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If I go to a high-altitude location and boil a pot of water, it boils at a lower temperature than at sea level. This is because the lower pressure lowers the boiling point. If I were to graph this, at what pressure would the boiling point and the freezing point intersect? I understand the freezing point is not affected by pressure, so it is a constant. Would they intersect at air pressure = 0? And if so, would this imply that there is a small temperature range on Mars where liquid water can exist since Mars' atmospheric pressure is not quite 0.

There's an article in June's Astronomy Magazine about whether or not dark streaks in Mars' craters are caused by dust avalanches or flowing water. According to the article, the evidence points towards running water. But it goes on to say that the problem with this is that in Mars' atmosphere, any liquid water exposed to the air would instantly freeze and evaporate. Some scientists speculated that briny water might be able to flow as liquid on Mars. But I was wondering if it might be that the ground warms to that exact point where water can be liquid. The water then seeps downhill until the ground temperature changes at which point it must freeze and evaporate if the temperature dropped, or just evaporate if the temperature rose. This could leave the dark stains that are seen in these craters. Any thoughts?

Here is link (in german) to answer your question:
http://www.uni-bayreuth.de/departments/didaktikchemie/umat/mars/int_e10.htm

Here is a shorter (english) version of the same text:
http://quest.arc.nasa.gov/mars/ask/water-ice/Boiling_water_on_Mars.txt

maxim

The English explanation is really too brief to be helpful, but the graph on the German site is useful even for non-German-speakers.
The freezing point is affected by pressure, but generally too little to be relevant. (Water is unusual in that its freezing point is reduced by increasing pressure, as the German graph shows - that's how ice skates work; the very high pressure under the skate blade melts a little film of water which lubricates the movement of the skate.)
The "triple point" is the point at which the freezing and melting curves meet, and for water that's at 273.16K and 611.2 Pa (= 6.112 mb). So at ambient pressures below 611.2 Pa, water can't exist as a liquid - ice converts directly to gas.
The interesting thing about Mars is that its atmospheric pressure is very close to the triple pressure (although it's usually colder than the triple temperature); and the atmospheric pressure changes significantly during the year as carbon dioxide freezes out at the poles during winter. So when atmospheric pressure is even marginally lower than normal, liquid water can't exist at all. In spring/autumn, when the atmospheric pressure edges up slightly, it's theoretically possible for liquid water to exist at low altitudes and in a very narrow range of temperatures close to zero Celsius. But the range is very narrow, the required temperatures are extreme for Mars, and the evaporating water would have to pretty well replace the entire overlying atmosphere with water vapour before equilibrium was reached - hence the usual statement that "liquid water can't exist on Mars." If you took a glass of water out on a warm spring day on Mars, when the temperature was marginally above zero Celsius and the atmospheric pressure was higher than the triple pressure (so that conditions were in the theoretical range for liquid water on the graph), you'd still see it evaporate away extremely quickly into the dry atmosphere - it would be like taking water at 99 Celsius out into a desert environment on Earth.

Grant

That phase diagram kinda sucks. Not really, but it's just a sketch.

Here's one a better one I stole from lsbu.ac.uk



You don't need to worry about the Roman numerals, because you'll never see anything like those kinds of pressures on Mars. They are labels for the different crystalling phase of ice, tho, if you're curious.

The image is from the top hit on Google for 'phase diagram of water', btw, if you want to read the text.

Yes, I'd heartily recommend the site from which revent clipped his picture: http://www.lsbu.ac.uk/water/phase.html. I've had it bookmarked for a while as the best resource for high-pressure ices that I've so far encountered on the web. Scroll down from the phase diagram and you'll hit a set of links to invidual, detailed pages describing each ice phase - a great resource to help understand the predicted "ice mantle" of theoretical ocean worlds.

Grant