Gas molecules are thought to move through liquids by diffusion. For oxygen in water around room temperature the diffusion constant is measured to be about 2 x 10^-5 cm^2/s. You can get the mobility from this using the Einstein relation. For other gases and media you can use an estimate using Stokes theorem based on viscosity of the medium and radius of the particle, but that's usually not very accurate.
If this is not what you mean, please rephrase the question.
Gert answered the question I thought was asked! Gas molecules move through water by diffusion, and so the diffusion constant is higher for oxygen than for carbon dioxide because the extra carbon atom makes carbon dioxide a larger molecule. Solubility of the gas in water is also important to a general understanding, but the solubility coefficient and diffusion constant should be available in a chemical handbook for most gases of interest...or you could calculate it.