Category: Van Der Waals Activity Models

12.1. The compositions of coexisting phases of ethanol(1) + toluene(2) at 55°C are x1 = 0.7186, and y1 = 0.7431 at P = 307.81 mmHg, as reported by Kretschmer and Wiebe, 1949. J. Amer. Chem. Soc., 71:1793. Estimate the bubble pressure at 55°C and x1 = 0.1, using a. The Scatchard-Hildebrand model with k12 = 0 b. The SSCED model with a default value of k12 c. The SSCED model with k12 matched…

P12.1. Acrolein + water exhibits an atmospheric (1 bar) azeotrope at 97.4 wt% acrolein and 52.4°C. a. Determine the values of Aij for the van Laar equation that match this bubble-point pressure at the same liquid and vapor compositions and temperature. (ANS. 2.97, 2.21) (You may use the shortcut vapor pressure equation for acrolein: Tc = 506 K; Pc = 51.6 bar; and…

This has been a somewhat theoretical chapter. We have gone through iterations of observation, prediction, testing, and evaluation with several theories (e.g., van Laar, Scatchard-Hildebrand, Flory-Huggins, SSCED, and MOSCED). With each iteration, we have achieved increasing precision and insight. Sulfuric acid and water may react very favorably toward each other (GE << 0), while 2-propanol and…

We have shown that the contribution to the excess internal energy in the Flory-Huggins theory is identical to that in the Scatchard-Hildebrand theory. We derived the Scatchard-Hildebrand theory from the excess internal energy function of the van der Waals equation on page 468 and 12.3 on page 471. Therefore, any potential difference between the Flory-Huggins theory and the van der…

Most systems encountered in chemical processes and formulations are multicomponent. If the application requires bypassing an azeotrope, a third component (called an entrainer) might be added. If a biomembrane is to be penetrated by a pharmaceutical treatment, the formulation must at least account for water, the pharmaceutical, the biomembrane, and any additive. The output of a…

The Scatchard-Hildebrand theory provides reasonable results for hydrocarbon mixtures, but the results can be highly unreliable if one of the components hydrogen bonds, especially if one of the components is water. The MOSCED, SSCED, and HSP models remedy this problem by accounting for hydrogen bonding as a separate contribution to the solubility parameter. MOSCED (pronounced…

In deriving the entropy of mixing ideal gases in Eqn. 4.8 on page 138, we applied the notion that ideal gases are point masses and have no volume. We considered the entropy of mixing to be determined by the total volume of the mixture. When we consider the entropy of mixing liquids, however, we realize that the volume…

Returning to Eqn. 12.10, G. Scatchard in Europe and Joel H. Hildebrand in the United States both made similar adjustments to match the van der Waals equation to experiment and provide a model capable of predictions for nonpolar fluids. They made an assumption that is equivalent to assuming k12 = 0 in Eqn. 12.4. Setting , and collecting terms, J.H.…

Johannes van Laar found that the parameters from the van der Waals equation of state were not accurate in predicting excess energy of mixing, and empirical fitting was required. He simplified the equation for the excess internal energy by arbitrarily defining a single symbol, “Q,” to represent the final term in the equation: J. van…

Empirical models like the Redlich-Kister expansion provide a significant improvement over the ideal solution approximation, but they lack the kind of connection with the molecular perspective that we have developed in Chapters 1 and 7. The empirical models of Chapter 11 are useful for determining the activity coefficients from a given expression for GE, but they suggest little about the form…