How to calculate the pressure at the floor of Ganges Cavus on Mars when it is filled to its edge with perfluorobutane?

Question

Perfluorobutane is an inert, high-density colorless gas and has a high Global Warming Potential value of 4800.
At about the same temperature of -1.7 ⁰C, it has a density of 11.2 kg/m³, opposed to 2 kg/m³ for CO₂ (both at 1 atm.)
Edit: Perflenapent (C₅F₁₂) has a molar mass of 288 g/mol, opposed to perfluorobutane with 238 g/mol, and according to this saturation curve could still be a gas at 25 kPa and 0⁰ C.
So this gas could cause a (considerable) higher pressure.
So if we ever will have serious intentions to terraform Mars, here are the gases to start with!
But first we could begin in a modest way, for instance with Ganges Cavus, a collapse feature lying in the eastern part of the Valles Marineris system of canyons.

Ganges Cavus, from File:Ganges Chasma

From the edges to its floor it is about 5 km deep (calculated with Mars Trek), and calculated with the Mars Atmosphere Model the atmospheric pressure at the edge would be 0.692 kPa.
With that pressure (of the CO₂ atmosphere) as a starting point at its edges, what would be the pressure at the floor of Ganges Cavus, if it was filled with perfluorobutane?

Liquid water of 15⁰ C would need a pressure of 1.8 kPa, water of 20⁰ C would need 2.4 kPa. (Steamtablesonline)
10⁰ C would need 1.3 kPa.

Different but related, with references to perfluorocarbons in Q and/or A: Are we still able to terraform Mars using greenhouse effect? and What would the full hypothetical Mars terraforming roadmap look like? and Is it possible to colonize planetoids by using perfluorocarbon lakes? — uhoh, Aug 31 '20 at 00:17
With the edge having a height of +1000 m., the atmospheric pressure there should be 638 Pa. — Cornelis, Sep 03 '21 at 16:30

score 5 · Accepted Answer · edited Aug 31 '20 at 02:04

5

What you are looking for is scale height--the distance required to reduce atmospheric pressure to 1/e of what it was.

Mars has a scale height of 11.1km with an atmosphere of 95% CO₂. I'll assume it's all CO₂. Your perfluorobutane has a density 5.6x as high. Scale height is linear on molecular weight, thus in the crater the scale height is 1.98 km. Thus we get 2.52 scale heights within the crater, e^2.52 = 12.46 the density at the bottom of the crater as at the top.

Combine this with your pressure at the crater rim and we have a pressure of 8,622 Pa at the bottom of the crater. Not enough to avoid spacesuits.

edited Aug 31 '20 at 02:04

Fred

13,060
4
41
78

answered Aug 31 '20 at 01:20

Loren Pechtel

11,529
26
47

Thank you, I've made an edit for another fluorocarbon ($C_5F_1$$_2$) that could more than double the pressure, so you could adjust your answer to that. – Cornelis Aug 31 '20 at 09:46
3

@Cornelisinspace You should not keep moving the goalposts by changing your question like that after an answer is posted. – Organic Marble Aug 31 '20 at 10:15
@OrganicMarble My question still is: "How to calculate...." . I added this information just because it would double the pressure, worthwhile noting i should think ! – Cornelis Aug 31 '20 at 10:27
That edit will not affect the quality of your answer, the title is still about perfluorobutane ! – Cornelis Aug 31 '20 at 11:13
4

@Cornelisinspace I don't recognize the formula to look up the density, but I explained the math, there should be enough there to figure it out for any other gas. Note that doubling the density will far more than double the pressure. – Loren Pechtel Sep 01 '20 at 02:33
1

It should be noted that 8.6 kPa is slightly above the Armstrong limit (6.3 kPa), so you could maybe survive uncomfortably on supplemental oxygen without a pressure suit for a few minutes. – WaterMolecule Jan 02 '21 at 15:34
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@WaterMolecule of possible relevance; What is the deepest place on Mars? Do humans need pressurized suits there? and very slightly Mars' atmosphere and the triple point of water – uhoh Jan 03 '21 at 22:55
@WaterMolecule about Armstrong Limit.. That is not the lower limit on survivability of pressure, it is merely the point where your body heat will cause your water to boil. The actual limit is where a pure O2 breathing gas will still not impart enough oxygen into your bloodstream to maintain consciousness. that figure is about 16 kPa – CuteKItty_pleaseStopBArking Aug 06 '21 at 14:36

How to calculate the pressure at the floor of Ganges Cavus on Mars when it is filled to its edge with perfluorobutane?

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