A discussion of Margules-type formulations for multicomponent solutions with a generalized approach
- Southern Methodist Univ., Dallas, TX (United States)
The generalized mathematical method for obtaining Margules-type formulations for the excess free energy of solution, G[sup xs], or any other excess molar thermochemical property, and RT 1n ([gamma][sub i]), or the corresponding partial molar quantity in multicomponent solutions, is presented in this paper. For the n-component system, the G[sup xs] function is approximated by a pth-order Taylor series involving (n [minus] 1) independent compositional variables. The expression for G[sup xs] is differentiated with respect to each compositional variable, and the resultant partial derivatives are evaluated at each of the compositional extremes to obtain the Margules parameters (activity coefficients at infinite dilution) replacing the constants in the Taylor series which have no thermodynamic meaning. When p = 2, the solutions are symmetric (strictly regular) and no ternary and higher order interaction parameters exist in ternary and higher order systems. For p = 3, the solutions are asymmetric (subregular) and no quaternary and higher order parameters exist in quaternary and higher order systems. As a special case of the latter system (p = 3) the constituent binaries can exhibit symmetric behavior, but the expressions for G[sup xs] and RT 1n ([gamma][sub i]) can contain ternary interaction parameters. Thus, the existence of nonbinary interaction parameters is a result of the complexity of the Taylor series approximation to the G[sup xs] function. In general, ternary interaction parameters cannot be completely defined by the binary interaction parameters. Simple expressions for the excess function and the activity coefficients in symmetric and asymmetric multicomponent solutions have been derived. Previously published binary, ternary, and quaternary symmetric and asymmetric solution models are discussed and compared to the solution models derived herein. 17 refs., 2 tabs.
- DOE Contract Number:
- FG05-90ER61015
- OSTI ID:
- 6716516
- Journal Information:
- Geochimica et Cosmochimica Acta; (United States), Vol. 57:2; ISSN 0016-7037
- Country of Publication:
- United States
- Language:
- English
Similar Records
Three-phase liquid-liquid-vapor behavior in multicomponent liquefied natural gas mixtures
Formation of pigeonite on the join hedenbergite-ferrosilite at 11. 5 and 15 kbar: experiments and a solution model