Fugacity of pure liquid

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

We find that the standard-state fugacity fV is the fugacity of pure liquid i at the temperature of the solution and at the reference pressure P. ... 

For condensable components, we use the symmetric normaliza-L as x - 1 therefore, the quantity in brackets is the fugacity of pure liquid i at system temperature and pressure. 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

If we use the symmetric convention for normalization,/ 0 is the fugacity of pure liquid / at the temperature of the mixture and at some specified pressure, usually taken to be the total pressure of the system. Equation (69) presents no problem for subcritical components, where the pure liquid can exist at the system temperature. However, for supercritical components in the symmetric convention,/,0 is a fictitious quantity which must be evaluated by some arbitrary extrapolation. 

Let us now continue with our discussion of how to relate the chemical potential to measurable quantities. We have already seen that the chemical potential of a gaseous compound can be related to pressure. Since substances in both the liquid and solid phases also exert vapor pressures, Lewis reasoned that these pressures likewise reflected the escaping tendencies of these materials from their condensed phases (Fig. 3.9). He thereby extended this logic by defining the fugacities of pure liquids (including subcooled and superheated liquids, hence the subscript L ) and solids (subscript s ) as a function of their vapor pressures, pil ... 

When the liquid phase is ideal, Ki depends only on the temperature, the pressure, and the vapor composition. The procedure for determining the dew point in such a case is to (1) guess a temperature (2) calculate the Kt, which equal f°/iP, where is the fugacity of pure liquid i at the system temperature and pressure, , is the fugacity coefficient of the i th species in the vapor phase, and P is the system pressure and (3) check if the preceding dew-point equation is satisfied. If it is not, repeat the procedure with a different guess. 

Thus, the expression for the standard state fugacity of pure liquid at pressure P and temperature T becomes... 

For the usual standard state for liquids f° is the fugacity of pure liquid / at the temperatiue of the system and at I bar. 

Both and ° represent fugacity of pure liquid i at temperature T, but at pressures P and P°, respectively. Except in the critical region, pressure has little effect on the properties of liquids, and the ratio fi/ff is often taken as unity. When this is not acceptable, this ratio is evaluated by the equation... 

By following the procedure given in 29f, with / representing the fugacity of pure liquid or solid, an equation exactly analogous to (29.22) is obtained for the variation of the fugacity with temperature at constant pressure. As before, H is the molar heat content of the gas, i.e., vapor, at low pressure, but H is now the molar heat content of the pure liquid or solid at the pressure P. The difference — H has been called the ideal heat of vaporization, for it is the heat absorbed, per mole, when a very small quantity of liquid or solid vaporizes into a vacuum. The pressure of the vapor is not the equilibrium value, but rather an extremely small pressure where it behaves as an ideal gas. 

The fugacity of pure liquid i at temperature T and pressure P is given by... 

Compute the fugacity of pure liquid -pentane and pure liquid benzene at 373.15 K and 50 bar using the Peng-Robinson equation of state. 

From the standard state for reactions, fX is the fugacity of pure liquid A at the system temperature and 1.0 atm. Again, this value is unknown, but we do know that is the fugacity of pure liquid A at the system temperature and the vapor pressure of A at this temperature. The dif-... 

For the fugacity of pure liquid at the temperature and pressure of the solution we use the Poynting equation, which relates this fugacity to the fugacity of the saturated liquid at same temperature ... 

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