# Re: [APD] Interesting idea

```Odd, I think the 12 versio is the only one no one subscribes to. It was originally developed as an approximation and eschewed for one based more closely onthings like molecular weight. Coming closer to the 3 version is probably not a test of accuracy since that was developed as an appriximation of a finnish chart.

The later discussions were over which of the 15 versions were more accurate -- I think the 3 and the 12 pretty much dropped out.

But in this hobby, things linger like an old man's underwear.

sh

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

http://www.aquatic-gardeners.org/convention.html

----- Original Message ----
From: Vaughn Hopkins <hoppycalif at yahoo_com>
To: aquatic plants digest <aquatic-plants at actwin_com>
Sent: Wednesday, October 18, 2006 8:55:50 PM
Subject: Re: [APD] Interesting idea

Just for the fun of it I tried something:  Make two determinations of
ppm of CO2, by measuring pH and KH.  Now, the question is, do the two

ppm CO2=3*KH*10exp(7-pH)    and  ppmCO2=12.839*KH*10exp(6.37-pH)

Assume the ppm is the same for both:    Therefore, 3*KH*10exp(7-pH)
=12.839*KH*10exp(6.37-pH)
The KH's cancel of both sides of the equation.    So, 3*10exp(7-pH)
=12.839*10exp(6.37-pH)
12.839 / 3 =  10exp(7-pH-6.37+pH)          The pH's cancel.
Leaving:  12.839 / 3 = 10exp(7-6.37) = 10exp.63
12.839 / 3 = 4.2796     10exp.63 =  4.2658

Therefore, within the rounding off of the constants, the two
equations are identical.  They must give the same result for any KH
and pH, within a small error due to the rounding off.

If the 12.839 constant were 12.797386, the equations would be the same.

Try it with KH = 4 and pH = 6
ppmCO2 = 3*4*10exp(7-6) = 120
ppmCO2 = 12.797386*4*10exp(6.37-6) = 120
ppmCO2 = 12.839*4*10exp(6.37-6) = 120.39

Vaughn H.

On Oct 18, 2006, at 1:47 PM, Dennis Dietz wrote:

> Then I guess I am the only one unnecessarily confused:)
>
> The .45 is the difference between an approx. pka for 76degree F water,
> 6.35- my CO2 injected pH of 5.9.= .45
>
> Guess I don't know how to do this complicated math but 10^.45 is
> 2.8184
> 2.8184 x kH (mine is 5) = 14.092
> 14.092 x 15.969= 225.04 ppm
>
> If I use the 3.6 constant then I find 50.7 ppm
>
> or Jerry's 3 gives me 42.3 ppm.
>
>
> Am I doing bad math here?
>
> Maybe it means 15.969(kH^(6.35-pH)) which gives me 32.9ppm?
>
> Dennis
>
> S. Hieber wrote:
>> 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:
>>
>> http://aquaticconcepts.thekrib.com/Co2/index.htm#table
>>
>> 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:
>>
>> http://fins.actwin.com/aquatic-plants/month.9707/msg00195.html
>>
>> 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:
>>
>> http://fins.actwin.com/aquatic-plants/month.200301/msg00125.html
>>
>>
>> All of which is great fun but might not make anyone a better
>> gardener than someone that pays more attention to the plants than
>>
>>
>> sh
>>
>> * * * * * * * * *
>> The aquatic plant convention is coming in November:
>>
>> http://www.aquatic-gardeners.org/convention.html
>>
>>
>> ----- 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
>>
>>
>> Scott,
>>     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
>>
>> Hmmm.....
>>
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>>
>
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