A version of this question is posted in Chemistry SE but doesn't seem to be getting traction there. Perhaps this SE is a bette place for this question? If you think it belongs on a different SE please let me know. The only other SE I can think might be a fit is Earth Sciences SE.

Something that's unclear to me is the exact mathematical relationship between gases within an atmosphere and the concentration of those gases within a the bodies of water under that atmosphere (like an ocean).

For example, the solubility of $CO_2$ at $298K$ and 1 bar of atmospheric pressure is ≈ 1.496 g/L in water. My understanding is that number indicates how much $CO_2$ can be dissolved within water before the water is saturated with $CO_2$ and won't accept any more. However this doesn't tell me what the concentration of $CO_2$ would be under given conditions, it just sets a maximum cap. So 1.496 g/L of $CO_2$ might be dissolved in water, but it could be much much less.

(I hope I have that correct! If not please let me know where my understanding is going astray.)

Key Question: What are the calculations I need to go through to figure out the amount of gases in a planet's oceans under a given atmosphere?

I know that's probably a very complex topic, so we could simplify this through looking at an idealized situations (below). I don't particularly care what the temperature, pressure, or gases are, they are simply there to give you something to work with. Feel free to substitute, or simplify as needed.

I'm looking for a result like: The atmosphere would have A% Nitrogen, B% Oxygen, C% Carbon Dioxide, D% Methane with concentrations in g/L of W of Nitrogen, X of Oxygen, Y of Carbon Dioxide, and Z of Methane in the water. Maybe also with how much in total of each gas moved from the atmosphere into the water.

...and of course the steps to get there.

Scenario I – 1 bar & 15C

Assume uniform temperatures at water surface. Assume no minerals dissolved in water. Assume no gases have yet dissolved in the water from the atmosphere....

SURFACE (Idealized Earth)

  • Total Surface Area: 510 million $km^2$
  • Water Surface Area: 361 million $km^2$
  • $15C$ Uniform Surface Temperature

ATMOSPHERE (Idealized Earth)

  • By Volume: 79% Nitrogen, 20.9% Oxygen, 0.09% Carbon Dioxide, 0.01% Methane
  • Surface Pressure: $1$bar

OCEAN (Idealized Earth)

  • Pure Water Ocean (nothing yet dissolved in it)
  • Volume: $1.4$ billion $km^3$

Q: What will be the equilibrium composition of gases in the atmosphere and in the water?
Q: How much nitrogen, oxygen, carbon dioxide, and methane will move into the water?

Scenario II – 10 bar & 5C

What would change if we increased atmospheric pressure to 10bar (by adding a correspondingly larger amount of each gas) and lowered temps to 5C? How would this effect the answer?

What I really want to know is both general principles as well as establishing those principles in actual numbers. My goal is to gain an understanding that will allow me to actually do the calculations. I also know real-world numbers will differ from an idealized scenario, so any input on how/why the numbers in real life would be different would be great!

  • $\begingroup$ Version of the question in Chemistry SE: chemistry.stackexchange.com/questions/118512/… $\endgroup$
    – n_bandit
    Commented Jul 26, 2019 at 2:27
  • 1
    $\begingroup$ "The solubility of CO2 at 298K and 1 bar of atmospheric pressure is ≈ 1.496 g/L in water … However this doesn't tell me what the concentration of CO2 would be under given conditions, it just sets a maximum cap. So 1.496 g/L of CO2 might be dissolved in water, but it could be much much less." This is not the case. Under those conditions, there will be exactly 1.496 g/L of CO2 in the water. That is where equilibrium is found for those conditions. $\endgroup$ Commented Jul 26, 2019 at 2:42
  • $\begingroup$ However, once there is 1.496 g/L of CO2 in your water, it is now a solution, so it will have slightly different properties to pure water. Finding the balance of gases that will dissolve is difficult, and beyond my level of chemistry. $\endgroup$ Commented Jul 26, 2019 at 2:44
  • 1
    $\begingroup$ "In chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid." (That's why one can increase the amount of CO2 dissolved in water by using high pressure; when this carbonated water is exposed to regular air the excess CO2 comes out of soluution as fizzy bubbles.) And a simple application at high-school level. Chlorinity and salinity have only small effects. $\endgroup$
    – AlexP
    Commented Jul 26, 2019 at 4:14
  • 2
    $\begingroup$ While I understand that you put this question here, I dont think it will help much more than the Chemistry stack-exchange. Its true that at Worldbuilding, there is more lee-way in questions being broad or opinion based, but we don't harbor the same expertise as other more specific sites would. I also fail to see how there is any worldbuilding in this question. You appear to be asking for a generalized equation to a very complicated problem.Chances are, any answer not fielded by an expert in the field would be making large assumptions which you don't seem to want. $\endgroup$
    – Shadowzee
    Commented Jul 26, 2019 at 4:30


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