Why are knowing melting and boiling points important?
Melting points are important because they indicate compound purity. If you synthesize a compound and measure its melting point and the melting point is well-defined (i.e., the compounds melts over a very small temperature range) and the temperature agrees with values reported in the literature (if those are available), then it is a strong piece of evidence that the sample is relatively pure. Boiling points are important for the same reason, a well-defined boiling point indicates purity. The general term to look for is colligative properties, specifically melting point depression, boiling point elevation, or Raoult’s Law for mixtures of liquids. There are other reasons why these properties are useful, assessing vapor pressures is one application (for example, vapor pressures are required if you want to model how smog forms in the atmosphere), but originally they were used as indicators of purity.
