Calculating CO2 - The Planted Tank Forum
 
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post #1 of 11 (permalink) Old 04-17-2016, 03:37 PM Thread Starter
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Calculating CO2

Hello!

I've recently started to research aquariums and water parameters a bit more in depth than I've ever looked into it before. I'm really enjoying learning about everything! Anyways, I've built an excel spreadsheet to track water parameters such as ammonia, nitrites, nitrates, pH, kH, CO2, and temperature with some line graphs and things.

I'm trying to figure out how to calculate CO2 based on kH and pH!

Now I understand that the formula to calculate CO2 is:
CO2=3*kH*(10^(7-pH))

Additionally, that this formula assumes that kH is measured in degrees not in parts per million (ppm).

I found a formula to convert kH from ppm to degrees. That formula is:
kH (degrees) = 0.056 * kH(ppm)
I'm going to be logging my kH in ppm. I'd like to have a formula to calculate the CO2 automatically in excel based upon the values that I enter for pH and kH.

Nooooow. Here's my question. I'd need to convert kH to degrees inside the equation.

The equation I *think* is the right one is as follows:

CO2 = 3 * (0.056*kH) * (10^(7-pH))

Would that be correct? I'm fairly decent with excel but it's been a loooooong time since I had to do any kind of math or formula related stuff and I'd appreciate some guidance

Also, I've been given to understand that this won't be a 100% accurate value on CO2 levels in the tank, but that it would give a general idea of what they are, yes?

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post #2 of 11 (permalink) Old 04-17-2016, 05:29 PM
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Yes, that should work. If you want to increase the resolution you could extend the decimal place of the multiplier to, 0.0560773999999999968385804976 rather than 0.56.

I prefer to use this equation. CO2 = 12.839 * dKH * 10^(6.37 - pH). That's what I use in my calculator.

Here's a nice write up explaining the chemistry and math behind it's use, Corrected pH-KH-CO2
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post #3 of 11 (permalink) Old 04-17-2016, 05:48 PM Thread Starter
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Quote:
Originally Posted by Zorfox View Post
Yes, that should work. If you want to increase the resolution you could extend the decimal place of the multiplier to, 0.0560773999999999968385804976 rather than 0.56.

I prefer to use this equation. CO2 = 12.839 * dKH * 10^(6.37 - pH). That's what I use in my calculator.

Here's a nice write up explaining the chemistry and math behind it's use, Corrected pH-KH-CO2
Thanks for the information Zorfox!! I especially appreciate the write up on the chemistry behind it! It's been a long time since I've looked at anything like that, but I'm really enjoying learning more about how everything works!

When you say "dKH" in your formula, that refers to degrees kH yes?

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Quote:
Originally Posted by Zorfox View Post
Yes, that should work. If you want to increase the resolution you could extend the decimal place of the multiplier to, 0.0560773999999999968385804976 rather than 0.56.

I prefer to use this equation. CO2 = 12.839 * dKH * 10^(6.37 - pH). That's what I use in my calculator.

Here's a nice write up explaining the chemistry and math behind it's use, Corrected pH-KH-CO2
Also. some of that article may have gone straight over my head LOL do you perhaps have a short explanation for that formula instead of the other?

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post #4 of 11 (permalink) Old 04-17-2016, 07:46 PM
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This calculation works great in a tank with nothing but water. It rarely works in an aquarium with substrate, rocks, wood, fertilizers, and plants.


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post #5 of 11 (permalink) Old 04-17-2016, 08:51 PM Thread Starter
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Quote:
Originally Posted by mistergreen View Post
This calculation works great in a tank with nothing but water. It rarely works in an aquarium with substrate, rocks, wood, fertilizers, and plants.


What would you suggest in that case?

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post #6 of 11 (permalink) Old 04-17-2016, 08:57 PM
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I'm glad you asked for a simple explanation. I learned something trying to explain it!

Basically, PH is a measure of H+ ions. The more H+ you have the more acidic the solution. In pure water there are equal numbers of H+ and hydroxide ions (OH−). So the water is considered neutral.

Acids and bases react with one another until an equilibrium is reached. Example, mixing vinegar (acid) and (baking soda) causes the mixture to bubble and release CO2. When the equilibrium is reached the reaction stops. The solution will either be acidic or alkaline based on the amounts added.

