Solution Thermodynamics: Applications Chapter 12-Part II

Example of data reduction The following is a set of VLE data for the system methanol(1)/water(2) at 333.15K 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

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

We have shown that:

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

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

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

Consistency test

Consistency test

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

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

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)

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.

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

Calculate the RMS for P RMS= SQRT (S (Pi-Picalc)2/n = 0.167 kPa