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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.

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    $\begingroup$ I have a felling maybe you better keep to Worldbuilding.SE Your questions are rather broad and speculative - standard for WB but not on other sites. $\endgroup$ – Mithoron Jul 25 at 19:54
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    $\begingroup$ CO2 content is effected by temperature, pressure, ionic strength, and acidity. The ocean content is therefore not homogeneous. To figure out a decent number is a complex problem. $\endgroup$ – MaxW Jul 25 at 20:12
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    $\begingroup$ @Mithoron Hmm...I don't feel this question is speculative. It's asking to show methodology for figuring out what should be the concentration of gases in water given the gases above that water. I don't see where in that there is any speculation. Here I've provided a simplified set of conditions to reference b/c I felt that would make it easier. Based on my pursuing of Chemistry SE is seemed this was the right place to go to ask for calculation-heavy answers. How would you recommend editing this question to better fit the spirit of Chemistry SE? $\endgroup$ – n_bandit Jul 25 at 20:19
  • $\begingroup$ @MaxW Well, I've outline temperature and pressure. Water is pH of 7 I think. Nothing is yet dissolved in the water (simplified scenario). We could assume a homogenous temperature in the water volume if it would help? $\endgroup$ – n_bandit Jul 25 at 20:21
  • $\begingroup$ If this question is too complex, would simplifying it into a format more like this one help? chemistry.stackexchange.com/questions/99550/… $\endgroup$ – n_bandit Jul 25 at 20:23
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Q1: The equilibrium concentration c of a gas in a solution (typically water) which is present in the atmosphere with partial pressure p dictated by Henry's Law:

$H_{cp} = c/p$

where $H_{cp}$ is Henry's coefficient for that specific gas.

This law states that the concentration of the gas in the solution is directly proportional to its pressure in the atmosphere above the liquid phase and it is a simplification generally applicable to inert, ideal gases.

Corrections must be taken into account when considering the following factors:

  1. Temperature: The enthalpy of dissolution of the gas changes according to van't Hoff's equation. The general result is that the solubility of most gases in water decline with temperature (i.e. solubility is inversely proportional to temperature).
  2. Chemical equilibria: Any transformations (ionization, deprotonation, etc.) that happens to the gas in solution must be taken into account by expressing its concentration by the according equilibrium equation.
  3. Ionic strength: Generally the higher the ionic strength of the solution, the smaller the solubility of the gases in it (Sechenov equation).
  4. Non-ideal solutions: Instead of concentrations, activities of the substances must be considered.

Q2: How much of each gas will dissolve into the water?

The calculation of the concentration for carbon dioxide, for example, is: $$c = [(0.45\%)\times(\pu{0.986923 atm})]\times[\pu{3.4 \times 10^{-2} M/atm}] = \pu{0.0001509957 M}$$

This calculation is a direct application of Henry's Law, where the first term is the partial pressure and the second is Henry's constant. The same type of calculation goes for the others.

Observation:

  • It is important to notice that those volume percentages given should already be considering measures taken for those gases in our atmosphere, so they are already taking in account the solubilization. The concentration of each gas in the atmosphere can be calculated by the ideal gas equation, where the number of moles divided by the volume will be the concentration.
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    $\begingroup$ Sorry that I don't know how to make sub and superscripts/ make equations! $\endgroup$ – Pedro Sansoldo Jul 26 at 5:35
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    $\begingroup$ Hi Pedro, this might help with the equations: math.meta.stackexchange.com/questions/5020/… $\endgroup$ – Felipe S. S. Schneider Jul 26 at 13:12
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    $\begingroup$ "The general result is that the solubility of most gases in water." Is this statement incomplete? $\endgroup$ – Keith McClary Jul 27 at 5:17
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    $\begingroup$ Thanks @FelipeS.S.Schneider for the link! Really appreciate it. $\endgroup$ – Pedro Sansoldo Jul 27 at 18:46
  • $\begingroup$ @KeithMcClary the sentence was indeed incomplete. I edited it to make it right. Thanks! $\endgroup$ – Pedro Sansoldo Jul 27 at 18:50

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