Relationship Between Ratio of Atmospheric Gases and Ocean Gases A version of this question was posted in Chemistry SE and Worldbuilding SE but I've been told it wasn't appropriate to either SE. I was told to give this SE a chance. If you think it doesn't belong on this SE please let me know how to appropriately edit or otherwise another SE to try.



Note: This problem comes from my interest in exoplanet sciences but is applicable to earth sciences.

Something that's unclear to me is the exact relationship between gases within an atmosphere and the concentration of those gases within 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. 

Key Question: What are the calculations I need to go through to figure out the amount (total and ratios) of gases in both a planet's oceans and atmosphere assuming I know either:


The total amount of gases within the ocean/atmosphere system, or...
The amount of gases present in the atmosphere but not the corresponding amount present in the waters.


I want to be able to figure out all the ratios of gases within an atmosphere and dissolved in a planet's waters. Ball-parking is fine if that's the best I can do.

I know this is probably a very complex topic, so if it's helpful you could look at the idealized  earth situation I've outlined (below) and rift off those numbers. Not necessary, but there if you need it.

You could also take the approach of looking at two gases with very different solubility in water, like $CH_4$ than $CO_2$ and look at what would happen to the ratios if there was a heck of a lot more of the less-soluble gas (Methane in this case) in the system than the more soluble gas. 

Whatever approach you take, I'd appreciate any insight you can provide. What I really want to learn is both general principles as well as how to establish those principles in actual calculations.



Scenario: If useful refer to these numbers

Assume uniform temperatures at water surface. Assume no minerals dissolved in water.

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, 20.95% Oxygen, 0.049% Carbon Dioxide, 0.001% Methane
Surface Pressure: $1$bar


OCEAN (Idealized Earth)


Water Ocean (What should be the corresponding dissolved gases?)
Volume: $1.4$ billion $km^3$


Bonus: What would change if we lowered/increased atmospheric pressure and/or lowered/raised temperature?
The law that governs the pressure of gas at equilibrium over a dissolved liquid is called Henry's Law. Note, the equilibrium assumption, as there is some time dependence. That is, if you start with no dissolved gas in pure water, then in a relatively short amount of time, the amount of dissolved gas will be less than equilibrium.
Let's talk in abstractions. Henry's law's temperature dependence resembles the Clausius-Clapeyeron equation, so we can draw some parallels. From the Wikipedia link, for a given gas, the Henry's law constant is $$H(T)=H(T_0)\exp\left[-\frac{\Delta K}{R}\left(T^{-1}-T_0^{-1}\right)\right]$$ .$-\frac{\Delta K}{R}$ is Wikipedia's version of $-\frac{\Delta_{sol} H}{R}$, but I used $K$ to not cause confusion. For pure water, this link shows the solubility of different gases at different temperatures, but most relevant is the temperature at 0$^\circ$C (that is, it gives $H(T_0)$).
But all of this doesn't answer the two questions that your question boils down to.

Raising the temperature decreases the solubility of a gas.
If the pressure increases, then the amount of gas that can be dissolved increases per Dalton's Law. If the system is not in equilibrium, then the amount of solute will increase in proportion to Henry's Law.