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Background:

Many aquarists keep freshwater planted tanks add $\ce{CO2}$ from a pressurized canister to their aquaria to promote plant growth. The injection is at a slow rate to get dissolved $\ce{CO2}$ in the neighborhood of 30 ppm. Methods vary, but ceramic discs to release a very fine mist of bubbles are popular, as are $\ce{CO2}$ reactors which trap the bubbles in a bell or canister and stir them around with a water pump.

In any case, within the hobby there is an odd fixation on getting the gas bubbles to dissolve completely, I suppose on the reasoning that a bubble that pops at the surface is $\ce{CO2}$ that escaped to air rather than being dissolved in the water.

I'm skeptical of this logic -- I'd think while the bubble is dissolving, water vapor and whatever other dissolved gasses will be diffusing into the bubble. At some point, the bubble becomes just humid air in equilibrium with the surrounding water, and no amount of stirring will get more $\ce{CO2}$ out of it. This is just my guess, based on casual observations where the bubbles will diminish to less than 10% of their initial volume within 30 seconds, and thereafter they don't seem to get any smaller.

Questions:

Is that correct, and does it mean the aquarist's quest for a "100% efficient" $\ce{CO2}$ bubbler that never lets bubbles pop at the surface is doomed to eventual failure?

And if so, what are the basic principles that describe this equilibrium and how can we figure how much $\ce{CO2}$ can be extracted from a bubble, and how big the bubble will be after it's become just humid air?

If not, why does it seem the bubbles will rapidly dissolve in the water at first, but never fully dissolve even though the solution is far from saturated?

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    $\begingroup$ There is a limit as to how much $\ce{CO2}$ will dissolve into water. I'd wonder about aggressively adding $\ce{CO2}$ in an aquarium with fish or other oxygen dependent animals. The excess $\ce{CO2}$ will sparge dissolved oxygen from the water. $\endgroup$
    – MaxW
    Commented Dec 22, 2020 at 22:35
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    $\begingroup$ @MaxW The rule of thumb in the hobby is to aim for 30 ppm, though it can vary by species. The $\ce{O2}$ released from photosynthesis is impressive, so there's plenty of oxygen if the tank is running well. I'm no biologist but I always figured excess $\ce{CO2}$ will kill the livestock directly by acidosis before oxygen deprivation does. $\endgroup$
    – Phil Frost
    Commented Dec 23, 2020 at 1:09
  • $\begingroup$ @Mithoron Thanks, I'm here to learn! Perhaps you could put that in an answer? $\endgroup$
    – Phil Frost
    Commented Dec 23, 2020 at 1:29
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    $\begingroup$ Questions: (1) Fresh water or salt water? (2) Are there fish or other animals that depend on dissolved oxygen in the aquarium? (3) Is the pH adjusted regularily in the aquarium? (4) To what value is pH adjusted? $\endgroup$
    – MaxW
    Commented Dec 23, 2020 at 10:40
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    $\begingroup$ @PhilFrost well I the liquid is saturated they certainly escape. They escape nevertheless as they move to the surface. That is why finer bubbles "dissolve better". If you imagine the smallest bubble you can have, it will enter the liquid basically already dissolve, in a limit case. Still, what you say is in principle true, the inside of the bubble will contain some oxygen and water, as they have vapour pressure. Bubble can certainly disappear entirely, tough unless the inlet is in the depth, it will be difficult to see that. Finally, a bubble of water can't form, it is a droplet among the othe $\endgroup$
    – Alchimista
    Commented Dec 24, 2020 at 9:03

2 Answers 2

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Situation at equilibrium

If you have pure water in contact with air in a closed system (like a capped bottle filled halfway with water), the $\ce{CO2}$ concentration will reach an equilibrium.

$$\ce{CO2(g) <=> CO2(aq)}$$

"(aq)" refers to aqueous concentration, not aquarium.

Currently, our outside air contains about 400 molecules of $\ce{CO2}$ in a million molecules total (400 ppm or 0.04% by volume or by number of particles). At room temperature, the concentration of $\ce{CO2}$ in the water will be about $\pu{13E-6 mol/L}$, corresponding to 0.6 mg of $\ce{CO2}$ per liter.

