what is the physical state of a single molecule of water at room
temperature? can it be considered liquid (or solid or gas) with only
one molecule? if so, how can you tell? if not, how many molecules is
required to determine a physical state?

The ordinary "states" of matter (solid/liquid/gas) are only meaningful
for a substantial collection of atoms or molecules.

However there is one "state" of matter, a Bose-Einstein condensation,
which we could say is meaningful for a "single" atom.  The twist is
that in such a condensation multiple atoms become superimposed in the
quantum sense and form a single "super atom" in which separate
identities as individual atoms disappear.

Ultra-low temperatures are required for this to happen.

[Bose-Einstein Condensation]
http://www.colorado.edu/physics/2000/bec/

regards, mathtalk-ga

This reminds me of "What is the sound of one hand clapping?"

I wonder, though, if you looked at a temp vs. time curve as you heated
the molecule, would it show the latent energies that are seen with a
group of molecules and that are used to distinguish the different
states of matter? This then would suggest that one atom does have
different states of matter.

My husband became interested in this question, and he asked a friend
who is a retired Professor of Physical Chemistry. The professor said
that it would take a few hundred molecules of water aggregated
together before you could consider them to have bulk properties and a
meaningful physical "state".