Phase Equilibria of a Pb–Sb–Ag Alloy during Vacuum Distillation

Abstract

The saturated vapor pressures of lead, silver, and antimony are calculated for Pb–Ag and Pb–Sb alloys at temperatures of 1073–1773 and 823–1073 K, respectively. High ratios (p_Sb*/p_Pb*) × 10³ = 15.0–1.8 and p_Pb*/p_Ag* = 2.9 × 10³–74.0 create theoretical possibilities for sequential selective separation of these metals by vacuum distillation, during which the vapor is enriched in antimony and then lead and the liquid is enriched in silver. For vapor–liquid equilibrium (VLE) diagram, the lever rule (the rule of line segments) can be used to predict the amounts of substance, residue, and sublimate at a given temperature. Calculations of the ternary-alloy parameters can be performed by the Wilson equation using parameters obtained for the binary systems. The fractional Gibbs free energy (–ΔG_Pb/Sb/Ag = (2.1–22.4)/(1.9–25.5)/(18.1–50.0)), the enthalpy (ΔH_Pb/Sb/Ag = ±(0.2–16.9)/–(0.2–1.8)/(105–140) J/(K mol)), and the entropy (ΔS_Pb/Sb/Ag = (2.4–13.4)/(2.2–15.2)/(20.8–30.0) J/(K mol)) of the components of the Pb–Sb–Ag melts are calculated. As the fractions of metals in a starting alloy increase, the thermodynamic parameters decrease. The negative and positive values of the enthalpy indicate exothermic and endothermic processes in the melt during distillation of components, respectively. The calculated and experimental thermodynamic parameters are shown to agree satisfactorily: the standard relative deviation is 1.9% and the root-mean square deviation is 0.1 kJ/mol.