Solution fugacity

Ebulliometry Summary of literature data Selected values From solute fugacity f and x... 

FIG. 4-11 Plot of solute fugacity vs. solute mole fraction. 

FIG. 4-7 Plot of solute fugacity/i versus solute mole fraction. [Smith, Van Ness, and Abbott, Introduction to Chemical Engineering Thermodynamics, 7th ed., p. 555, McGraw-Hill, New York (2005).]... 

Actual Account for non-idealities in solution (fugacity vs pressure, for example). 

Figure 9.7-3 Solute fugacity in real and ideal Henry s law solutions, (ri) Solute fugacity versus mole fraction. (b) Solute fugacity versus molality.

The ratio of the solute fugacities in the liquid and vapor phases can be computed as described in Chapter 9 (see Eq. 9.7-8b). 

When intermolecular forces are independent of composition, each fugacity deviates from its ideal-gas value by an amount that is also independent of composition. This means each ideal-solution fugacity coefficient does not depend on composition. 

Since the ideal-gas fugacity is linear in the mole fraction x,- while q) is independent of mole fraction, the ideal-solution fugacity must also be linear in x,-. We write that linearity in this form ... 

This shows that, although the ideal-solution fugacity coefficient is independent of composition, it does depend on the choice made for the standard state. Consequently, the ideal-solution fugacity coefficient is not the same as the standard-state fugacity coefficient unless we choose = P. That is, in general... 

To obtain expressions for the partial molar properties of ideal solutions, we first determine the chemical potential. Using the ideal-solution fugacity (5.1.6) in the integrated definition of fugacity (4.3.12) we find... 

In 5.1 we observed that every ideal-solution fugacity (5.1.2) is linear in its mole fradion. We now write (5.1.2) in a more explicit form. 

Then, substituting this into (5.4.7), we obtain the ideal-solution fugacity, which is that of a Lewis-Randall ideal solution. 

But while we can pick any straight line and use it to represent an ideal-solution fugacity, in practice we always choose a line that intersects or lies tangent to the curve for the real fugacity at the standard-state pressure. This means that we choose fi%T, P°, x° ) = fi(T, P°, x° ) at some composition x then, at that composition, the activity coefficient must be unity. At other mole fractions, the fugacity of the ideal solution is given by the equation for the straight line. 

We prefer to avoid these competing effects by using FFF 4 rather than FFF 5 then the effects of all nonidealities combine into a single activity coefficient, which we evaluate at the system pressure rather than a standard-state pressure. With this choice, the solute fugacity takes the form... 

Equation 9.4.24, derived using fugacity, is valid even if the solute has such low volatility that its fugacity in an equilibrated gas phase is too low to measure. In principle, no solute is completely nonvolatile, and there is always a finite solute fugacity in the gas phase even if immeasurably small. 

V Total solution fugacity R-i Dipole moment of species i... 

---