If you let water stand in pure $\ce{CO2}$ at atmospheric pressure (or bubble pure $\ce{CO2}$ through pure water that is not in contact with air), the concentration of $\ce{CO2}$ at equilibrium will be about 2500-times higher, so $\pu{0.033 mol/L}$. This corresponds to 1400 mg of $\ce{CO2}$ per liter.

Getting "30 ppm"

In the aquarium, the goal is to have 30 mg of $\ce{CO2}$ per liter (confusingly described as 30 ppm, which is different from 30 ppm in the gas phase). This is 50-times higher than the equilibrium concentration you get with air, and about 50-times lower than you get in an atmosphere of pure $\ce{CO2}$.

So what happens in the aquarium is that $\ce{CO2}$ enters the water from the $\ce{CO2}$ bubbles, and exits when water has contact with the air. In a covered aquarium, the rate of $\ce{CO2}$ removal is a bit slower because the air has more $\ce{CO2}$ than fresh air. There are also biological processes (plants, fish, microbes) that produce or use up $\ce{CO2}$. For these reasons, you monitor the $\ce{CO2}$ content and adjust the $\ce{CO2}$ flow (input) to maintain the desired concentration.

The $\ce{CO2}$ concentration is measured with a "drop checker" via the pH of a test solution of defined carbonate hardness (4 dHK, or degrees of carbonate hardness). As the $\ce{CO2}$ concentration in the aquarium changes, the $\ce{CO2}$ partial pressure in the air gap between aquarium water and test solution changes, eventually changing the $\ce{CO2}$ concentration in the test solution, and with it its pH. This takes a while, so the measurement lags by minutes or hours.

Your questions

Update I edited this after Poutnik posted a comment

I'm skeptical of this logic -- I'd think while the bubble is dissolving, water vapor and whatever other dissolved gasses will be diffusing into the bubble. At some point, the bubble becomes just humid air in equilibrium with the surrounding water, and no amount of stirring will get more $\ce{CO2}$ out of it.

If the bubble is pure $\ce{CO2}$, it should dissolve completely given sufficient pure water. However, the aquarium water is not pure water, and some oxygen, nitrogen and water will be transferred from the liquid into the gas bubble while $\ce{CO2}$ dissolves in the water. I would guess that in the vicinity of the $\ce{CO2}$ bubbler, the concentration of $\ce{CO2}$ in the water is already near its maximum, so the $\ce{CO2}$ concentration in the bubble does not go to zero. On the other hand, the partial pressure of oxygen and nitrogen will increase in the bubble until it matches the vapor pressures of the solutes. What the final volume of the bubble will be depends on the kinetics, but if you prevent it from escaping to the surface, it will not disappear completely.

[...] does it mean the aquarist's quest for a "100% efficient" $\ce{CO2}$ bubbler that never lets bubbles pop at the surface is doomed to eventual failure?

In pure water, if the bubble is small and there is plenty of time before it reaches the surface, it should be possible for bubbles to completely dissolve.

And if so, what are the basic principles that describe this equilibrium and how can we figure how much $\ce{CO2}$ can be extracted from a bubble, and how big the bubble will be after it's become just humid air?

It is not an equilibrium situation. If you let the system come to equilibrium, the composition of the bubbles (near the surface, i.e. at ambient pressure) will be the same as the air on the surface. However, as explained in the first section, the system is never at equilibrium if you bubble in $\ce{CO2}$.

If not, why does it seem the bubbles will rapidly dissolve in the water at first, but never fully dissolve even though the solution is far from saturated?

I suspect the solution surrounding the bubble becomes saturated very quickly, and then the $\ce{CO2}$ has the diffuse away from the bubble before more can dissolve. Also, once nitrogen and oxygen have entered, they will maintain the bubble as long the water is saturated with nitrogen and oxygen.

