Chemistry - Does desalination work?
Solution 1:
This is a classic science experiment. Where saltwater (using $\ce{NaCl}$) is heated, as it does, the water evaporates and most, if not all, of the salt remains - increasing the concentration of salt.
Evaporating half the water would approximately double the concentration of $\ce{NaCl}$.
Eventually, the salt concentration becomes supersaturated and crystallises. The reason is due to:
As the water evaporates less and less water molecules are present to keep the salt particles apart. The salt therefore recrystalises and can be collected.
Source
This process is also used in salt evaporation ponds, where
seawater or brine is fed into large ponds and water is drawn out through natural evaporation which allows the salt to be subsequently harvested.
As Curt F mentioned in the comments, different salts and mixtures of salts can have different outcomes in terms of vaporisation.
Solution 2:
Note Kevin's comment on another answer. The key observation here is that it is not a question of whether $\ce{NaCl}$ vaporises but whether there is a temperature range in which water vaporises and $\ce{NaCl}$ doesn't, the answer to which question is yes. The wider the gap between the solvent and the solute, the easier and more completely you can separate them.
$\ce{NaCl}$ will certainly vaporise but it also has a liquid phase, and in this phase is used to cool nuclear reactors. Going by the 600 degrees between Kevin's figures for melting point and boiling point it doesn't tend to sublimate.
Everything vaporises at any temperature above 4K. Atmospheric agitation is knocking bits off my keyboard even as I type, but for the most part they're big heavy lumps so they fall back down and either re-bond or sit there serving as ablative armour. Molecules small and light enough to float away mostly did so fairly promptly. Think new car smell. These are called volatiles, which simply means they are small and light enough to float away with modest stimulation.
(Why 4K? Helium liquefies. Drop the temperature even further and you get a Bose condensate which is super interesting stuff with directly observable quantum behaviour but doesn't have much to do with chemistry as we know it.)
So where was I? Oh yes, melting point and boiling point are inflection points in a continuum. They are temperatures which bound dominant behaviors.