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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