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!