Re: Will water freeze under the conditions described below?

Before getting to the question, let me quickly suggest that you (and 
others) should avoid the term "STP" because not everybody uses it in the 
same way.  Sometimes 0 degrees C is meant, sometimes (more often, I think) 
25 degrees C.  So people should always just state the T and P to remove 
all chance of confusion.

On to this hypothetical question.  What makes it non-trivial is the way 
water freezes (at least around normal atmospheric pressure), which is that 
the density gets lower (not higher as most things do when they freeze).  
But with a fixed volume, there is no place for the ice to "go".  So one 
might think it would never freeze, at least not completely.  But that 
would be wrong ...

The constraint is that the overall density stays the same as it was at 
STP.  Assuming that by STP you mean 25 degrees C, by the time you get down 
to the freezing point the liquid water will be more dense, leaving "room" 
for some ice.  So quite soon you would get coexisting ice and liquid water 
near 0 degrees C, with the relative amounts of the phases determined by 
the constraint on the overall density.  At the same time, the removal of 
more heat and freezing would cause the pressure to go up, compressing both 
the ice and the liquid water.  At very high pressures, you could reach a 
state where the density of the ice was *higher* than the water you began 
with, so you could get it all frozen.

A nice picture of the T/P boundaries for water and the various forms of 
ice is on this page: http://users.bigpond.n
et.au/Nick/Mars/NH1.htm
Unfortunately, I don't know a convenient place to point you for the 
densities of these phases.  What I can tell you is that the minimum in 
freezing temperature, where the equilibrium ice phase becomes Ice III, is 
the point at which the ice structure becomes more dense than the 
coexisting liquid water, so at higher pressures the freezing behavior of 
water is "normal."