pH/dHK/CO2 formula?

BradB

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Wikipedia gives me the formula (without a source) for pH (p), CO2 (c) in ppm and alkalinity in dKH (a):
c = 3a × 10^(7-p)

If this is right and I haven't done anything embarrassing with algebra, I get the more useful:
p = log10(3a) - log10(c) + 7

So a tank with a high alkalinity (10 dKH) and no more CO2 than outside air (409.8ppm) should have a pH of 5.9 which I know is wrong.

My first assumption is I made an algebra error, so I double checked this with:

Which gives me a much more complicated equation with natural logs, but I still get a pH of 5.9

I've seen tables, but having a formula for this would be useful to me.
 

Randy Holmes-Farley

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Wikipedia gives me the formula (without a source) for pH (p), CO2 (c) in ppm and alkalinity in dKH (a):
c = 3a × 10^(7-p)

If this is right and I haven't done anything embarrassing with algebra, I get the more useful:
p = log10(3a) - log10(c) + 7

So a tank with a high alkalinity (10 dKH) and no more CO2 than outside air (409.8ppm) should have a pH of 5.9 which I know is wrong.

My first assumption is I made an algebra error, so I double checked this with:

Which gives me a much more complicated equation with natural logs, but I still get a pH of 5.9

I've seen tables, but having a formula for this would be useful to me.


The relationship is not as simple as you post. It is not a diy calculation, but there are online calculators:


and the link to the equation he uses:

 
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arking_mark

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If your looking into the pH/CO2/Alk relationship I suggest using the Python Library: PyCO2SYS
 
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BradB

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What you posted is more useful, but I found my mistake. If I plug in the pH of 5.9 that I got with 10dKH into Randy's link, it gives me a CO2 level of 178ppm - less than half the CO2 level I used.

I assumed the CO2 level in ppm in the tank would be the same as in the atmosphere, as well as the O2 and Nitrogen. But the atmosphere is 78% Nitrogen. Obviously, my tank's water is not 78% Nitrogen. So the CO2 level in my tank is probably much lower than the CO2 level in the room as well.
 

Randy Holmes-Farley

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The CO2 in the water does not match the air, even at equilibrium.

I show a graph of the relationship between total alk and pH at a few different CO2 levels in the air here:


it uses this equation that you must know the constants K1, K2 and KH, and then determine the relationship using excel, rather than trying to exactly solve the equation.

Alk = (K1KHPCO2 / [H+]) + 2(K1K2KHPCO2 / [H+]2)

1632774190377.png
 

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