To calculate the fugacity of a pure liquid at a specified temperature and pressure, we may use an equation of state capable of representing the liquid phase and first calculate (L (See Chap. 6) and then use Eq. (8-2.2b). Alternatively, we may use the two primary thermodynamic properties: the saturation (vapor) pressure, which depends only on temperature, and the liquid density, which depends primarily on temperature and to a lesser extent on pressure. Unless the pressure is very large, it is the vapor pressure which is by far the more important of these two quantities. In addition, we require volumetric data (equation of state) for pure vapor i at system temperature, but unless the vapor pressure is high or unless there is strong dim-merization in the vapor phase, this requirement is of minor, often negligible, importance.
The fugacity of pure liquid i at temperature T and pressure P is given by fP VL(T P)
p JPvpi R1
where Pvp is the vapor pressure (see Chap. 7) and superscript s stands for saturation. The fugacity coefficient (s is calculated from vapor-phase volumetric data, as discussed in Sec. 6-7; for typical nonassociated fluids at temperatures well below the critical, ( is close to unity.
The molar liquid volume ViL is the ratio of the molecular weight to the density, where the latter is expressed in units of mass per unit volume.f At a temperature well below the critical, a liquid is nearly incompressible. In that case the effect of pressure on liquid-phase fugacity is not large unless the pressure is very high or the temperature is very low. The exponential term in Eq. (8-3.1) is called the Poynt-ing factor.
To illustrate Eq. (8-3.1), the ratio of the fugacity of pure liquid water to the vapor pressure (equal to the product of (f>s and the Poynting factor) is shown in Table 8-2 at four temperatures and three pressures, the vapor pressure, 40 bar, and 350 bar. Since (s for a pure liquid is always less than unity, the ratio is always less than one at saturation. However, at pressures well above the vapor pressure, the product of ( s and the Poynting factor may easily exceed unity, and then the fugacity is larger than the vapor pressure.
Sometimes it is necessary to calculate a liquid fugacity for conditions when the substance does not exist as a liquid. At 300°C, for example, the vapor pressure exceeds 40 bar, and therefore pure liquid water cannot exist at this temperature and 40 bar. Nevertheless, the value 0.790 shown in Table 8-2 at these conditions can f For volumetric properties of liquids, see Chap. 4.
8.12 CHAPTER EIGHT
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