Freezing point of water on Mars?

[Evil Dr Ganymede]

OK. I know the boiling point of liquid water changes with pressure - it gets lower as the pressure decreases. (here's a more detailed explanation)

I'm trying to figure out the boiling and freezing points of water on Mars (at 6 millibar atmosphere pressure). So far I've got the boiling point at -4.7 degrees C... since that's below the freezing point (at 1 atm pressure at least) I presume this is why liquid water can't exist on Mars under current conditions - as soon as it melts, it boils into a gas, yes?

But I wanted to be sure that the freezing point on Mars isn't affected by the decreased pressure too. If so, can anyone point me to an equation for it (I presume it can't be affected anywhere near as much as the boiling point anyway)?

[selden]

Oh, Evil One,

So you cut chem class that day, huh?

http://chemistry.uttyler.edu/~pchem/fall/lectures/num11.ppt includes the necessary background and has a phase diagram for water that might help, although it's too large a scale in the interesting region of temperature and pressure.

The problem is that the surface pressure of the Martian atmosphere is extremely close to water's triple point. i.e. water essentially cannot exist as a liquid on the surface, so the boiling point is essentially identical to the freezing point.

http://www.sv.vt.edu/classes/MSE2094_NoteBook/96ClassProj/examples/triplpt.html has a slightly better plot of the triple-point region.

[ added later ]
To clarify for those who may have forgotten or who haven't had a chance to learn about it yet: when talking about the different "phases" of a substance (solid, liquid, gas, plasma) the "triple point" is the lowest combined temperature and pressure where that substance can exist in all three common states: solid, liquid and gas. At temperatures and pressures greater than that, a liquid state is possible. At temperatures and pressures less than the values at that point, the liquid form of the substance (or mixture) cannot exist.

For pure water, the "triple point" is at a pressure of 6.11 milliBar (i.e. about 0.6% of the pressure of the Earth's atmosphere at sea level) and a temperature of 0.0098° C. Since the Martian surface pressure is about 6 milliBar, one has to be very careful when doing the appropriate calculations.

[added even later]
To put it another way, liquid surface water might very well be possible in the deepest Martian valleys during an early summer afternoon, but it's extremely unlikely over most of the surface. One discussion of this can be found at http://humbabe.arc.nasa.gov/mgcm/faq/liquid.html

[Evil Dr Ganymede]

Thanks Selden!

So if the freezing point and the boiling point become one and the same at low pressures, then the freezing point must also decrease with pressure with the boiling point. Interesting...!

Of course, now I'm getting confused between water vapour and boiled water. The first are tiny droplets of liquid water suspended in the air, and the latter is H2O gas, right? You wouldn't be able to get water vapour in Mars' atmosphere, but you could get gaseous H2O? Or am I really losing the plot here?!

(yes, I'm crap at this... what would you call it -'Physical Chemistry'?)

[selden]

Thanks Selden!

You're quite welcome.

So if the freezing point and the boiling point become one and the same at low pressures, then the freezing point must also decrease with pressure with the boiling point. Interesting...!

Right.

[ added slightly later: "boiling" is usually the term used for the liquid-to-gas transition, "sublimation" is the solid-to-gas transition. ]

Here's a simplistic diagram:

(which links to a somewhat larger image)

Of course, now I'm getting confused between water vapour and boiled water. The first are tiny droplets of liquid water suspended in the air, and the latter is H2O gas, right? You wouldn't be able to get water vapour in Mars' atmosphere, but you could get gaseous H2O? Or am I really losing the plot here?!

When the pressure is low, you either have free-flying individual molecules (a gas) or you have molecules that are so tightly bound together that their positions don't change with respect to one another (a solid). If there's enough energy available for them to change positions, then it's enough for them to escape entirely. You need the external pressure (plus their natural attraction for one another) to maintain a fluid state.

[added slightly later: Normally, water vapor == water gas.]

(yes, I'm crap at this... what would you call it -'Physical Chemistry'?)

That's it. The other major category is organic chemistry, which is the chemistry of carbon compounds.

[granthutchison]

So if the freezing point and the boiling point become one and the same at low pressures, then the freezing point must also decrease with pressure with the boiling point.

In general, but not in the case of water - the melting point increases with pressure for water, because the solid phase of water is (very unusually) less dense than the liquid - so increasing pressure makes the liquid phase more thermodynamically favoured. For other substances, in which the solid is denser than the liquid, the reverse applies, as can be seen by the slope of the melting point line in Selden's graph - but for water, that line slopes the other way, up and to the left from the triple point.
(Which is how ice-skates and sled runners work - the extra pressure causes micromelting which reduces friction. But if it gets too cold, the pressure isn't enough to cause melting, and suddenly your sled feels like you're hauling it through sand, as poor old Scott of the Antarctic found out. It also means that you won't be able to skate on solid ammonia, in the unlikely event the desire and opportunity ever coincide in your life. )

Grant

[JackHiggins]

It also means that you won't be able to skate on solid ammonia, in the unlikely event the desire and opportunity ever coincide in your life.

Damn. That holiday on Titan is off then I guess...

[granthutchison]

Oops.
In answer to your original question, Evil Doctor, melting point varies with pressure according to the approximate formula:

T = mp + [(1-P)*deltaV/deltaH]*mp

where mp = melting point at one atmosphere, in kelvin; P = pressure, in atmospheres; deltaV = change in volume with melting, in kg/cube metre; deltaH = specific latent heat of melting, in J/kg; and T is the new melting point at pressure P.
It's a pretty damn steep slope for most substances, so you can usually ignore it at pressures within an order of magnitude of atmospheric. (Notice deltaV is negative for water, which reverses the slope, as previously described.)

Grant

[granthutchison]

Damn. That holiday on Titan is off then I guess...

You could still ski. Just wrap up warm.

Grant

[selden]

One must also note that with increasing pressure, many materials form different types of solids which have different characteristics. These different types of solids are called "allotropes." For example, coal and diamond are allotropes of carbon. Water has an unusually large number of allotropes: don't forget Ice-9!

[Evil Dr Ganymede]

Thanks everyone

Grant - funny you should mention Scott, I just finished reading his diaries the other day. That explains why he had so much trouble... (though there were also the er... wavy undulations in the glaciers, whose name I've forgotten but it sounded like a cross between 'satsuma' and 'tortuga'.)

[granthutchison]

Sastrugi.

G

[t00fri]

I am impressed.

F

[Evil Dr Ganymede]

Sastrugi

Well, I was vaguely on the right track at least . Thanks Grant!