The document discusses various methods of separating mixtures and determining purity, including paper chromatography, distillation, crystallization, filtration, and decanting. Paper chromatography can separate pigments in a mixture using their differing solubilities and attractions to filter paper. Distillation and fractional distillation can separate liquids based on their different boiling points. The purity of a substance can be determined by its sharp melting or boiling point compared to a mixture which melts or boils over a range. Methods like filtration and crystallization are used to purify mixtures by separating solids from liquids.