1988 Volume 29 Issue 10 Pages 798-804
A novel integration of the Gibbs-Duhem equation has been presented for quaternary solutions containing two volatile components. The new integration formulae relate to calculation of the activities of nonvolatile third and fourth components from the measured activities of volatile first and second components. These formulae are more complex than the conventional ternary or quaternary integrations for solutions consisting of all nonvolatile (or only one volatile) components with constant concentration ratios, in that it contains an additional third term and it also involves integration of a product of two partial derivatives. The present formulae are essential to activity calculations for S-bearing slags or oxygen-containing sulfides, among others. An application of the new formulae has been demonstrated for the S–O–Fe–Cu system mattes by calculating the activities of iron and copper from the observed partial pressures of sulfur and oxygen.
