CHEE 311 Lecture 15 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 terms this can be written as

• 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)

Liquid Phase Properties from VLE Data SVNA 12.1

0.1ˆ i

CHEE 311 Lecture 15 2

7. Liquid Phase Properties from VLE Data SVNA 12.1

The mixture fugacity of a component in non-ideal liquid solution is defined by:

(11.46)

We also define the activity coefficient:

(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:

How do we calculate/measure these properties?

lii

li f̂lnRT)T()P,T(

lii

li

i fx

f̂

liiii

li fxlnRT)T()P,T(

CHEE 311 Lecture 15 3

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 4

Liquid Solution Fugacity from VLE Data

Our understanding of molecular dynamics does not permit us to predict non-ideal solution fugacities, fi

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,

The vapour mixture fugacity for component i is given by,(11.52)

If we conduct VLE experiments at low pressure, but at the required temperature, we can use

by assuming that iv = 1.

Pyˆf̂ ivi

vi

Pyf̂ ivi

vi

li f̂f̂

CHEE 311 Lecture 15 5

Liquid Solution Fugacity from Low P VLE Data

Since our experimental measurements are taken at equilibrium,

What we need is VLE data at various pressures (all relatively low)

Py

f̂f̂

i

vi

li

Table 12.1

CHEE 311 Lecture 15 6

Activity Coefficients from Low P VLE Data

With a knowledge of the liquid solution fugacity, we can derive activity coefficients. Actual fugacity

Ideal solution fugacityOur low pressure vapour fugacity simplifies fi

l to give:

and if P is close to Pisat:

leaving us with

sati

sati

lsati

sati

li

P

RT

)PP(VexpPf

i

lii

li

i fx

f̂

lii

ii fx

Py

satii

ii Px

Py

CHEE 311 Lecture 15 7

Activity Coefficients from Low P VLE Data

Our low pressure VLE data can now be processed to yield experimental activity coefficient data:

satii

ii Px

Py

Table 12.2

CHEE 311 Lecture 15 8

Activity Coefficients from Low P VLE Data