# Example 3-14: Draw the isothermal phase diagram of the binary mixture of hexane + benzene with the Flory-Huggins activity coefficient model

The Flory-Huggins method is rather convenient as it is fully predictive (no binary interaction parameter to fit) and rather simple to use. It describes both enthalpic non-ideal behaviour, through the regular solution expression, and entropic deviations using the Flory term. It is not very precise, but provides a good indication regarding trends. In the example proposed here, it is applied to the binary system n-hexane (1) + benzene (2)

## Analysis:

The Flory-Hugging activity coefficient model requires two pure component parameters for each component: the molar volume in the liquid phase and the solubility parameter. The molar volume can be calculated from the molar density which should be explained using DIPPR correlation (often, the value at 25°C is used, but this may be an improvement):

The calculation of the phase behaviour also requires to know the vapour pressure behaviour. In this work, the DIPPR correlation is used:

For both components, all of the parameters are found in the DIPPR database:

Table 1: Parameters extracted from the DIPPR database (Molar density)
DIPPR Density Coef. (Pa)
A B C D
n-hexane 0.70824 0.26411 507.6 0.27537
Benzene 1.0259 0.26666 562.05 0.28394
Table 2: Parameters extracted from the DIPPR database (Vapour pressure and Solubility parameters)
Solub param DIPPR Psat Coef. (Pa)
(Pa^1/2) A B C D E
n-hexane 1487 104.65 -6995.5 -12.702 1.2381E-05 2
Benzene 1874 83.107 -6486.2 -9.2194 6.9844E-06 2

## Solution:

### See complete results in file (xls):

Some help on nomenclature and tips to use this file can be found here.

All calculations are available in the “FloryHuggins” sheet. The calculations are performed as follows:

• the activity coefficient are calculated as a function of the liquid phase molar fractions (columns G to J in the excel sheet)
• The partial pressures (columns E and F) are then easily calculated
• The total pressure is the sum of the partial pressures (column D).
• From the partial pressure and the total pressure, the vapour phase molar fractions are found (column B)

In a last sheet, called “Data”, some experimental data have been collected. Figure 1 shows the good agreement between these data and the prediction of the model.