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:  i l ( 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:  i l ( 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

fˆ i v  i v y i P is given by, (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

Liquid Solution Fugacity from Low P VLE Data

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

Activity Coefficients from Low P VLE Data

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

Activity Coefficients from Low P VLE Data

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

Activity Coefficients from Low P VLE Data

CHEE 311 Lecture 15 8