Determination of Internally Consistent Thermodynamic Data from Phase Equilibrium Experiments

Abstract

A technique has been devised for evaluating the internal consistency of experimental data in any particular chemical system. The sequence of steps is: (1) Each experimental point is expressed as an inequality in terms of the free energy change of the reaction to which it applies. For example, in a solid-solid reaction, the sum $${\Delta}G_{R}^{\circ} - (T - 298) {\Delta}S_{R}^{\circ} + (p - 1){\Delta}V_{R}^{\circ}$$ is greater than zero if the reactants are stable, or less than zero if the products are stable. (2) Linear relationships between the standard state free energies and entropies of different reactions are expressed as linear equations. (3) The resulting system of inequalities and equations is solved by the techniques of linear programming, maximizing and minimizing the standard state free energy and entropy of each reaction in turn. (4) If the experimental data are internally consistent, the limits of each of the thermochemical constants for each reaction are obtained. If the experiments are inconsistent, the offending experiments may be identified. Application of the technique to the results of experimental investigations of 18 reactions in the system CaO-Al₂O₃-SiO₂-H₂O-CO₂ indicates that the data tested are all consistent. The procedure may be extended to determine thermodynamic properties of individual phases.