Let's say we add some NH4+ (ammonium) to alkaline water. Remember, alkaline water has lower concentration of H+ and more OH- ions. Well, the positive charge of that NH4+ molecule will react with the extra OH- ions. So the ammonium molecule will lose one of it's H+ resulting in NH3 (ammonia). Sound familiar?

So NH4+ and NH3 can break apart or combine based on the PH of the solution. They are simply losing or gaining one H+ ion. So NH4+ and NH3 are called conjugate pairs. NH4+ is a conjugate acid and NH3 is the conjugate base. Since the reaction can occur in both directions NH4+ is considered a weak acid.

Strong acids such as HCL will only react in one direction. When you add HCL to water the hydrogen falls of forming Cl-. Cl- won't recombine with the H+ in the presence of water.

There are formulas for equilibrium constants for weak acids.

Acid equilibrium
Ka = [H+][A-] / [HA]

Base equilibrium
Kb = [HA][-OH] / [A-]

HA is the weak acid, example NH4+
A- is the conjugate of the acid (NH3)
[-OH] is hydroxide ions

I won't bore you with all the constants and math here. I just realized this post is getting quite long lol.

We can calulate the PH of a solution using a formula called the Henderson Hasselbalch Equation. We can also rearrange this formula to allow us to estimate CO2 levels



It's basically rearranging the basic formulas above to calculate PH.

What the article was about was that we can substitute the weak acid (HA) with CO2 and (A-) with HCO3-

Same as with NH4 and water,
CO2 + H20 <=> H2CO3

Genius really!

However, I was trying to decide how to explain it and noticed a problem with the equation presented. You can't interchangeably use mg/L CaCO3 and mg/L HCO3. Of course I'm a "big boy with google" so I looked into it. Apparently this is old news that I was not aware of. You can google "Corrected pH-KH-CO2" and see several discussion about this. Here is one on this forum which seems to describe it pretty well.

Here is the updated formula which I agree with,

CO2 = 15.65 * dKH * 10^(6.35-pH)

If you have not seen Khan Academy yet you should check it out. I like the tutorials there. They explain thing in plain english from beginning to end. It's like a free online college! Here is a link explaining the Henderson-Hasselbalch equation.

Sorry for stopping the explanation so abruptly. I realized it would simply take far too long lol. I would like to echo what mistergreen said. This is only an estimation since our tanks are not buffered entirely by carbonates.
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post #7 of 11 (permalink) Old 04-17-2016, 09:05 PM Thread Starter
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Quote:
Originally Posted by Zorfox View Post
I'm glad you asked for a simple explanation. I learned something trying to explain it!



Basically, PH is a measure of H+ ions. The more H+ you have the more acidic the solution. In pure water there are equal numbers of H+ and hydroxide ions (OH−). So the water is considered neutral.



Acids and bases react with one another until an equilibrium is reached. Example, mixing vinegar (acid) and (baking soda) causes the mixture to bubble and release CO2. When the equilibrium is reached the reaction stops. The solution will either be acidic or alkaline based on the amounts added.



Let's say we add some NH4+ (ammonium) to alkaline water. Remember, alkaline water has lower concentration of H+ and more OH- ions. Well, the positive charge of that NH4+ molecule will react with the extra OH- ions. So the ammonium molecule will lose one of it's H+ resulting in NH3 (ammonia). Sound familiar?



So NH4+ and NH3 can break apart or combine based on the PH of the solution. They are simply losing or gaining one H+ ion. So NH4+ and NH3 are called conjugate pairs. NH4+ is a conjugate acid and NH3 is the conjugate base. Since the reaction can occur in both directions NH4+ is considered a weak acid.



Strong acids such as HCL will only react in one direction. When you add HCL to water the hydrogen falls of forming Cl-. Cl- won't recombine with the H+ in the presence of water.



There are formulas for equilibrium constants for weak acids.



Acid equilibrium

Ka = [H+][A-] / [HA]



Base equilibrium

Kb = [HA][-OH] / [A-]



HA is the weak acid, example NH4+

A- is the conjugate of the acid (NH3)

[-OH] is hydroxide ions



I won't bore you with all the constants and math here. I just realized this post is getting quite long lol.



