QUESTION:
Is it possible that Mars has iron distributed through it much more uniformly
than Earth?  If this is true, is it possible that most of the surface water
on Mars combined with the iron creating iron oxide and releasing hydrogen. 
And if this is true, because hydrogen is so light, wouldn't there be a much
greater tendency for the hydrogen to be lost into space?

The ANSWER comes from Mary Urquhart on July 14, 1997:
What an excellent question!  When the hydrogen is separated from the oxygen
in water to make hydrogen gas it certainly does have a greater tendency to
be lost into space. If a large amount of water was lost by binding the
oxygen to iron and losing the hydrogen it could indeed affect the evolution
of the atmosphere and the water abundance on Mars. So the real questions
are: how much material on Mars is oxidized and what process (or processes)
caused the oxidation?

Mars does apparently have iron oxides in the form of the dust and soil
material distributed across the surface of the planet.  However, in many
places the layer of soil material may be quite thin.  We don't really know
how much of the Martian surface materials have been oxidized.

One possibility: on the Earth massive iron formations called banded iron
formations were produced early in the Earth's history.  If large bodies of
water ever existed for long periods of time on Mars (a BIG if) then it is
quite possible that beds of oxidized iron like those found on the Earth
exist on Mars.  These beds may even be the source for some of the dust and
soil material.

It is also possible that the oxidizing reactions occurred in an entirely
different way such as interaction of individual grains in the dust and soil
with the Martian atmosphere.  Other possibilties exist as well. Whatever the
cause, it is also quite possible that the oxidization has only affected a
relatively tiny but highly visible portion of the surface of Mars.

Now as to how the material was oxidized, there are several ways.  One way is
to react the material with free oxygen gas. The free oxygen can come from
several sources including dissociation of carbon dioxide, and some reactions
can produce extremely short lived free oxygen near the surface of the grains
that will be oxidized. Another is to have ultraviolet light react with iron
in solution with water.  Yet another way is to expose the iron to hydrogen
peroxide.  Some of these processes will cause water to be lost from Mars,
some may cause other gases like carbon dioxide to be lost over time.  No one
really knows which is correct, or how much of these gases have been lost.

Mary Urquhart