## Derivation of an infinite-dilution activity coefficient model and application to two-component vapor-liquid equilibria data

##### Author

Roper, Vaughan Phillip

##### Date

1988##### Advisor

Kobayashi, Riki

##### Degree

Doctor of Philosophy

##### Abstract

Infinite-dilution fugacity coefficients were obtained for the binary system fluorene/phenanthrene at thirteen temperatures by fitting total pressure across the entire mole fraction range by a computer routine. A thermodynamically consistent routine, that allowed for both positive and negative pressure derivations from the ideal values, was used to correlate data over the full mole fraction range from 0 to 1. The four-suffix Margules activity coefficient model without modification essentially served this purpose since total pressures and total pressure derivatives with respect to mole fraction were negligible compared to pressure measurement precision.
The water/ethanol system studied by Kolbe and Gmehling and binary systems studied by Maher, Srivastava and Smith comprised of aniline, chlorobenzene, acetonitrile and other polar compounds were fit for total pressure across the entire mole fraction range for binary Vapor-Liquid-Equilibria (VLE) using the rigorous, thermodynamically consistent expression derived by Ibl and Dodge from the Gibbs-Duhen Relation. Data correlation was performed using a computer least squares procedure. Infinite-dilution fugacity coefficients were obtained using a modified Margules activity coefficient model which gives residual values of x$\sb1$ dly$\gamma\sb1$ + x$\sb2$ dln$\gamma\sb2$ across the mole fraction range that lie between the value of vd$\Pi$/dx$\sb1$/RT at x$\sb1$ = 0 and x$\sb1$ = 1. x$\sb1$ and $\gamma\sb1$ and x$\sb2$ and $\gamma\sb2$ are the mole fraction and activity coefficient of components 1 and 2 respectively. v is the mixture liquid molar volume, $\Pi$ is total pressure, R is the ideal gas constant, and T is temperature in absolute units.
This correlational procedure, a modified Margules model, yielded infinite-dilution fugacity coefficients differing from the non-rigorous Margules model (derived for a binary at constant pressure) by a few percent but in some cases by as much as ten percent. The modified version is necessary in fitting binary total pressure versus mole fraction data to an expression totally consistent with Gibb's Phase Rule. Its application implies that the derivative of pressure with respect to mole fraction may affect the values of activity coefficients determined, especially at either infinite-dilution axis where the absolute value of this derivative is greatest.

##### Keyword

Chemical engineering