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**To**:**aquatic plants digest <aquatic-plants at actwin_com>****Subject**:**Re: [APD] Interesting idea****From**:**Vaughn Hopkins <hoppycalif at yahoo_com>**- Date: Wed, 18 Oct 2006 20:55:50 -0700
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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..... >> >> _______________________________________________ >> Aquatic-Plants mailing list >> Aquatic-Plants at actwin_com >> http://www.actwin.com/mailman/listinfo/aquatic-plants >> >> > > _______________________________________________ > Aquatic-Plants mailing list > Aquatic-Plants at actwin_com > http://www.actwin.com/mailman/listinfo/aquatic-plants _______________________________________________ Aquatic-Plants mailing list Aquatic-Plants at actwin_com http://www.actwin.com/mailman/listinfo/aquatic-plants

**Follow-Ups**:**Re: [APD] Interesting idea***From:*Dennis Dietz

**References**:**Re: [APD] Interesting idea***From:*S. Hieber

**Re: [APD] Interesting idea***From:*Dennis Dietz

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