# 11.09 - Fitting Activity Coefficients to Multiple Data

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### Fitting Activity Models to Multiple Data Points (6:40)

Fitting Activity Models to Multiple Data Points (6:40) (msu.edu)

In early sections of chapter 11, we discussed fitting a single point. This technique is good pedagogically, but using a single point can lead to spurious results. Fitting of multiple data is preferred. Various options are discussed, as well as the bubble line method used in the textbook.

### Fitting Pxy data using Excel (9:00) (msu.edu)

Fitting Pxy data using Excel (9:00) (msu.edu)

An illustration of using Excel for fitting Pxy data of the IPA+water system using the M2 model and some suggestions for working with the GammaFit.xls file, showing that the sum of squared deviations is 14 mmHg^2. Dividing by the number of points (18 including x1=0 and x1=1), and taking the square root gives a root mean square deviation (rmsd) of 0.89 mmHg. Noting that the pressure ranges from roughly 30-60 mmHg, this corresponds to roughly 2%rmsd. This effectively corresponds to sample validation of the M2 model for the IPA+water system since the deviation of 2% is quite small. We could argue that a model is valid as long as the rmsd is less than 10%, but you need to report the %rmsd and show the plot in order to be clear. For example, if the plot shows that there is systematic deviation from the experimental data, then a better model probably exists and should be sought. If there is no systematic deviation and the data are simply very scattered, then the model is probably as good as can be expected.

Comprehension Questions:

1. If experimental data for vapor pressures are included for a particular data set, should you use the values from the data set or the values calculated from Antoine's equation?
2. What is the objective function applied by the GammaFit spreadsheet?
3. Apply the procedure illustrated here optimize the M2 model for the ethanol+benzene data given in HW 10.2. What values do you obtain for A12 and A21 in that case? What is the value of the rmsd that you obtain?
4. Explain how you would modify this spreadsheet to apply to the M1 model.
5. Explain how you would modify this spreadsheet to apply to data obtained at constant pressure instead of constant temperature.