I am tutoring my nephew for his science GCSEs; and his chemistry textbook states that you can tell how pure any compound is by how close its melting and boiling points are to the "official" mp and bp for that compound. It says that impurities will always lower the melting point of any compound, but - paradoxically (intuitively speaking) - will always raise the boiling point. But it just states this as a fact and offers no explanation!
I found a simple explanation for why the melting point is reduced in the case of crystalline solids:
Foreign substances in a crystalline solid disrupt the repeating pattern of forces that holds the solid together. Therefore, a smaller amount of energy is required to melt the part of the solid surrounding the impurity. This explains the melting point depression (lowering) observed from impure solids.
... although this doesn't explain why impurities in solids that are not crystalline also lower the melting point.
But I can't find any easy to understand explanation anywhere for why impurities would always increase the boiling point of any compound. I've found explanations that are specific to water (and even then, the explanations I've seen only make sense if the impurity binds more strongly to water molecules than water molecules bond to each other, which isn't always the case); and I found one explanation that says it's because of increased solution phase enthalpy, without explaining what on earth that means!
So I emailed a Professor of Physical Chemistry about this and she replied
The reason for impurities lowering the melting point yet increasing the boiling point is because the impurities stabilise the liquid phase, making it more energetically favourable. This extends the liquid range to lower temperatures (lowering the melting point) and to higher temperatures (raising the boiling point). The liquid phase is stabilised due to the entropy increase when you have the impurity (or any solute) in the liquid. Normally solids do not dissolve the impurities, so the melting point involves transition to pure solid (with impurity separating out or staying in the liquid state).
She made it clear she didn't have time to answer any follow-up questions, and I can't make full sense of her answer, so I am hoping someone here can understand her explanation and elucidate it.
I think I understand why impurities increase the entropy of a substance in its liquid phase by more than they increase the entropy of the same substance in its solid or gasseous phases - I presume impurities don't significantly affect the entropy of a solid because the solid can't rearrange itself into different configurations without absorbing a lot of energy; and they don't affect the entropy of a gas because the gas can disperse over an almost infinite distance to all intents and purposes, so it will be almost infinitely disordered even when pure; but they do increase the entropy of a liquid because there are many more ways of arranging the molecules within a liquid if there is more than type of molecule in that liquid, and the molecules in a liquid can rearrange themselves in all those different configurations without any input of energy.
First of all, have I got that much right?
But even if I have, I don't understand why increasing the entropy of the liquid by adding an impurity to it would make it energetically more stable - and therefore both more difficult to freeze and more difficult to vapourise.
Can anyone help to explain this?