Consider the experimental data for ethyl acetate (1) + cyclohexane (2) system at 293.15 K given in Table3.1 (Slavin and Abramzon, 1977). Please fit this system to the 2-parameter Margules equation and plot thePxy curve for the system (along with the experimental data and Raoult’s law predictions). Also, plot thenatural logarithm of activity coefficients and the excess molar Gibbs free energy (divided by RT) both onthe same curve.Table 3.1 – ethyl acetate (1) + cyclohexane (2) system at 293.15 KP [kPa] x 1 y 110.386 0 011.132 0.025 0.07511.666 0.05 0.14812.199 0.075 0.19712.959 0.144 0.28613.732 0.218 0.3513.919 0.274 0.3914.066 0.347 0.42514.132 0.406 0.44214.132 0.494 0.47614.052 0.575 0.50513.719 0.69 0.55612.946 0.787 0.61912.026 0.887 0.7310.986 0.948 0.849.786 1 12Hint: Follow the approach given in Example 11.4 in the textbook for “data reduction” using the 2-parameter Margules equation. The example also explains both the graphs you are required to generate forthis problem:a. Similar to the example worked out in class, find the experimental value of G E /RT using the generalequation based on Summability Relationship:b. …and determine the model values of G E /RT using the 2-parameter Margules Equation per se.c. However, unlike the single data point case seen in class, this is a data reduction problem with multipleexperimental data points to being with. Hence an objective function needs to be developed in Excelsuch that both (a) and (b) are simultaneously addressed to get the best fit for the parameters spanningacross your entire data range (except the two end points – pure component equivalence).d. Thus, write an objective function for each value of x 1 in the data above, except for the purecomponent end points (i.e. N=14, not 16 for your objective function), and minimize this function tofind both A 12 and A 21 simultaneously using Solver. Note that you are squaring the objective function toaid Excel in overcoming the negative iteration syndrome (square of negative minima = positive).e. Note that your objective function need not be minimized exactly to zero; anywhere close to zero (Eg.0.004) is sufficient.f. Once you have found the best fit values for A 12 and A 21 from your minimized objective function, therest of the procedure is straight forward. For the model values, use the following equations:g. Finally, plot the following graphs: (i) P-xy graph in terms of mole fraction of ethyl acetate, and (ii)ln(γ i ) v/s mole fraction of ethyl acetate and (G E /RT) v/s mole fraction of ethyl acetate, both on thesame graph. Plot both experimental data (as points) and the model (as lines); print in color to easilydifferentiate between the data clusters.33. You desire to flash 20 moles/min of a liquid mixture containing 20% by mole ch
Consider the experimental data for ethyl acetate (1) + cyclohexane (2) system at 293.15 K given in Table
3.1 (Slavin and Abramzon, 1977). Please fit this system to the 2-parameter Margules equation and plot the
Pxy curve for the system (along with the experimental data and Raoult’s law predictions). Also, plot the
natural logarithm of activity coefficients and the excess molar Gibbs free energy (divided by RT) both on
the same curve.
Table 3.1 – ethyl acetate (1) + cyclohexane (2) system at 293.15 K
P [kPa] x 1 y 1
10.386 0 0
11.132 0.025 0.075
11.666 0.05 0.148
12.199 0.075 0.197
12.959 0.144 0.286
13.732 0.218 0.35
13.919 0.274 0.39
14.066 0.347 0.425
14.132 0.406 0.442
14.132 0.494 0.476
14.052 0.575 0.505
13.719 0.69 0.556
12.946 0.787 0.619
12.026 0.887 0.73
10.986 0.948 0.84
9.786 1 1
2
Hint: Follow the approach given in Example 11.4 in the textbook for “data reduction” using the 2-
parameter Margules equation. The example also explains both the graphs you are required to generate for
this problem:
a. Similar to the example worked out in class, find the experimental value of G E /RT using the general
equation based on Summability Relationship:
b. …and determine the model values of G E /RT using the 2-parameter Margules Equation per se.
c. However, unlike the single data point case seen in class, this is a data reduction problem with multiple
experimental data points to being with. Hence an objective function needs to be developed in Excel
such that both (a) and (b) are simultaneously addressed to get the best fit for the parameters spanning
across your entire data range (except the two end points – pure component equivalence).
d. Thus, write an objective function for each value of x 1 in the data above, except for the pure
component end points (i.e. N=14, not 16 for your objective function), and minimize this function to
find both A 12 and A 21 simultaneously using Solver. Note that you are squaring the objective function to
aid Excel in overcoming the negative iteration syndrome (square of negative minima = positive).
e. Note that your objective function need not be minimized exactly to zero; anywhere close to zero (Eg.
0.004) is sufficient.
f. Once you have found the best fit values for A 12 and A 21 from your minimized objective function, the
rest of the procedure is straight forward. For the model values, use the following equations:
g. Finally, plot the following graphs: (i) P-xy graph in terms of mole fraction of ethyl acetate, and (ii)
ln(γ i ) v/s mole fraction of ethyl acetate and (G E /RT) v/s mole fraction of ethyl acetate, both on the
same graph. Plot both experimental data (as points) and the model (as lines); print in color to easily
differentiate between the data clusters.
3
3. You desire to flash 20 moles/min of a liquid mixture containing 20% by mole ch
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