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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  
determinations lead to the same answer?

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

Therefore:   much ado about nothing.

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
>>
>> 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:
>>
>> 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  
>> the tests and gadgets.
>>
>>
>> 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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