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I was on a site that had an online calculator for CO2 level based on reading the pH of the water then shaking the sample until the CO2 was driven out and reading the pH again. Unfortunately something in their formula was wrong and the answer didn't make sense.

I did a little algebra and came up with this equation.

Let a = pH before shaking
Let b = pH after shaking

CO2 = 2 x 10^7-b / 10^7-a

Could anyone tell me if there is any flaw in my assumptions or math. I assumed that the CO2 level after shaking is equal to 2ppm ? because that is the value I get by the formula used in the standard charts based on KH and pH when I test my tap water.

I have an acidic substrate so the standard formula doesn't work for me, and I'm too lazy and cheap to mess with a drop checker.
 

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There's too many variable in aquarium water to use the pH/KH/CO2 chart/calculator. There are phosphates, tannins, acids, bases, etc. that will give you a false CO2 measurement which, in most instances, indicates that you have more CO2 than you actually have in your aquarium. A drop checker is the best way to monitor your CO2 level unless you spend $$$ for testing equipment.

From: http://www.csd.net/~cgadd/aqua/art_plant_co2chart.htm
This is the section that contains the information to help you understand this relationship a little better.

"The pH-KH-CO2 Relationship
pH, KH, and CO2 have a fixed relationship as long as carbonate is the only buffer present (no phosphate buffers like pH-UP and- DOWN, Discus Buffer, etc). There are some parts of the country that have high levels of phosphates in their water supply. For those cases, determining CO2 levels will be difficult, as the phosphate will throw off the pH-KH-CO2 relationship, which means the CO2 charts and calculator below won't work. Note that the commercially available CO2 test kits will also be invalidated by the phosphates.

NOTE: If you aren't adding CO2 to your water, and the CO2 level based on the pH and KH indicates more than 5ppm, then it is very likely that some other buffer (such as phosphate) is present in your water. In an inhabited aquarium, the amount of CO2 produced by the fish will not have an effect on CO2 levels in the water. Any excess CO2 created by fish will dissipate into the air, leaving a fairly constant CO2 level of about 3-4ppm. If you test your pH and KH, and without adding any CO2, the chart says you've got 20ppm CO2, don't believe it.

In some cases, water coming right from the tap can contain very high or very low levels of CO2. This can result in tap water with a high KH, and low pH. But, in just a few hours, that excess CO2 will dissipate from the water, leaving the normal 3-4ppm, and the pH will rise. Sometimes, the water might come from the tap with extremely little CO2, which can result in tap water with a low KH, and a very high pH. Again, after a few hours, the CO2 level will equalize, and the water will end up with 3-4ppm CO2.

CO2/pH/KH calculator and chart
NOTE: This calculator (and the chart based on this formula) will only work if your water is carbonate buffered. If your water contains high levels of phosphates, it will alter your water properties, and invalidate these CO2 calculations.

You can not alter the KH levels other than by adding or removing carbonate. You can not alter the CO2 levels other than by adding or removing CO2.

Adding certain "pH altering additives" can cause much confusion as well. Additives like "Proper pH 7.0" which force the pH to a certain value completely invalidate the CO2 / KH / pH relationship. This is because these pH altering additives contain phosphates. Phosphates replace the carbonates in the buffering system. And the CO2 / KH / pH relationship is only valid in a system that is buffered by Carbonates.

There is on case I've seen where the addition of CO2 resulted in an increase in KH. This can happen when you have something in the tank that dissolves carbonate into the water. Seashells, crushed coral, and many gravels and rocks will do this. With the addition of CO2, the water turns more acidic, which will increase the dissolving of the minerals. It appears that increasing CO2 raises the KH, which isn't really the case. The dissolving minerals raise the KH, and the increase in KH results in an increase in pH. In a system using a pH probe and controller to regulate CO2 levels, this can have fatal consequences, since the pH controller will keep trying to lower the pH, but as more CO2 is dissolved, it lowers the pH, which raises the KH, which raises the pH. So you now have more CO2, but the same pH. So the controller adds even MORE co2. And it will keep going. So it's important to know your KH whenever using pH to judge CO2 levels."
 

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I commented on this in the other forum where you posed the question, but to summarize, any formula that relies on calculating ppm of CO2 from the change in pH from "degassed" water to "in tank" water will fail, because we have no way to know how much CO2 is in the "degassed" water.
 

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Here is a simple safe way to estimate the correct pH change

Here is a simple safe way to estimate the correct pH change to get to the required ppm of CO2 for any tank buffer system.

Get a selzer siphon. Fill it with 1 L of distilled water. Charge it with one 8 gram CO2 cartridge and put it in the refrigerator overnight.

This is your standard 8000ppm solution.

To figure out how much CO2 to add to get to 20 ppm use this calculation:

Qty = 20mg./L * 3.78 L/gal *TV / 8

Qty = the volume of the 8000 ppm solution to add in ml.
TV is your tank volume in US gallons.

Now here is what you do.

Measure the pH before adding the calculated amount of CO2 then measure the pH after adding the CO2. The difference is the pH change need to bring your tank to 20 ppm CO2.

Now here is a thought. Why even bother, just add the right amount at lights on. The pH will change when you add the CO2 but if you have a well buffered system, it will not change much!
 

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Buffering normally means that the pH of a solution will remain the same with small additions of acids or bases. In our aquarium we use KH to keep the pH higher than it would otherwise be, but that doesn't prevent acids from dropping the pH. If I increase the concentration of CO2 in a container of water, whether it is an aquarium or a beaker, by a factor of 10, the pH will drop by 1.0, assuming that water contains nothing else that affects pH except carbonates and CO2. That will be true if the KH is 0.1, 1 or 10 dKH. So KH doesn't really buffer the water in the usual meaning of the word.
 
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