Wilson parameters

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

A number of workers have observed that the strength of binding of monovalent counterions depends on ionic radius. However, the effect of ionic radius is somewhat obscure as it depends on hydration phenomena and whether the size of the bare ion or that of the hydrated ion is the significant parameter (Wilson Crisp, 1977). 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

According to the local composition (LC) concept, the composition in the vicinity of any molecule differs from the overall composition. If a binary mixture is composed of components 1 and 2 with mole fractions Vi andv2, respectively, four LCs should be considered the local mole fractions of components 1 and 2 near a central molecule 1 x and X2 ) and the local mole fractions of components 1 and 2 near a central molecule 2 (xn and V22). Many attempts have been made to express LC in terms of bulk compositions and intermolecular interaction parameters (Wilson, 1964 Renon Prausnitz, 1968 Panayiotou Vera, 1980, 1981 Lee, Sandler, Patel, 1986 Aranovich Donohue, 1996 Wu, Cui, Donohue, 1998 Ruckenstein Shulgin, 1999). In the calculations that follow, the Aranovich and Donohue (1996) expressions will be employed, because they have a theoretical basis. These expressions are... 

The effectiveness of Wilson s model lies in the fact that only two parameters are required to describe the Gibbs energy at a given temperature. Its weakness lies in the fact that there is no clear molecular interpretation of these parameters. Wilson s approach works for a great variety of systems but when the departures from ideality are complex, more detailed models are required. Some extensions of Wilson s work have been discussed by Renon and Prausnitz [8] but they require introduction of more adjustable parameters. 

P5.10 Calculate the activity coefficients in the system methanol (l)-toluene (2) from the data measured by Ocon et cd. [71] at atmospheric pressure assuming ideal vapor phase behavior. Try to fit the untypical behavior of the activity coefficients of methanol as function of composition using temperature independent g -model parameters (Wilson, NRTL, UNIQUAC). Explain why the activity coefficients of methanol show a maximum at high toluene concentration. 

The expression is very useful in cases where only limited data are available. An interesting such application is the case where only one infinite dilution activity coefficient for a binary system - obtained usually through gas-liquid chromatography (GLC) - is available. A combination of such GLC measurements and the single-parameter Wilson equation in predicting the solubility of SO2 as a function of its partial pressure in several solvents is demonstrated by Bogeatzes(1973). 

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