Analysis of activity data in three component systems by means of an augmented Redlich–Kister formalism

Abstract

In a three component system, the activity coefficient (and other thermodynamic properties) of each species can be expressed as a Redlich–Kister expansion in the sum of the other two mole fractions, T=X_j+X_k: log γ_i=T²[A_i+B_i(–3 + 4T)+C_i(–5 + 6T)(–1 + 2T)+D_i(–7 + 8T)(–1 + 2T²)+…]. The coefficients in this equation are functions of S defined as X_j/(X_j+X_k), the Redlich–Kister coefficients for the three binary subsystems, and an additional set of parameters describing interactions of all three components at once (B^a₃, C^a₃, C^b₃, etc.).

Typical equations for the calculation of the coefficients A_i, B_i, etc., were derived and were programmed for computer calculation. By transforming the parameter matrix, the activity coefficients and activities can be calculated and printed for each of the three components.

The terms required beyond those for the binary systems, B^a₃, etc., correspond to equations for the excess quantities of mixing of the form: Y^e=N₃X₁X₂X₃T^n–2(–1 + 2S)^i–1. An alternative form with orthogonal functions is considered briefly. Parameters are shown for three component systems, and calculations of phase equilibria are outlined and compared to the original experimental data for the solid and liquid phases in the iron+nickel+carbon system.

As an example of the use of a large quantity of data for a ternary system to determine the parameters in the equations, the system benzene+carbon tetrachloride+acetonitrile is analysed.