It is unlimited. Do you know how large the atmosphere is?
I didn't say that oxygen in the atmosphere is limited exactly.
The reason I said that limited amount of oxygen from the unlimited source of oxygen in the atmosphere will enter the water, is because oxygen dissolves in water by diffusion laws as you said,but only until the saturation level(dissolved oxygen in water) has reached 100%.
Theoretically, after saturation levels have reached 100% and more percent, the opposite process of degassing happens, when oxygen leaves the water and goes into the atmposphere.
Right, but there is a limitless source of oxygen available to reach saturation. That means that you can treat the source as infinite, and you get equations that describe a diffusion front that will eventually reach 100% saturation everywhere. It doesn't matter what the specific saturation or diffusion numbers are... an infinite source means that everything will evenutally reach 100%. And this started by your claiming that diffusion alone can't do that, which is wrong. Diffusion very much can and does.
Regarding the second point there, nature always tends toward equilibirum. The only way water would achieve a level greater than 100% saturation is if conditions change -- such as the water warms up quickly. Given constant conditions, nature won't overshoot equilbirum and then have to come back down. Outgassing would only occur if conditions significantly changed from a previous state.
I don't think that diffusion of oxygen in water and diffusion of oxygen in air will give you exactly the same results.
Then you would think wrong. Because the laws of diffusion do not change depending on the medium it is diffusing through. Diffusion through a gas, liquid, or a solid are identical. Now, the specific diffusion rates will be different, but the laws remain identical, and hence the mathematical forms of the solution remain identical.
Oxygen diffusion through nitrogen (in effect air) has a diffusion rate of around 0.250 cm[sup]2[/sup]/s
Oxygen diffusion through water has a diffusion rate around 0.000025 cm[sup]2[/sup]/s.
About 4 orders of magnitude difference (the specific values will be a function of temperature, in both cases), as is typical when comparing diffusion rates in liquids and gases.
But here is what I found from an article about the diffusion law you are talking about:
"Oxygen is absorbed in water by direct diffusion and by surface-water agitation. Solubility of oxygen in water is so small and by diffusion process alone in still water, it was calculated that it would take 6 years for oxygen to diffuse from surface to a depth of 6 meters in quiet water.
The low diffusion of oxygen in water referred to already and the stratification of gases even in small bodies of water, unlike atmospheric air which is uniform, make each water body distinct in its nature."
(http
/www.fao.org/docrep/field/003/AC183E/AC183E04.htm)
I am not sure that 6 years is completely accurate. It really is doing to depend on a lot of factors. Nonetheless, the bigger point is that diffusion alone CAN saturate the water. It will take time.
A bigger point is that this has strayed quite some ways from seeking an answer for some of the original questions. No fish tank is completely quiescent. They all have mixing from filter returns and even the fish swimming in them provide significant mixing. What started this was a question whether bubbles or the tank surface provides more gas in a typical fish tank.
You can't compare the case of diffusion from only bubbles AND use the mixing bubbles provide to the case of a completely still tank with diffusion only from the surface. You need to compare actual use cases; or in other words, you need to compare apples to apples, instead of apples to orangutans. If you want to compare diffusion through the surface of a still tank with diffusion through 250 bubbles somehow suspended in a still tank, then the top of the tank will provide orders of magnitude more oxygen because of the greater surface area. Or, if you want to compare the mixing caused by the filter return and the diffusion from the top of the tank to the mixing causes by rising bubbles and the diffusion out of those bubbles, the top of the tank will once again be much greater.
In any situations that are comparable, the top of the tank provides a much greater surface area than any reasonable amount of bubbles. It is simply that greater area that shows that the vast, vast majority of the gas mass transfer that occurs comes from the top.