Liquid Phase Properties from VLE Data SVNA 12.1
Purpose of this lecture:
To illustrate how activity coefficients can be calculated from experimental
VLE data obtained at low pressures
Highlights
• For our calculations we take advantage of the fact that as P->0 the vapour phase molecular interactions in a mixture at VLE become very weak, hence the vapour behaves as an ideal gas. In thermodynamic
 ˆ 
1 .
0
• The modified form of Raoult’s law can then be used for the estimation of the activity coefficients from experimental low P VLE
Reading assignment: Section 12.1 (pp. 430-432)
CHEE 311 Lecture 15 1

7. Liquid Phase Properties from VLE Data SVNA 12.1
The mixture fugacity of a component in non-ideal liquid solution is defined by:
 l i
( T , P )
  i
( T )

RT ln fˆ i l
(11.46)
We also define the activity coefficient:
 i
 x i fˆ i l f i l
(11.91) which is a measure of the departure of the component behaviour from an ideal solution.
Using the activity coefficient, equation 11.46 becomes:
 l i
( T , P )
  i
( T )

RT ln
 i x i f i l
How do we calculate/measure these properties?
CHEE 311 Lecture 15 2

Liquid Phase Properties from VLE Data
Suppose we conduct VLE experiments on our system of interest.
 At a given temperature, we vary the system pressure by changing the cell volume.
 Wait until equilibrium is established (usually hours)
 Measure the compositions of the liquid and vapour
CHEE 311 Lecture 15 3

Liquid Solution Fugacity from VLE Data
Our understanding of molecular dynamics does not permit us to predict non-ideal solution fugacities, f i l . We must measure them by experiment, often by studies of vapour-liquid equilibria.
Suppose we need liquid solution fugacity data for a binary mixture of A+B at P,T. At equilibrium, fˆ i l  fˆ i v
The vapour mixture fugacity for component i is given by, fˆ i v  i v y i
P
(11.52)
If we conduct VLE experiments at low pressure, but at the required temperature, we can use fˆ i v  y i
P by assuming that
 i v = 1.
CHEE 311 Lecture 15 4

Since our experimental measurements are taken at equilibrium, fˆ i l  fˆ i v
 y i
P
What we need is VLE data at various pressures (all relatively low)
Table 12.1
CHEE 311 Lecture 15 5

With a knowledge of the liquid solution fugacity, we can derive activity coefficients.
 i fˆ i l
Actual fugacity
 x i f i l
Ideal solution fugacity
Our low pressure vapour fugacity simplifies f i l to give:
 i
 y i
P x i f i l and if P is close to P i sat : f i l   i sat
P i sat exp 
 

V i l
( P

RT
P i sat
)

 


P i sat leaving us with
 i
 x i y i
P
P i sat
CHEE 311 Lecture 15 6

Our low pressure VLE data can now be processed to yield experimental activity coefficient data:
 i
 x i y i
P
P i sat
Table 12.2
CHEE 311 Lecture 15 7

CHEE 311 Lecture 15 8