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  • $\begingroup$ Hm, until CO2 strips out O2 and N2, bubbles would not dissolve completely, not being CO2 bubbles. Water is in equilibrium with 0.78 atm N2 and possibly oversaturated by O2 wrt 0.21 atm O2. Dissolved O2 and N2 would rush into bubbles with pure CO2 and no O2 nor N2. $\endgroup$
    – Poutnik
    Commented Oct 15, 2022 at 7:19
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    $\begingroup$ @Poutnik I guess it is a question of kinetics. If a bubble has the same composition as the bulk gas the solution is in contact with, it is stable. If it has any components with higher or lower partial pressure than in the bulk gas, the component will go into solution or come out of solution. I will have to edit my answer, thanks for the comment. $\endgroup$
    – Karsten
    Commented Oct 15, 2022 at 13:17
  • $\begingroup$ @Poutnik There might also be an effect similar to Ostwald ripening so that the bubbles eventually disappear (in favor of the biggest "bubble", the water-air interface at the surface of the aquarium), see foam ripening. $\endgroup$
    – Karsten
    Commented Oct 15, 2022 at 19:37
  • $\begingroup$ See also researchgate.net/publication/… $\endgroup$
    – Karsten
    Commented Oct 15, 2022 at 19:39
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To improve your CO2 intake and not lower dissolved oxygen levels, an apparent solution is to make the water in your fish tank more alkaline and also consider increasing the surface turbulence.

The logic is that there is an equilibrium based dissociation of CO2 in water creating Carbonic acid. However, in the presence of OH- ions, the formation of an insoluble carbonate (like CaCO3) will continue to drive the reaction to the right.

On the effect of turbulence from an air pump agitation of the water or perhaps a waterfall creating mist, will capture the carbon dioxide.

So, as solutions consider adding alkaline stones. There is also a supporting article: Limestone Rocks in Aquariums and Water pH, to quote:

Have you set up an aquarium and then noticed that the pH of the water continues to rise? Could rocks or gravel that were added as decor in the aquarium affect the water pH? Yes. If your rocks are actually limestone, they are the cause for the pH elevation in your aquarium water. Limestone is calcareous (contains calcium) and is known for its ability to both harden the water and increase the pH. In fact, if someone asks how to raise water pH, one method we suggest is to place crushed limestone, coral, oyster shell or any highly calcareous material in the filter.

On the waterfall idea a reference, to quote:

Speaking of pond health and waterfalls, they're a great way to aerate your pond, but you might not want to overestimate how much oxygen is getting into your pond from the waterfall. Specifically, the larger your pond is, the higher the waterfall would need to be to effectively aerate it alone.

Hope this helps.

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    $\begingroup$ This is interesting, but it doesn't really answer the question, "Will CO2 bubbles ever fully dissolve in water?" $\endgroup$
    – Phil Frost
    Commented Dec 23, 2020 at 15:36
  • $\begingroup$ On a practical note, increasing the pH and the hardness of the water interferes with nutrient uptake for the tropical species commonly used in freshwater planted aquaria which are adapted to soft, acidic water; and I don't think carbonate is bioavailable for photosynthesis. Oxygen saturation is really not a concern: photosynthesis converts $\ce{CO2}$ and water into carbohydrates and $\ce{O2}$, which is so abundant it bubbles off the plants. It's not difficult to get oxygen saturation over 100%: the concern for livestock is the toxicity of $\ce{CO2}$ but 30 ppm isn't harmful for most species. $\endgroup$
    – Phil Frost
    Commented Dec 23, 2020 at 16:24
  • $\begingroup$ Phil getting CO2 gas to dissolve becomes increasingly difficult when it has been effectively 'salted out' (because of other dissolved compounds) or due to elevated water temperatures. However, as the chemistry discussed in my answer notes, no matter how reduced this level, once dissolved in an alkaline solution, it is removed (via, for example, CaCO3) and more CO2 can be dissolved. The release of acidic products from organisms in the fish tank can release this stored CO2. $\endgroup$
    – AJKOER
    Commented Dec 23, 2020 at 16:44
  • $\begingroup$ That makes sense, but my question isn't about the total amount of CO2 in the water, but rather the fate of an individual bubble. My observation is that if I take a fresh tank, which could absorb many, many grams of CO2, and trap just a single CO2 bubble under a bell in that tank, the bubble will be mostly dissolved in about 30 seconds and then get no smaller. Surely this isn't because the solution is saturated, because adding a second bubble the same thing happens: rapidly mostly dissolved, then no further visible process. Why is that? $\endgroup$
    – Phil Frost
    Commented Dec 23, 2020 at 16:55
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    $\begingroup$ In the frame of the question posed by OP, this is waste of CO2. $\endgroup$
    – Alchimista
    Commented Dec 24, 2020 at 9:08

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