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Well, one obvious answer is that you learn how to measure a melting point and boiling point in a laboratory setting. Another thing you learn is that you can identify an unknown solid by taking its melting point and comparing it to other known solids with known melting points. You can also identify an unknown liquid in the same way. If you measure the melting/boiling point accurately, then you should readily be able to match it up against a list of potential candidates and make a positive identification. Another thing that you learn is that purer substances generally have smaller melting point ranges while impure substances have larger melting point ranges.
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