A mixture of ethanol and water vapor is being rectified in an adiabatic distillation column. The alcohol is vaporized and transferred from the liquid to the vapor phase. Water vapor condenses—enough to supply the latent heat of vaporization needed by the alcohol being evaporated—and is transferred from the vapor to the liquid phase. Both components diffuse through a gas film 0.1 mm thick. The temperature is 368 K and the pressure is 1 atm. The mole fraction of ethanol is 0.8 on one side of the film and 0.2 on the other side of the film. Calculate the rate of diffusion of ethanol and of water, in kg/m2-s. The latent heat of vaporization of the alcohol and water at 368 K can be estimated by the Pitzer acentric factor correlation (Reid et al., 1987)... 

For the calculation of thermodynamic properties, Equation 23 was used in an empirical manner. Only data for nonpolar normal paraffin hydrocarbon systems were used in the correlation development so that as an approximation, the Pitzer acentric factor, < >, could be taken as an estimate of the collective strength of molecular anisotropies (i.e., 82 = to). Because the use of the resultant correlation for polar systems was anticipated, the parameter y (y =82), referred to herein as the orientation parameter, was used instead of the acentric factor (y < > for other fluids). The equation of state in Equation 23 then takes the form... 

Thermodynamic properties of nonideal hydrocarbon mixtures can be predicted by a single equation of state if it is valid for both the vapor and liquid phases. Although the Benedict-Webb-Rubin (B-W-R) equation of state has received the most attention, numerous attempts have been made to improve the much simpler R-K equation of state so that it will predict liquid-phase properties with an accuracy comparable to that for the vapor phase. The major difficulty with the original R-K equation is its failure to predict vapor pressure accurately, as was exhibited in Fig. 4.3. Following the success of earlier work by Wilson, Soave added a third parameter, the Pitzer acentric factor, to the R-K equation and obtained almost exact agreement with pure hydrocarbon vapor pressure... 

A quantity often used in calculations on real gases is the Pitzer acentric factor, co. Pitzer defined the factor as a means of characterizing deviation from spherical symmetry for use in corresponding state modeP . The acentric factor is obtained from experimental data, as follows co = og P[) —1.0 in which P is the reduced pressure P/P at the reduced temperature of 0.7°C, P being the critical pressure. This definition is consistent with acentric factor values of zero for rare gases. 

The shape factors, 6 and (f, are weak functions of temperature (T) and density (p) and can be regarded as characteristic of the Pitzer acentric factors of fluids a and o, respectively. The superscript c denotes the critical point value. 

So much for historical matters. The current situation is in practice rather simpler than suggested by the function FFor practical reasons it is easier to use Pc and Tc than a and e, and it turns out that the whole set of parameters at can often be condensed into a single parameter. This parameter is now usually based on the slope of the vapor-pressure curve and is called the Pitzer acentric factor a> (Schreiber Pitzer 1989). Values of Pc, Tc and (o have been tabulated for a large number of substances. 

To accomplish this objective, we introduce a third parameter characteristic of classes of molecules. There are many ways to introduce a parameter for classes of molecules we will explore only one— the Pitzer acentric factor, (o. It characterizes how nonspherical a molecule is, thereby assigning it to a class. The definition of (o is somewhat arbitrary ... 

We can extend the principle of corresponding states to account for different classes of molecules, based on the particular nature of the intermolecular interactions involved. One way to accomplish this objective is by introducing a third parameter— the Pitzer acentric factor, w.We then write the compressibiUty factor in terms of z , which accounts for simple molecules, and a correction factor for the nonsphericity ... 

Table 7.1 summarizes expressions for fugacity coefficients of pure species and mixtures for three cubic equations of state the van der Waals equation, the Redhch-Kwong equation, and the Peng-Robinson equation. You can develop these expressions using Equation (7.8) for pure species or Equation (7.14) for mixtures (see Problems 7.16, 7.17, 7.35, and 7.36). The parameters a, h, and a can be obtained from the critical temperature, the critical pressure, and Pitzers acentric factor, as discussed in Chapter 4. Eor the mixtures, mixing rules given by Equations (7.15), (7.18), and either (7.16) or (7.17) are typically used however, others have proposed alternative mixing rules. 

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