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To introduce the calculation of fugacity for liquids, consider Fig. 9.5. The shape of an isotherm below the critical temperature differs significantly from an ideal-gas isotherm. Such an isotherm is illustrated which begins in the vapor region at low pressure, intersects the phase boundary where vapor and liquid coexist, and then extends to higher pressure in…

The principle of calculation of the fugacity coefficient is the same by all methods—Eqn. 9.23 or 9.24 is evaluated. The methods look considerably different, usually because the P–V–T properties are summarized differently. All methods use the formula below and differ only in the manner the fugacity coefficient is evaluated. Equations of State Equations of state are the dominant method used in process…

We began the chapter by showing that Gibbs energy was equivalent in phases at equilibrium. Here we show that equilibrium may also be described by equivalence of fugacities. Since we may subtract Gig from both sides and divide by RT, giving Substituting Eqn. 9.22, which becomes Therefore, calculation of fugacity and equating in each phase becomes the preferred method of…

In principle, all pure-component, phase-equilibrium problems could be solved using Gibbs energy. Historically, however, an alternative property has been applied in chemical engineering calculations, the fugacity. The fugacity has one advantage over the Gibbs energy in that its application to mixtures is a straightforward extension of its application to pure fluids. It also has some empirical…

We have seen that the Gibbs energy is the key property that must be used to characterize phase equilibria. In the previous section, we have used Gibbs energy in the derivation of useful relations for vapor pressure. For our discussions here, we have been able to relate the two phases of a pure fluid to one…

We found that the Clausius-Clapeyron equation leads to a simple, two-constant equation for the vapor pressure at low temperatures. What about higher temperatures? Certainly, the assumption of ideal gases used to derive the Clausius-Clapeyron equation is not valid as the vapor pressure becomes large at high temperature; therefore, we need to return to the Clapeyron…

We can apply these concepts of equilibrium to obtain a remarkably simple equation for the vapor-pressure dependence on temperature at low pressures. As a “point of view of greatest simplicity,” the Clausius-Clapeyron equation is an extremely important example. Suppose we would like to find the slope of the vapor pressure curve, dPsat/dT. Since we are talking…

As an introduction to the constraint of phase equilibrium, let us consider an example. A piston/cylinder contains both propane liquid and vapor at –12°C. The piston is forced down a specified distance. Heat transfer is provided to maintain isothermal conditions. Both phases still remain. How much does the pressure increase? This is a trick question.…