pH/dHK/CO2 formula?

[BradB]

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:

Logarithmic Equation Calculator

Free log equation calculator - solve log equations step-by-step

www.symbolab.com

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 Verified Community Expert]

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:

Logarithmic Equation Calculator

Free log equation calculator - solve log equations step-by-step

www.symbolab.com

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:

Marine CO2 Level Calculator

Aquarium calculator; Estimate the carbon dioxide (CO2) concentration given a few relevant parameters.

www.hamzasreef.com

and the link to the equation he uses:

https://www.ncei.noaa.gov/access/ocean-carbon-data-system/oceans/glodap/Mojica_Millero_2002.pdf

 

[arking_mark]

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

 

[BradB]

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 Verified Community Expert]

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:

Chemistry And The Aquarium: The Relationship Between Alkalinity And pH

Randy answers many questions in this complex relationship.

reefs.com

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)