Why can't I dry/concentrate ethanol using calcium chloride ... or can I?
The apparent answer is yes, to quote from a source (composed from extracts of old chemistry journal):


  Calcium chloride forms addition compounds with the alcohols. On evaporating a solution in ethyl alcohol at a low temperature rectangular plates of $\ce{2CaCl2.7C2H5OH}$ are deposited. The compounds $\ce{CaCl2.3C2H5OH}$ and $\ce{CaCl2.CH3OH}$ have also been separated, as well as a mono- and a di-acetone compound, and compounds with isobutyl and amyl alcohols.


So, if you are working with a cold solution of $\ce{C2H5OH}$ with $\ce{CaCl2}$ exposed to air undergoing evaporation, it is possible to form an addition compound (taking the form of rectangular plates) with the formula, $\ce{2CaCl2.7C2H5OH}$ or $\ce{CaCl2.3C2H5OH}$.