1. Solution Thermodynamics: Applications
Chapter 12-Part II

2. Example of data reduction
The following is a set of VLE data for the system methanol(1)/water(2) at K
P/kPa x1 y1
19.953
60.614
0.5282
0.8085
39.223
0.1686
0.5714
63.998
0.6044
0.8383
42.984
0.2167
0.6268
67.924
0.6804
0.8733
48.852
0.3039
0.6943
70.229
0.7255
0.8922
52.784
0.3681
0.7345
72.832
0.7776
0.9141
56.652
0.4461
0.7742
84.562 1

3. Find parameter values for the Margules equation that give the best fit of GE/RT to
the data, and prepare a P x y diagram that compares the experimental points with
curves determined from the correlation
1) Calculate EXPERIMENTAL values of activity coefficients g1 and g2 and GE

4. We have shown that:

5. Now we have our analytical model
Lets calculate ln g1, ln g2, GE/x1x2RT, and:

6. RMS= SQRT (S (Pi-Picalc)2/n = 0.398 kPa

7. Thermodynamic consistency
We need to check that the experimentally obtained activity coefficients satisfy the Gibbs-Duhem equation.
If the experimental data are inconsistent with the G-D equation, they are not correct

8. Consistency test

9. Consistency test

11. Solid lines are the result of data reduction adjusting GE/RT

12. The experimental data is not thermodynamically consistent
Avg values within +0.1 and -0.1
are acceptable
The experimental data is not thermodynamically consistent

13. An alternative objective function: Barker’s method
Fit the model GE/RT to make the calculated pressures the closest possible to the experimental data.
For example, obtain A12 and A21 for the Margules equation to minimize the calculated pressures with respect to the experimental values. (see dashed lines in Figure 12.7)

14. example
Using Barker’s method, find parameters for the Margules eqn that provide the best fit of GE/RT to the data, and prepare a Pxy diagram that compares the experimental points with curves determined form the correlation.

15. solution Minimize the sum of squares of the following function:
Starting with A12=0.5, A21=1, get A12= 0.758, A21=0.435

16. Calculate the RMS for P
RMS= SQRT (S (Pi-Picalc)2/n = kPa