Thermodynamic Considerations of Infinite Dilute Solutions of Metal-Oxygen Liquid Binary Systems Based on Associated Solution Model

Abstract

Equations (\ efe1) and (\ efe2) have been derived by applying an ideal associated solution model assuming associated compounds, M_pO(a), for the analysis of the thermodynamics of oxygen dissolution into liquid metals, 1/2O₂(g)→O(at%).
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\ oindentStandard free energies, ΔG_MpO^°(a), enthalpies, ΔH_MpO^°(a), and entropies, ΔS_MpO^°(a), of formation of the associated compounds, M_pO(a), have been calculated from eq. (\ efe1) and (\ efe2) using the published values of ΔH_sol^° and ΔS_sol^° of the reaction, 1/2O₂(g)→O(at%). Variations of the standard enthalpies and entropies of formation of M_pO with the atomic number of constituent metal, M, are analogous in the solid, liquid (associated compounds), and gaseous states. Linear relations are found in the following combinations of the quantities; ΔH_MpO^°(s) vs ΔH_MpO^°(a), ΔH_MpO^°(a) vs ΔH_MpO^°(g), ΔH_MpO^°(s) vs ΔH_MpO^°(g), ΔS_MpO^°(s) vs ΔS_MpO^°(a), ΔS_MpO^°(a) vs ΔS_MpO^°(g), and ΔS_MpO^°(s) vs ΔS_MpO^°(g). Except for the relation of ΔS_MpO^°(s) and ΔS_MpO^°(a), this linear relation is sub-divided into two different lines; one of which consists of transition metal oxides and the other of non-transition metal oxides. Standard enthalpies, ΔH_M^° and ΔH_B^°, of M_pO(a) of melting and boiling are proportional to the melting and boiling temperatures T_M and T_B, respectively, and the relation between ΔH_B^° and T_B^° agrees with Trouton’s rule. If the associated solution is not ideal, the following equations hold.
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\ oindentIn this case the thermodynamic values, ΔH_MpO^\invdiameter(a) and ΔS_MpO^\invdiameter(a), of the infinite dilute associated compounds M_pO(a) in liquid metal, not pure M_pO(a), are calculated from eqs. (\ efe3) and (\ efe4). It is to be noted that all the results based on eqs. (\ efe1) and (\ efe2) are also effective when ΔH_MpO^°(a) and ΔS_MpO^°(a) are replaced by ΔH_MpO^\invdiameter(a) and ΔS_MpO^\invdiameter(a).