Relationship Atmospheric Gases and Ocean Gases
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:


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).
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.
Ionic strength: Generally the higher the ionic strength of the solution, the smaller the solubility of the gases in it (Sechenov equation).
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.