1. Pure Component VLE in Terms of Fugacity
Purpose of this lecture:
To derive an expression for the calculation of fugacity of pure liquids
Highlights
Phase equilibrium expressed in terms of fugacities
The fugacity of a pure liquid at a given temperature can be calculated through its vapour-phase fugacity coefficient and saturation pressure
The effect of pressure on liquid-phase fugacity is captured by the Poynting factor
Reading assignment: Section 11.5 (pp )
CHEE 311
Lecture 10

2. Pure Component VLE in Terms of Fugacity
Consider a pure component at its vapour pressure:
Phase rule tells us, F=2-2+1 = 1 degree of freedom
Therefore, at a given T, there can only be a single pressure, Psat for which a vapour and a liquid are in equilibrium
Along the phase boundary, the chemical potentials are equal
How do the fugacities of the liquid and gas relate?
P liquid
gas T
CHEE 311
Lecture 10

3. Pure Component VLE in Terms of Fugacity
For the non-ideal, pure gas we can write:
11.38a
For a non-ideal liquid, we can define an analogous expression:
11.38b
At equilibrium
11.39
In terms of fugacity:
11.41
CHEE 311
Lecture 10

4. Review of Chemical Equilibrium Criteria
We have several different criteria for phase equilibrium. While they stem from the same theory, they differ in practical applicability.
A system at equilibrium has the following properties:
the total Gibbs energy of the system is minimized, meaning that no change in the number of phases or their composition could lower the Gibbs energy further
the chemical potential of each component, i, is the same in every phase within the system
in p phases
the fugacity of each component, i, is equal in every phase of the system
CHEE 311
Lecture 10

5. Calculating the Fugacity of Pure Liquids
The derivation of the fugacity of a pure liquid at a given T, P is comprised of four steps:
Step 1. Calculate the fugacity of a vapour at Pisat
Step 2. Calculate the change in Gibbs energy between Pisat and the given pressure P using the fundamental equation:
dG = VdP - SdT (constant T)
which after integration yields:
Given that liquids are nearly incompressible (Viliq is not a strong function of P) the integral is approximated as:
(A)
CHEE 311
Lecture 10

6. Calculating the Fugacity of Pure Liquids
3. Using the definitions of fugacity:
we can take the difference:
(B)
4. Substituting A into B: or
11.44
CHEE 311
Lecture 10

7. Calculating the Fugacity of Pure Liquids
We can now calculate the fugacity of any pure liquid using two equations:
11.44
and
11.35
The exponential within Equation accounts for the change in Gibbs energy as we compress the liquid from Pisat to the specified pressure, P. This is known as the Poynting factor.
This contribution to fugacity is slight at all pressures near Pisat, and is often assumed to be unity.
CHEE 311
Lecture 10

8. Example Problem
Calculate the fugacity of n-pentane at T= 25 oC and P=101 kPa. The saturation pressure of n-pentane at 25 oC is Pisat =67.5 kPa.
CHEE 311
Lecture 10