We can calulate the PH of a solution using a formula called the Henderson Hasselbalch Equation. We can also rearrange this formula to allow us to estimate CO2 levels







It's basically rearranging the basic formulas above to calculate PH.



What the article was about was that we can substitute the weak acid (HA) with CO2 and (A-) with HCO3-



Same as with NH4 and water,

CO2 + H20 <=> H2CO3



Genius really!



However, I was trying to decide how to explain it and noticed a problem with the equation presented. You can't interchangeably use mg/L CaCO3 and mg/L HCO3. Of course I'm a "big boy with google" so I looked into it. Apparently this is old news that I was not aware of. You can google "Corrected pH-KH-CO2" and see several discussion about this. Here is one on this forum which seems to describe it pretty well.



Here is the updated formula which I agree with,



CO2 = 15.65 * dKH * 10^(6.35-pH)



If you have not seen Khan Academy yet you should check it out. I like the tutorials there. They explain thing in plain english from beginning to end. It's like a free online college! Here is a link explaining the Henderson-Hasselbalch equation.



Sorry for stopping the explanation so abruptly. I realized it would simply take far too long lol. I would like to echo what mistergreen said. This is only an estimation since our tanks are not buffered entirely by carbonates.


Thanks for the explanation though!!

I'm not really looking for a precise value of CO2. At least not as precise as I would want for something like ammonia or pH.

What I'm looking for is some idea of what it might be around, as I'm planning on doing a low tech setup but one or two of the plants I'm going to use don't need tons of CO2 but a bit isn't bad so I'm gonna try out liquid. If that works then I'll stick to that. If not I might invest in an injector. Not really wanting to do that though since it'll be a small set up and I don't want to spend a ridiculous amount!

I am and always will be the optimist. The hoper of far-flung hopes and the dreamer of improbable dreams. The Doctor, Season 1, Episode 213. Optimist
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post #8 of 11 (permalink) Old 04-17-2016, 09:15 PM
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Excel works nice for low tech setups. Nothing wrong with that route. The CO2 measures won't change using it though. You're not actually adding CO2 gas with it. It is however a decent carbon source alternative. The CO2 charts are NEVER fully accurate. They are intended to give a ball park idea of where your are. They can also be used to track trends of increasing or decreasing CO2 levels, which IMO, is more important than the actual level itself. At least you have an idea of the basic chemistry behind CO2. There's nothing wrong with learning things you may never need.
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post #9 of 11 (permalink) Old 04-17-2016, 09:18 PM Thread Starter
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Quote:
Originally Posted by Zorfox View Post
Excel works nice for low tech setups. Nothing wrong with that route. The CO2 measures won't change using it though. You're not actually adding CO2 gas with it. It is however a decent carbon source alternative. The CO2 charts are NEVER fully accurate. They are intended to give a ball park idea of where your are. They can also be used to track trends of increasing or decreasing CO2 levels, which IMO, is more important than the actual level itself. At least you have an idea of the basic chemistry behind CO2. There's nothing wrong with learning things you may never need.


Always true!! I'm enjoying learning everything. I'm still in the planning phase but I'm trying to research everything as much as possible. I hadn't realized the excel wouldn't be accounted for like co2! But like you said probably not a bad idea to have some idea of what's going on in there!

I am and always will be the optimist. The hoper of far-flung hopes and the dreamer of improbable dreams. The Doctor, Season 1, Episode 213. Optimist
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post #10 of 11 (permalink) Old 04-17-2016, 09:47 PM
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Originally Posted by shellsie View Post
What would you suggest in that case?
I would suggest not keeping track of CO2 or use an underwater CO2 sensor. You'd be off as much as 30ppm off in an aquarium environment since lots of things affect the pH & kH beside CO2.


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post #11 of 11 (permalink) Old 04-17-2016, 09:52 PM Thread Starter
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Quote:
Originally Posted by mistergreen View Post
I would suggest not keeping track of CO2 or use an underwater CO2 sensor. You'd be off as much as 30ppm off in an aquarium environment since lots of things affect the pH & kH beside CO2.


Alright thanks!!

I am and always will be the optimist. The hoper of far-flung hopes and the dreamer of improbable dreams. The Doctor, Season 1, Episode 213. Optimist
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