Fugacity charts

For precise equilibrium ratios it is necessary to resort to elaborate sets of curves or tabulations. Ratios for the lighter hydrocarbons are available in the NGAA Equilibrium Data Book, or the Equilibrium Copstsmt and Fugacity Charts of the M. W. Kellogg Co. Information on hi er-boiling oils is scant. 

The fugacity coefficient departure from nonideaHty in the vapor phase can be evaluated from equations of state or, for approximate work, from fugacity/compressibiHty estimation charts. References 11, 14, and 27 provide valuable insights into this matter. 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

Another property which can be represented by generalized charts is fugacity, ( ). The fugacity of a substance can be regarded as a corrected vapor pressure. At low pressures (below atmospheric) the use of pressure in the place of fugacity leads to tittle error in calculations. The fugacity coefficient is defined by... 

Use only the following data and the fugacity coefficient chart. 

The fugacity coefficients (f/P) for the various species may be determined from the generalized chart in Appendix B if one knows the reduced temperature and pressure corresponding to the species in question. Therefore,... 

The Level I calculation suggests that if 100,000 kg (100 tonnes) of benzene are introduced into the 100,000 km2 environment, 99% will partition into air at a concentration of 9.9 x 10-7 g/m3 or about 1 pg/rn3. The water will contain nearly 1% at a low concentration of 4 pg/rn3 or equivalently 4 ng/L. Soils would contain 5 x 10-6 pg/g and sediments about 9.7 x 10 6 pg/g. These values would normally be undetectable as a result of the very low tendency of benzene to sorb to organic matter in these media. The fugacity is calculated to be 3.14 x 10-5 Pa. The dimensionless soil-water and sediment-water partition coefficients or ratios of Z values are 2.6 and 5.3 as a result of a Koc of about 55 and a few percent organic carbon in these media. There is little evidence of bioconcentration with a very low fish concentration of 3.0 x FT5 pg/g. The pie chart in Figure 1.7.6 clearly shows that air is the primary medium of accumulation. 

Related Calculations. If experimental P-V-T data are available, either as an analytical expression or as tabular values, the fugacity coefficient may be calculated by integrating the data (numerically or otherwise) as shown in step 3 above. However, if such data are not available, use the generalized fugacity coefficient chart to estimate fugacity values. Refer to Hougen, Watson, and Ragatz [4] for deviation-correction terms for values of Zc above and below the standard value of 0.27. 

Equations for fugacity coefficients are derived from equations of state or are approximated from activity coefficient charts as functions of reduced temperature and pressure. Table 13.1 includes them for the popular Soave equation of state. At pressures below 5-6 atm, the ratio of activity coefficients in Eq. (13.7) often is near unity. Then the VER becomes... 

The calculation of fugacity coefficients and the use of generalized charts are discussed in the standard thermodynamics texts. If the fugacity coefficients are known then in the nonideal case we find that... 

Alternatively if compressibility factor charts are available, these Z factors may be used to compute the fugacity of pure component i by use of the following equation which is readily obtained by commencing with Eqs. (14-12) and (14-26)... 

The standard state of each species is taken as the pure material at unit fugacity. Use only the following critical properties, thermochemical data, and a fugacity coefficient chart. 

Determine the equilibrium composition that is achieved at 300 bar and 700 K when the initial mole ratio of hydrogen to carbon monoxide is 2. You may use standard enthalpy and Gibbs free energy of formation data. For purposes of this problem you should not neglect the variation of the standard heat of reaction with temperature. You may assume ideal solution behavior but not ideal gas behavior. You may also use a generalized fugacity coefficient chart based on the principle of corresponding states as well as the heat capacity data listed below. 

Generalized fugacity coefficients of pure gases and liquids (Z = 0.27). (Reprinted from O. A. Hougen, K. M. Watson, and R. A. Ragatz, Chemical Process Principles Charts, 3rd ed. Copyright 1964. Reprinted by permission of John Wiley Sons, Inc.)... 

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