The Great Tetraborate Experiment!

[chem geek]

Yes, the boric acid buffering does not contribute the the outgassing of carbon dioxide. This is very similar to CYA since that also does pH buffering (in addition to its primary role as a chlorine buffer) and also does not contribute to CO2 outgassing.

Gee, you guys really like throwing out numbers to explain, don't ya!
OK, here goes. We now know that the ppm number for borates is really a measurement of Boron which has a molecular weight of 10.8117 while the TA is measured as ppm CaCO3 which has a molecular weight of 100.0892 (but remember that CaCO3 is CO3(2-) for alkalinity which counts twice as much as a single charged species such as OH-).

Now the alkalinity from Sodium Borate comes from the following reaction:

B(OH)3 + H2O <--> B(OH)4(-) + H+ pKa is about 9.0

So -log( [B(OH)4(-)] ) + pH + log ( [B(OH)3] ) = 9.0
and at a pH much less than 9, say at 7.5 or so, most borate is in the form of B(OH)3 whereas the alkalinity comes from B(OH)4(-)

30 ppm Borate = 30 mg/l Borate
(30 mg/liter) / ( (1000 mg/g) * 10.8117 g/mole) = 2.775x10^(-3) moles/liter

log( [B(OH)4(-)] ) = pH + log(2.775x10^(-3)) - 9 = -4.06
so [B(OH)4(-)] = 10^(-4.06) moles/liter
technically I should subtract this from the 2.775x10(-3) number and iterate (or solve the equation directly which is what I usually do), but this is an error of only about 4% so I'll ignore it.

So, converting to ppm CaCO3:
(10^(-4.06) moles/liter) * (100.0892 g/mole) * (1000 mg/g) / (2 B/CO3) = 4.4 ppm CaCO3

Unless I did something wrong, it looks to me like they forgot the factor of 2 needed to convert from the alkalinity of single charged B(OH)4(-) to the "twice as much" alkalinity of double charged CO3(2-). Either that or they made a different assumption for pH such as 7.86 which would give me a result of 10. Or they are using an equilibrium constant pKa of 8.64 (that's more likely). As is the usual case, I found a variety of different equilibrium constants from different sources but finally chose the one that I thought was most accurate and also had a temperature dependence that I could derive and put into the spreadsheet.

I had already put the equilibrium equation and constants with temperature dependence into the spreadsheet -- I just didn't hook up all the exact calculations for the different species since that's a pain due to the interations for ionic strength that I have. I'll get to it...

Richard