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Re: [APD] Interesting idea

Lest anyone get unnecessarily confused, I note that there appears to be a typo in Dennis's presentation of the formula I attributed to Roger, there is an errant ".45" at the start of the exponent -- although ignoring the ".45" does yield the result 225.
Putting that aside let me just say that, if you think how to measure light energy (PAR, wpg, etc.) or what color is water in a bucket are topics for extended discussion, then you'll appreciate that more than one, more than two, more than three. . . formula have been presented for calculating CO2 from KH and pH.
Put simply, the formula that starts with a factor of 3 is more of an approximation; the one I attributed to Roger is less so. And you can fine tune the latter formula if you're really hell bent on fine tuning, with adjustments to the pka value in accordance with temperature. I don't know what pka value or temperatures the "Vaughn" formula assumes. The pka is the equilibrium constant for the dissociation of carbonic acid. The "Vaughn" formula has been presented by George and Karla Booth as is still shown on their excellent website:
and I believe it was intended as a simple and handy formula for approximating results that would be adequate for aquatic gardening purposes. The Booth's might have been aiming toward the results they found in a CO2 table from a Finnish magazine.

At more likely aquarium values for pH given a KH of 5, say, pH 6.9, the one formula yields 22.5 ppm and the other 18.8 ppm. Diff results? Obviously. Which is more accurate, other things being equal?  Well, there is tons of stuff in the archives about the CO2/KH/pH formula and the various versions thereof. Some easy to find, some not so easy. When I used to do the "Stranded" column in _The Aquatic Gardener_ I had reason to pour through the archives for over a year or so (no applause please, I was only in it for the money, which was a shame since it was volunteer work). But it was a learning experience and luckily I can still remember some of what I have read. But more of what I've learned is like the wind, so I went back through the archives and pulled out a few things regarding CO2 and the formulae:
Roger commented on two versions of the formulas, one was "CO2 = 12.839 *KH * 10^(6.37-pH)" and the other was the Booth version using a factor or 3. The version with a factor of 12 at the start was developed by Roger and George as evidenced by this post:
in a later thread, after someone asked about diffs from diff formula, Roger commented:
"When we start throwing formulae around we should keep in mind that there is a 
problem here.  Some people (including myself) disagree with the unit 
conversions that lead to the value of 12.839 in the first formula above.  The 
value of 3 in the second formula is based on the same unit conversion.   
There's fairly extensive discussion of the difference in the archives, but it 
really isn't easy to find.  For the alternate versions replace the first of 
these formulae with
CO2 = 15.664*KH*10^(6.37-pH)
and the second with
CO2 = 3.6*KH*10^(7-pH)
The KH-pH-CO2 charts and tables have never been changed to reflect this 
difference because (1) when you consider all the other possible problems with 
the method the change would be a fairly insignificant improvement (2) because 
George has never agreed and (3) because no one has bothered to do the work to 
recalculate everything.
And Paul Sears commented further when I presented two formulas and asked, which was correct. The two formulas were "12.839*KH*10^(6.37-pH)" and "15.664*KH*10^(6.37-pH) (Roger's" version)". Of these, Paul said much including the following:
". . .To add to the motes and nits, if you want the factor at the
start to lots of decimal places, I make it 15.696 to three places.  :)
That is using accurate atomic weights.
 Now to start reading my KH test kit to four significant figures....
 16*KH*10(6.34-pH) looks good to me for about 27 C."
So the final revision, slightly diff from Roger's and using a factor of 15.696, comes from Paul and it's the one I'll stick with.
Btw, the pka values I stated previously came from Paul Sears, who in turn looked it up in a reference (he doesn't says which reference, but I trust Paul on this). 
Even fruther, btw, Roger's excellent helpful post regarding alkalinity and acids and pH titration is here in this thread:
All of which is great fun but might not make anyone a better gardener than someone that pays more attention to the plants than the tests and gadgets. 

* * * * * * * * * 
The aquatic plant convention is coming in November: 

----- Original Message ----
From: Dennis Dietz <dennisdietz at verizon_net>
To: aquatic plants digest <aquatic-plants at actwin_com>
Sent: Tuesday, October 17, 2006 9:27:02 PM
Subject: Re: [APD] Interesting idea

    for the math challenged, why do I keep getting 225ppm with your 
(Roger's) equation?

15.969 x 5 (kH degrees) x 10^.45 (6.35-5.9)= 225.03

Vaughn's gives me 188.84ppm


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