CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be...
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Transcript of CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be...
![Page 1: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/1.jpg)
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
![Page 2: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/2.jpg)
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(
![Page 3: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/3.jpg)
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
![Page 4: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/4.jpg)
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
![Page 5: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/5.jpg)
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
![Page 6: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/6.jpg)
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
![Page 7: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/7.jpg)
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
![Page 8: CHEE 311Lecture 151 Purpose of this lecture: To illustrate how activity coefficients can be calculated from experimental VLE data obtained at low pressures.](https://reader036.fdocuments.net/reader036/viewer/2022072008/56649d755503460f94a56181/html5/thumbnails/8.jpg)
CHEE 311 Lecture 15 8
Activity Coefficients from Low P VLE Data