This paper presents a mathematical model for the ultrapurification of substances via distillation in a closed vaporization–condensation system, where vapor condenses on a flowing down liquid film. We jointly analyze the mechanisms behind vaporization, vapor transport, condensation, condensate motion, and impurity diffusion in vaporizing liquid. Examining the removal of cobalt impurities from iron pentacarbonyl as an example, we assess the degree of purification as a function of vaporization and condensation temperatures, vaporization area, the fraction of liquid vaporized, and the radius and height of the condensation tube. Using experimentally determined temperature-dependent effective separation coefficients and the mathematical model, we find diffusion coefficients and equilibrium separation coefficients of cobalt, tungsten, and chromium impurities in iron pentacarbonyl.