If this question is better suited for the Earth Science StackExchange or another StackExchange please let me know.
Edit 1: Modified for clarity and brevity.
Something that's unclear to me is the exact relationship between gases within an atmosphere and the concentration of those gases within a large body of water under that atmosphere (like an ocean).
For example, the solubility of $\ce{CO2}$ at $298\ \mathrm K$ and $1\ \mathrm{bar}$ of atmospheric pressure is $\approx 1.496\ \mathrm{g/L}$ in water. My understanding is that number indicates how much $\ce{CO2}$ can be dissolved within water before the water is saturated with $\ce{CO2}$ and won't accept any more. However, this doesn't tell me what the concentration of $\ce{CO2}$ would be under given conditions, it just sets a maximum cap. For one thing it could be much less because there isn't enough $\ce{CO2}$ in the atmosphere to saturate the ocean.
(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 body of water under an atmosphere of a given gaseous composition and pressure?
We could clarify this question through looking at an idealized situation (below). I'd like to know the steps to take to figure this out. If we need to ballpark it then that's ok, though I'd prefer to keep it as reasonably accurate as feasible.
Scenario
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
- Total surface area: 510 million $\mathrm{km^2}$
- Water surface area: 361 million $\mathrm{km^2}$
- $15\ \mathrm{^\circ C}$ uniform surface temperature
ATMOSPHERE
- By volume: $99.5\ \%$ nitrogen, $0.45\ \%$ carbon dioxide, $0.05\ \%$ methane
- Surface pressure: $1\ \mathrm{bar}$
OCEAN
- Pure water ocean (nothing yet dissolved in it)
- Volume: $1.4$ billion $\mathrm{km^3}$
Q: What will be the equilibrium composition of gases in the atmosphere and in the water?
Q: How much of each gas will dissolve into the water?
… and of course how you got there.
What happens when you increase pressure and decrease temperature? How would that effect the answer?
What I really want to know is both general principles as well as establishing those principles in actual numbers. I'd also love any insight you may have on how real-world numbers are likely to differ and why.