CO2: dissolved CO2 and the pH scale
Dissolved carbon dioxide is correlated with the pH scale. The carbon dioxide dissolved in water has even more effect than the oxygen. Oxygen remains as an O2 molecule, whether it's in its gas phase or in solution, but when CO2 is dissolved in water, a small proportion of it reacts chemically with H2O to form carbonic acid, H2CO3. (There's no mystery about that: just add up the six atoms.) In water carbonic acid dissociates rapidly to form a H+ ion and HCO2 (bicarbonate), so it affects the carbonate equilibrium, and pH values change as a result.
Dissolved CO2 lowers the average pH of rainwater to 5.7, even where "acid rain" caused by pollution isn't a factor. The gentle acidity of rainwater is a major source for the weathering of minerals, which the carbonic acid leaches from rocks and which eventually find their way to the ocean.
Bicarbonate. In waters that are neither strongly acid nor alkaline, (and also in tissue fluids in your fish) most of the carbon exists as bicarbonate ions rather than as dissolved CO2. This carbonate reservoir is the underlying reason why water holds so much more CO2 than oxygen...
Let's ignore that bicarbonate for a moment. What about that H+ ion? Does it look familiar somehow? You know that the pH value of water is a measure of the water's acidity or alkalinity. This could be stated another way: the pH is at the same time a measure of the ratio of hydrogen ions (H+) to hydroxyl ions (OH-). At any moment, a minute fraction of the molecules of water are temporarily dissociated, giving a free hydrogen ion with a positive charge (H+) and a hydroxyl radical with a negative charge (OH-). That H+ ion (it's a proton) doesn't remain free for long. It constantly forms and breaks weak bonds with surrounding water molecules, forming an unstable hydronium ion, H3O, which has a positive charge. Such charged hydroxide ions and protons play essential roles in all kinds of vital acid-base chemistry, pumping ions across biological membranes or regulating cellular acidity, or providing energy in photosynthesis.
Let me emphasize that only a tiny fraction of the H2O molecules are broken into these two ions. In pure distilled water, which is "neutral," the hydrogen ions (H+) are just equivalent to the hydroxyl (OH-). In water that is "acidic" there are more hydrogen ions, and in "basic" or "alkaline" water the hydroxyl ions predominate. Acidic water will have a pH that tests below 7.0, and alkaline water will test above pH 7.0.
Adjusting pH values can be tricky and rarely leads to long-term success and stability. Sometimes the motivation for lowering the pH is to breed fish that are said to require a pH below 7.0. Attempting to adjust the pH in water that has a strong carbonate buffer can feel like trying to submerge a beach ball. Phosphate pH buffers are dis-commended in planted aquaria, even by the manufacturers. See the results of a search for the ingredients of Aquarium Pharmaceuticals' "Proper pH7.0" in the Skeptical Aquarist's material on water conditioners.
Recent experiments are showing that environmental cues for fishes' gonad maturation are connected to decreases in water conductivity rather than to low pH values themselves. Reducing the total dissolved solids (TDS) is a better way to go; some methods for water softening have their own page in the "Filtration" folder here.
The balance between KH and CO2 results in pH. The pH can also be considered as the result of the balance between the CO2 level and the alkalinity or "KH" ("carbonate hardness"). Just as you'd imagine, this interrelationship can be tabulated. One widely-used chart of KH and pH giving corresponding CO2 levels can be found in George Booth's discussion in the context of CO2 injection, archived at Bruce Hallman's website.
The pH/"KH"/CO2 charts have some failings, however. The charts commonly used seem to overestimate actual CO2 levels, by as much as 20%. They don't take into account various biogenic acids, aside from carbon dioxide. Or any humic acids, tannins and the like. And all bets are off if part of your buffer is based on phosphates. Details of CO2 and hardness have been discussed at length in extracts from the Aquatic-Plants Digest archived The Krib, where you can find out "All you ever wanted to know about CO2 but were afraid to ask".
The most important thing— more important than blindly reading CO2 values off the tables— is to realize that the three parameters cannot be disconnected. There's a good explanation of "alkalinity"— the ability of buffered water to resist acidity— contrasted with "hardness" in Adrian Tappin's notes on "Water Chemistry" at his site "Home of the Rainbowfish".
To return to carbon dioxide, when CO2 is dissolved in water, the carbon can participate in three further forms: some is immediately dissociated as carbonic acid, and it's then rapidly incorporated into bicarbonates and carbonates, both of calcium and of magnesium. You'll follow more material about them in the notes on dissolved minerals.
Your drinking water straight from the tap is likely to have temporary higher levels of all the atmospheric gases, because it has recently been under pressure, until it was released from the tap, and it was probably quite cold. Conceivably, well water could either be supersaturated with CO2, thus depressing the pH value, or conversely it could be depleted, thus temporarily raising it; if you have well water, letting it sit for 24 hours is always a wise fishkeeping precaution.
I recently tested New York's soft tapwater, straight from the tap into the measuring vial, and I got pH 7.0 or 7.2. Then I took a second sample, capped the vial and shook it vigorously for a full minute. It re-tested at pH 6.2. Either my tapwater the other morning got depleted of CO2 on its way here in the watermains, or possibly I super-saturated the water with CO2 (and other atmospheric gases) by shaking it.
CO2, nutrients and light. In any group of factors that are necessary for the growth of an organism, the factor that is in the shortest supply becomes the "limiting factor." This is clear: all the other factors may be present for additional growth, but the one missing necessary factor puts the cap on what's possible. How many cakes can you bake with 100 dozen eggs and one cup of sugar?
If plant growth is strong enough in the presence of nutrients and sufficient light, CO2 could become the limiting factor. Various symptoms exhibited by plants in sufficient light, with sufficient carbon dioxide, but suffering from the limiting factor of a mineral "deficiency" are well-known: a good description of the range of symptoms of nutrient deficiency is at The Krib.
If carbon dioxide itself is the limiting factor, nutrients and light can still be present in excess amounts, but plants can't use them. Your decision, now that supplementary CO2 diffusion is an available option, is whether you want more surface water movement in order to bring more CO2-depleted water in contact with air, so that atmospheric CO2 will diffuse into the water. Or alternately, whether you want to use a CO2 diffuser to bubble CO2 through the water, and consequently whether you want to minimize diffusive interaction between atmosphere and water surface. The additional carbon dioxide will also scavenge carbonates, so the pH will drop, because CO2 is involved in the CO2/carbonates/pH balance as well.
Still, beyond a certain maximum level of CO2 some other factor limiting plant growth will begin to operate. In an aquarium with fish and biofilm and decay processes all contributing ammonia and other nitrogenous waste, nitrogen is unlikely to become that limiting factor. But more intense light may be called for. Or fertilizer.