Predicting VLE from Infinite-Dilution Activity Coefficients Determined from Ebulliometry

A recent ebulliometric study of n-pentane–propionaldehyde at 40°C has found that $\gamma_{1}^{\infty}=3.848$ and $\gamma_{2}^{\infty}=3.979$ . Use this information to prepare the P-x -y diagram for this system at 40°C.

Question

Predicting VLE from Infinite-Dilution Activity Coefficients Determined from Ebulliometry

A recent ebulliometric study of n-pentane–propionaldehyde at 40°C has found that [latex]\gamma_{1}^{\infty}=3.848[/latex] and [latex]\gamma_{2}^{\infty}=3.979[/latex]. Use this information to prepare the P-x -y diagram for this system at 40°C.

Accepted Answer

The van Laar activity coefficient model will be used. From Eqs. 10.2-19, we have

[latex]\ln \gamma_{1}^{\infty}=\alpha \quad ext { and } \quad \ln \gamma_{2}^{\infty}=\beta[/latex] (10.2-19)

[latex]\alpha=\ln \gamma_{1}^{\infty}=\ln (3.848)=1.3476 \quad ext { and } \quad \beta=\ln \gamma_{2}^{\infty}=\ln (3.979)=1.3810[/latex]

These values are in reasonable agreement with, but slightly different from, those found in the previous illustration. Using the values for the van Laar parameters, we obtain the y and P values in Table 10.2-3. Clearly, the agreement is excellent.

Table 10.2-3 Comparison of Measured Pressures and Vapor-Phase Mole Fractions for the n-Pentane–Propionaldehyde System at 40°C with Values Calculated Using [latex]\gamma^{\infty}[/latex] Data
[latex]x_{1}[/latex]	[latex]y_{1}^{\exp }[/latex]	[latex]y_{1}^{calc }[/latex]	[latex]y_{1}^{\exp }[/latex]	[latex]y_{1}^{calc }[/latex]
0	0	0	0.7609	0.7609
0.0503	0.2121	0.2131	0.9398	0.9312
0.1014	0.3452	0.3352	1.0643	1.0555
0.1647	0.4288	0.4267	1.1622	1.1618
0.2212	0.4685	0.4798	1.2173	1.2257
0.3019	0.5281	0.5307	1.2756	1.2846
0.3476	0.5539	0.552	1.2949	1.3067
0.4082	0.5686	0.5752	1.3197	1.3208
0.4463	0.5877	0.5879	1.3354	1.3379
0.5031	0.6416	0.6056	1.3494	1.349
0.561	0.6311	0.6232	1.3568	1.3566
0.6812	0.6827	0.6652	1.3636	1.3604
0.7597	0.7293	0.7028	1.3567	1.35
0.8333	0.7669	0.7528	1.3353	1.3244
0.9180	0.8452	0.8432	1.2814	1.264
1.0	1.0	1.0	1.1541	1.1541

[The folder Aspen Illustrations>Chapter 10.2>10.2-6 on theWiley website for this book contains the Aspen Plus R[latex]^R[/latex] files for correlating the experimental data (given in this illustration) using the NRTL and UNIQUAC models. The results of each of thesemodels are given in appropriatelynamed Excel (.xlsx) files.]

Question 10.2.6: Predicting VLE from Infinite-Dilution Activity Coefficients ...

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