Is there anyway to derive the number of water molecules in a hydrated salt, given just the formula for the anhydrous salt?

That's pretty much it. If not, why?

For coordinated water, my guess is counting the number of unfilled pairs in the metal ion or something like that would give us an indication of the number of water molecules.

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    $\begingroup$ No.$\mathstrut$ $\endgroup$ – Ivan Neretin May 14 '18 at 17:02
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    $\begingroup$ For a given salt there may be lots of hydrates. $\endgroup$ – Mithoron May 14 '18 at 17:11
  • $\begingroup$ @Mithoron Come on! Science can't be that arbitrary. There must be something $\endgroup$ – Varad Mahashabde May 14 '18 at 18:48
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    $\begingroup$ I disagree that this question is too broad, other than the fact that it is of general interest, even if the answer is not much more complicated than "no". $\endgroup$ – pentavalentcarbon May 14 '18 at 20:49
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    $\begingroup$ @Mithoron "No doubt there's middle ground between these approaches" If such an approach exists, I have never heard of it, and it would make a great answer. $\endgroup$ – pentavalentcarbon May 14 '18 at 21:22

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