**A. A. Korolev, S. A. Krayukhin, G. I. Maltsev**

**ABSTRACT:**

In the processing of lead is formed of silver foam (*SF*), which requires complex processing, with commercial production of single products. One of the possible ways of *SF *recovery is vacuum distillation, which is considered one of the most effective and environmentally friendly methods for the separation and purification, processing and refining of various metals. To preselect the temperature and pressure of the system, evaluate the effectiveness of component separation in a vacuum distillation using phase diagrams. The aim of this work consists of calculating the equilibrium “gas–liquid” *VLE *(vapor liquid equilibrium), including 449 Фазовые равновесия для Pb–Zn–Аg сплава the dependence of phase composition on temperature (*T–x*) at a given pressure for binary alloys of Pb–Ag and Pb–Zn in the vacuum distillation based on the model *MIVM *(мolecular interaction volume model); in the prediction parameters of the ternary alloy Pb–Zn–Ag on the basis of the equation of Wilson. In the temperature range 1073–1773 K for Pb–Ag alloy and *T *= 873–1573 *K *for Pb–Zn alloy calculated vapor pressure for Zn (1.55 ⋅ 10^{3}–1.76 ⋅ 10^{6}), Pb (1.5 ⋅ 10^{–1}–4.86 ⋅ 10^{2}) and Ag (5.1 ⋅ 10^{–5}–6.6). High values of the ratio (*P*^{*}_{Zn}/*P*^{*}_{Pb} ) ⋅ 10^{4} = 1.71–123.2 and *P*^{*}_{Pb/}*P*_{*Ag}= 2.9 ⋅ 10^{3}–74.0 create a theoretical background for sequential selective separation of these metals by vacuum distillation, when the zinc, and then lead are enriched in the gas phase, and silver in liquid. For phase diagrams *VLE *can be used by the lever rule (rule lines) to help predict quantities of substances, residues and sublimates at a predetermined temperature. When calculating the parameters of the ternary alloy according to the equation of Wilson is enough to use the parameters obtained for binary systems. Equity is defined the free Gibbs energy, enthalpy and entropy for components in a Pb–Zn_Ag melts. Increasing the share of metals in the initial alloy the values of thermodynamic parameters decrease. Negative values of enthalpy indicate the exothermic nature of the processes in the melt by distillation of the components. Shown satisfactory correspondence between calculated and experimental values of thermodynamic parameters: average relative deviation of 1.9%; the average standard deviation of 0.1 kJ/mol. Acceptable compliance *VLE *phase diagrams with experimental data shows that the used method of calculation is a reliable method to predict conditions for separation of components of the original alloy and the composition of products obtained under vacuum distillation, which ensures effective and convenient way to manage the process.

**KEY WORDS: **

equilibrium phase diagram, vacuum distillation, molecular volume interaction model, the Gibbs energy, the equation of Wilson