Showing papers on "Gibbs–Duhem equation published in 1999"

On the necessity of using activities in the gibbs equation

Abstract: We show that using mole fractions xs instead of activities as in the Gibbs equation for analyzing surface tension curves for onset of amphiphilic association may be open for discussion. First, we determined the activity coefficients for the simple binary water−ethanol and water−n-propanol systems from vapor pressure measurements. The activity coefficients are neither unity nor are they constant in the range where the surface tensions σ of the binary systems decrease from the water value down to the value of the pure alcohols. Second, a break in the σ vs ln xs curves disappears when proper σ vs ln as curves are constructed. The implication for determining critical micelle concentrations and headgroup areas of surfactants from surface tension curves is addressed.

Thermodynamic Constraints to Describe Gibbs Energies for Binary Alloys

Abstract: Thermodynamic constraints are introduced to describe Gibbs energies for a CALPHAd-type calculation; available data on the pure elements and phase diagram data were used to optimize relevant parameters. Constraints can be applied to the mathematical description of Gibbs energies for three regions of phase diagrams: those with complete miscibility, those with an intermetallic compound, and those with a miscibility gap. The authors examine the present thermodynamic constraints in construction of Gibbs energies for the Ag-Pd, Mg-Sn, and Au-Ni binary systems as typical examples for these cases. The optimization procedure for obtaining parameters for models of the Gibbs energies is divided mainly into four steps to reach the final parameters, and the results obtained in each step are compared in detail. The authors also present assessed parameters for the Gibbs energies concerning these three binary systems by the available thermodynamic data in addition to the phase diagram data with the present thermodynamic constraints.

Use of Linear Free Energy Relationship to Predict Gibbs Free Energies of Formation of MUO4 Phases

Abstract: In this paper, the Sveijensky-Molling equation derived from a linear free energy relationship is used to calculate the Gibbs free energies of formation of MU0 4 , MW0 4 , and MMo0 4 phases from the known thermodynamic properties of the corresponding aqueous divalent cations (M). The Sveijensky-Molling equation is expressed as AG°f.MvX = AMVX AG°„.M + bMwX + /?Μϊχ rM2+, where the coefficients aMvX, bMwX, and /?MvX characterize a particular structural family of MVX, rM2* is the ionic radius of M + cation, AG°F, MvX is the standard Gibbs free energy of formation of MVX, and AG°n. „2· is the standard non-solvation energy of cation M + . The coefficients for the family of a -M 2 + U0 4 phases are: oMvX = 1.0552, bMwX = —510.40 (kcal/mole), and /?MVX = 73.0 (kcal/mole · A). This relationship can be used to predict the Gibbs free energies of formation of various phases of MU0 4 , MW0 4 , MMO04.

Chemical potential of a binary solution

Abstract: The chemical potential of a binary solution is calculated using the Gibbs free energy method. With the aid of certain assumptions on the microscopic structure of the solution, the well-known expression is derived for a simple solution. It is shown that the empirical interaction parameter is expressed in terms of the change in enthalpy and entropy accompanying the exchange of atoms between the pure components.