# Ph profile, co2 and 0kh

#### MrClockOff

##### Member
The formula that I use is CO2 = 12.839 * dKH * 10^(6.37 - pH). Indeed the relationship pH to CO2/dKH is logarithmic, not linear. It is important to understand that also outgassed pH is not a constant, but dependant on KH and ambient air CO2 concentration.
Most importantly, a given pH drop (from degassed) will indicate an X% CO2 increase, irrespective of KH. (pH drops 1.0, means 10 fold CO2 compared to starting CO2, from the above formula). This is also true for KH below 1, from all references that I've seen.
@Yugang could you please elaborate with more details on the formula CO2 = 12.839 * dKH * 10^(6.37 - pH) please?
Please correct me if I'm wrong CO2 - achieved ppm concentration
12.839 - what is this? Initial ppm of CO2 in the water
dKH - carbonate hardness in degrees
10^ what is this?
6.37 - degassed water PH
pH - current PH

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#### _Maq_

##### Member
@MrClockOff , leave the numbers as they are. 12.839 and 6.37 are constants.
(6.37 - pH) is an exponent - power.

#### Yugang

##### Member
@Yugang could you please elaborate with more details on the formula CO2 = 12.839 * dKH * 10^(6.37 - pH) please?
Please correct me if I'm wrong CO2 - achieved ppm concentration
12.839 - what is this? Initial ppm of CO2 in the water
dKH - carbonate hardness in degrees
10^ what is this?
6.37 - degassed water PH
pH - current PH
This formula produces the same CO2 ppm data as the well known pH/KH table.

In my excel spreadsheet it reads =12.839*I\$6*POWER(10,(6.37-F10)) , where cell I6 has the KH and cell F10 has the pH in it.

So indeed 10^ refers to a power of 10. The inverse is a logarithmic.
12.8 and 6.3 are constants, don't worry what exactly they mean other than that they are necessary for the formula. They may be a bit off, depending on the situation, which is not a major worry as we are more concerned with CO2 stability than with the exact value.

I used the formula, rather than pH/KH table, as I wanted to do some modelling calculations on pH profile. For most, the pH/KH table is an easier tool. I quoted the formula above because
• it illustrates so clearly that a 1.0 pH drop always (irrespective of KH) represents a 10 fold increase of CO2 ppm. (This is a exponential/logarithmic relationship)
• it illustrates how 10% KH change (at constant pH) represents a 10% CO2 ppm change. (This is a linear relationship)
Once we have this high level understanding what is actually in the pH/KH table, we don't need to reference it that often any more. And, relevant to this thread, the relationship between CO2 and pH does not fundamentally change when KH is low (although strange things happen when KH is exactly, mathematically 0).

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• dw1305, _Maq_ and MrClockOff

#### MrClockOff

##### Member
Awesome explanation! Thank you @Yugang

• dw1305 and Yugang

#### dw1305

##### Expert
UKAPS Team
Hi all,
• it illustrates so clearly that a 1.0 pH drop always (irrespective of KH) represents a 10 fold increase of CO2 ppm. (This is a exponential/logarithmic relationship)
• it illustrates how 10% KH change (at constant pH) represents a 10% CO2 ppm change. (This is a linear relationship)
We have an old thread somewhere. I'll see if I can find it. This one:

@Jose comments in this one <"Question about pressurised CO2 and water disturbance">.

cheers Darrel

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• Yugang