# Re: [APD] Interesting idea

```Its not much ado about nothing, not for me.  I know they should give the
same answer, no question there.  Obviously I am treating the
10exp(pH-pH) function incorrectly and am wondering  /how./  Are you
using 10 to the power of the difference, ie. 10^(difference)?

As posted below, this is exactly what I am doing.  Where am I going wrong? :

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

Now, when I do what you did, 10exp.63=4.2657 that checks so obviously we are doing the same math, as in 10 to the power of the difference.

so, for fun again:
ppm CO2= 3*kH*10exp(7-pH)
= 3*5*10exp(1.1)
=188.8

or:
ppm CO2= 12.839*kH*10exp(6.37-pH)
= 12.839*5*10exp(.47) -->note, I was using a slightly different pka since my water is ~76F
=189.5

Pretty close adn all well and good, but my original example uses someone elses formula with a 15.969 constant rather than a 12.839.  Either way, I can't believe I have ~200ppm CO2 in my tank with fish and BBA:)  kH is from Lamotte and pH from calibrated probe.

I/m not trying to be horribly precise but obviously something is wrong with this.  Hence, the reason the kH/pH relationship does not work in our tanks with many other buffers and acids.  This may well work for a buffered RO/DI solution and a probe.

Thanks,
Dennis

Vaughn Hopkins wrote:
> 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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>>> Aquatic-Plants at actwin_com
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>>>
>>>
>>>
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