Physical Chemistry isn't really a syllabus topic. There isn't really an equation, because it's not a chemical change, it's a physical change. The industrial process for the manufacture of pure liquid oxygen and liquid nitrogen starts with liquid air, which contains 20% O2 and 79% N2 and about 1% Ar.
Liquid air exists in equilibrium with a partial pressure of nitrogen gas and partial pressure of oxygen gas. Oxygen boils at -183 deg C, nitrogen boils at -196 deg C. By gently warming liquid air, at -196 deg C, the gas phase coming off will be almost pure gaseous nitrogen. When the remaining liquid is sufficiently enriched in oxygen, the boiling point gradually rises and in another multi-stage separation, a pure liquid oxygen fraction is separated by fractional distillation.