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