A friend asked "how can you lower the boiling point of water so that
it is the same as water's freezing point?"  How can you make the
boiling and freezing points the same?  His solution was to place it in
a vacuum but he seemed unsure what that would do.  What would happen
to water in a vacuum?  Is there a way to make water's freezing and
boiling points the same?  It seems to me that that question is
equivilant to asking "how can you make 0 degrees the same as 100
degrees?"

Hello Halek-ga.

There is a phenomenon in science similar to what you are talking
about, the point where the freezing and boiling points of water are in
equilibrium.  This is called the "triple point" of water.  It is where
water is a gas, a liquid and a solid at the same time.  This is a
known scientific phenomenon, and occurs at 273.16° Kelvin, or 0°C. 
(See references 2 and 3).

This is not, however, exactly the same as that possible phenomenon you
refer in your question, which is to have water that boils and freezes
at the same time.  This is possible (see reference 4).

Water molecules will constantly leave the water and return - some are
lost, and this is why when you leave a cup out for a long time it will
loose water.  When you lower the pressure exerted on water, you
increase the evaporation of the water.

When you increase the heat of the water, you increase the energy in
the water molecules.  At the point when you increase the energy
enough, you give the molecules that leave more energy than the
surrounding water - this is where the water starts to boil, and we see
the bubbles generated by water vapour.

Now when you take those two facts and put them together it is apparent
that lowering the pressure on the water will cause the boiling point
to lower, that is the amount of energy that you need to put into the
water before it will boil.  Eventually, you can lower that amount of
energy to be equal to the point where water freezes - this occurs in a
vacuum chamber, and you get frozen boiling water.

If you read reference 4, you will find two scientists explanations of
this, showing why the water will boil, and how then the water freezes
while it is boiling.

However, as to your comment on "make 0 degrees the same as 100
degrees" - the temperature as marked on the celcius scale is that of
the freezing and boiling points of water at "normal atmospheric
pressure", or around 760 barometric millimeteres of pressure (See
reference 5).  While you change the boiling and freezing points of
water when you lower the pressure, you do not change the temperature
scale itself.

The searches I made:

(google) boiling point freezing point identical
(1) [ http://www.hii.horiba.com/non/it540/allabout/4.html ] -
Interesting facts on temperature

(google) Kelvin Temperature
(2) [ http://www.unidata.ucar.edu/staff/blynds/tmp.html ] - About
Temperature

This led to the following link:
(3) [ http://www.unidata.ucar.edu/staff/blynds/3pt.html ] - Triple
point of water

(google) Water boil freeze same time
(4) [ http://newton.dep.anl.gov/askasci/chem99/chem99558.htm ] - Ask a
scientist, can water boil and freeze at the same time?

(google) how celsius is defined
(5) [ http://www.cchem.berkeley.edu/ChemResources/temperature.html ] -
The conversion of Temperature Units

I hope this answers the questions brought up in you and your friends
minds.

LazerFX-ga

very thorough.  thank you for teaching as well as answering questions.

I'd like to elaborate on this.  The state that H2O is in depends on both
its temperature and pressure.  As you lower the pressure of the water,
i.e. bring it closer to a vacuum, the boiling point continually drops and
the freezing stays relatively the same (it actually increases a minute
amount).  Eventually the boiling and freezing point meet.  This happens
approximately at 612 Pa and 0°C.  Standard atmospheric pressure is 101,325 Pa,
and a vacuum is of course 0 Pa.  If you drop the pressure below 612 Pa, then
H2O is no longer stable as a liquid and can exist only as ice or steam.

This page has a decent phase diagram of water showing this:
http://wine1.sb.fsu.edu/chm1045/notes/Forces/Phase/Forces06.htm

If you want to get more into it check out this page:
http://www.sbu.ac.uk/water/phase.html

Here is shown all the various states H2O can occupy including
different types of ice.

I once saw a film of a demonstration of this phenomenon... a pan of
water was placed in a large vacuum chamber (run by NASA in the 60s, I
think). The air was pumped out. At some point the water began to boil.
When water turns to a gas there is a "heat of vaporization" that must
be supplied (which is why sweating cools you), in this case by the
remaining water. Eventually the water cooled enough to freeze, but it
was still boiling! (Which made a really big mess--ice chunks flying
everywhere.)

Anyway, I have no idea whether this film has been digitized and placed
on the Net, or where to find it otherwise (you might try asking the
people in charge of freshman physics at a local university), but it is
well worth seeing.

A gross revival of an old topic, I know. 

How does this property differ from sublimation?