1. Solution Thermodynamics: Applications
Chapter 12-Part III

3. Other models for GE/RT

4. Obtain activity coefficients from the one-parameter Margules equation

5. problem
For methanol(1)/methyl acetate(2), the 1-parameter Margules equation gives a reasonable prediction of the activity coefficients, with A = T.
Vapor pressures as functions of T are known. T are in Kelvin.
a) Calculate P and {yi} for T = K and x1 =0.25

6. Calculate P and {yi} given T = 318.15K and x1 =0.25
VLE, BUBL P calculation
For i =1, 2
Calculate g1 and g2 at T and x1 =0.25 using Margules 1-parameter
A(T) = 1.107
g1 = 1.864
g2 = 1.072
and calculate P = 73.5 kPa and y1 = 0.282

7. Calculate P and {xi} given T = 318.15K and y1 =0.60
VLE, DEW P calculation
P1sat, P2sat, and A are the same as in the first part
But, we don’t know xi, and g1, g2 are functions of x1, x2
For good initial guesses, solve the problem with Raoult’s law 1)
Solution:
P = kPa
x1 = 0.817
g1 = 1.038
g2 = 2.094
Evaluate g1, g2, and return to 1)
until P converges

8. Calculate T and {yi} given P = 101.33 kPa and x1 =0.85
VLE, BUBL T calculation
To obtain an initial T, get the saturation temperatures of both components (from Antoine)
T1sat = ; T2sat = K
Use a mole-fraction weighted average of these values to get T
For that T calculate A, g1, g2 and a =P1sat/P2sat
(1)
Then calculate
Get T from Antoine
and return to (1)
Once T converges,
calculate y1

9. Calculate T and {xi} given P = 101.33 kPa and y1 =0.40
VLE, DEW T calculation
Same P as in BUBLT calculation, saturation temperatures are the same, get weighted
mole fraction average for initial T = K
Since we don’t know {xi} use Raoult’s law to initialize {gi}
(1) At the initial T, evaluate A, P1sat, P2sat, a
Calculate x1 = y1P/g1 P1sat
Calculate g1, g2
New value of T from Antoine
and return to (1)
Once T converges,
calculate x1

10. Find the azeotropic pressure and the azeotropic composition for T = 318.15 K
Define the relative volatility
How much is a12 at the azeotrope?
Get a12 from the VLE equations

11. From the one-parameter Margules equation
Calculate these values from the data at T = K
This means that a12 is =1 at some point
between x1 = 0 and x1 = 1

12. Double azeotrope

13. At the azeotrope, a12 = 1

14. The Van-Laar equation