Hi Dave,
Thanks for supporting APC!
The relationship between pH, KH and CO2 is quite complex. I'll try and summarize it here using a quote from someone on the APD quite a long time ago.
Changing pH necessarily involves changing KH, CO2 concentration or both. The 3 parameters are related via the Henderson-Hasselbalch equation:
pH = pKa + log([HCO3-]/[H2CO3])
where pKa is a constant (6.35 in FW), [HCO3-] is bicarbonate ion concentration (which is essentially equal to KH in FW), and [H2CO3] is effectively the dissolved CO2 concentration. This equation holds irrespective of whether other buffers are present or not.
Some methods of changing pH directly target KH (e.g. adding baking soda) or CO2 (injecting). Other methods also change KH (and CO2 in the short term) but do so slightly less directly and hence wouldn't necessarily be thought of in terms of manipulating these variables. For example, adding NaOH to increase pH wouldn't normally be described as increasing KH or reducing dissolved CO2, but that is nonetheless what happens. The removal of H+ ions by combination with OH- ions causes more H2CO3 to ionise, reducing dissolved CO2 (temporarily) and increasing HCO3-. This increases the numerator and reduces the denominator of the log term in eq.1 and allows the equation to balance at a higher pH. The reduction in CO2 (and most of the increase in pH) is temporary because the long-term equilibrium level of CO2 in an aquarium is mainly determined by physical and biological processes (exchange with the atmosphere, respiration and photosynthesis), and the end result when all the dust has settled is a (very) small increase in both pH and KH.
So it is true that changing pH is synonymous with changing KH (or CO2 concentration), but perhaps sometimes a bit misleading to put it that way, especially if another buffer is introduced.
Additionally, it may be helpful to use the pH/CO2/KH table as your reference as you try to target a specific CO2 concentration. I've attached it below.
How are you reconstituting the purified water to add back KH?