Partial pressure and liquid water

[jf22901]

Hi everyone

I'm reading up on the possibility of liquid water existing on the surface of Mars, and have confused myself!

During my reading, I have come across various definitions that say liquid water can exist if the temperature is above 273 K and the atmospheric pressure is above 611 Pa, but others say it is the partial pressure of water vapour that needs to be above 611 Pa.

As an example, say there is an ice deposit on Mars in a region where the atmospheric pressure is 1000 Pa, and the temperature increases from 270 K to 280 K. What happens in this case? Does the ice turn to liquid or sublime to vapour? The temperature and atmospheric pressure are high enough for liquid water to exist, but how does the partial pressure of water vapour come into things in this situation?

I must be missing something blindingly obvious, but I can't see what it is!

Thanks,

Jack

 

[Mapes]

During my reading, I have come across various definitions that say liquid water can exist if the temperature is above 273 K and the atmospheric pressure is above 611 Pa, but others say it is the partial pressure of water vapour that needs to be above 611 Pa.

The second statement is correct. Condensed matter (solid or liquid) will sublimate or evaporate if the vapor pressure is higher than the partial pressure in the gas phase. The vapor pressure of water at 273 K is 611 Pa, so any liquid water would evaporate unless the partial pressure of water vapor in the gas phase were at least 611 Pa.

As an example, say there is an ice deposit on Mars in a region where the atmospheric pressure is 1000 Pa, and the temperature increases from 270 K to 280 K. What happens in this case? Does the ice turn to liquid or sublime to vapour? The temperature and atmospheric pressure are high enough for liquid water to exist, but how does the partial pressure of water vapour come into things in this situation?

The ice will sublimate into vapor. See the phase diagram http://www.colorado.edu/physics/phys4230/phys4230_sp03/images/phase.gif" , keeping in mind that the pressure is that of the water vapor, not the total pressure.

Also, if the original atmospheric pressure (at 270 K) did not include at least ~600 Pa of water vapor partial pressure, the ice would be sublimating already. Does this make sense?

 

[jf22901]

The ice will sublimate into vapor. See the phase diagram http://www.colorado.edu/physics/phys4230/phys4230_sp03/images/phase.gif" , keeping in mind that the pressure is that of the water vapor, not the total pressure.

Also, if the original atmospheric pressure (at 270 K) did not include at least ~600 Pa of water vapor partial pressure, the ice would be sublimating already. Does this make sense?

Hi Mapes

Thanks for the reply. I think it makes sense now, but let me just try another example to make sure I have actually understood it! It's strange that I am comfortable with what what might be classed as 'difficult' physics topics (such as quantum mechanics, electromagnetism, calculus of variations etc.), but thermodynamics confuses the heck out of me!

Right... let's say there is a block of ice on Mars, the pressure of the atmosphere is 10⁶ Pa, and the temperature rises from 200 - 350 K (in no way realistic, but it'll do as an example, as it is easier to follow on the phase diagram!). Let's also assume the partial pressure due to water vapour in the atmosphere is less than 611 Pa. In this case, although the total atmospheric pressure falls above the triple point, because the partial pressure is below, the ice will sublime directly to vapour as the temperature increases.

But, as the vapour enters the atmosphere, the atmosphere (at least the thin layer close to the block of ice) will become more saturated with vapour, and in this small layer, the partial pressure of the water vapour may increase to above 611 Pa. In such a situation, with the temperature above 273 K (but below the boiling temperature), and the partial pressure due to vapour now above 611 Pa, would the ice begin to melt rather than sublime?

And if it did melt, the liquid would be stable against freezing and boiling, but not necessarily evaporation, unless the air was completely saturated with water vapour?

Thanks once again,

Jack

 

[Mapes]

Yes, this reasoning looks good.

 

[PJC01]

Hi Jack,

Your confusion is understandable, as the concept of partial pressure can be tricky to grasp at first. Essentially, the partial pressure of a gas in a mixture is the pressure that gas would exert if it were the only gas present in the same volume. In the case of water vapor, it is the pressure it would exert if it were the only gas in the Martian atmosphere.

In the example you provided, at a temperature of 270 K and an atmospheric pressure of 1000 Pa, the partial pressure of water vapor would be less than 611 Pa. This means that the conditions are not suitable for liquid water to exist, and the ice would likely sublime (turn directly from solid to gas).

However, at a temperature of 280 K, the partial pressure of water vapor would be greater than 611 Pa, meaning that liquid water could potentially exist. In this case, the ice may melt and form liquid water. The partial pressure of water vapor is important because it determines how much water is present in the atmosphere and whether it can exist in a liquid state.

I hope this helps clarify the concept of partial pressure and its role in the existence of liquid water on Mars. Keep exploring and asking questions!

Best,