Errors in pH-kH-CO2 - Quantified! - The Planted Tank Forum
 
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post #1 of 5 (permalink) Old 09-07-2004, 06:00 PM Thread Starter
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Errors in pH-kH-CO2 - Quantified!

OK, since we killed this in a prior thread, I thought this should be the first post in a new thread. One point I want everyone to understand though - the online CO2 calculator appears to use incorrect conversions between dKH and ppm HCO3-, so it is not "right" even if the numbers sometimes agree with reality.

After the discussions in that thread regarding errors and limitations in the pH-kH-CO2 relationship, I was determined to either do the experiment OR find a prior example of the experiment (why duplicate what's been done). I stumbled on a VERY powerful program put out by the USGS which models aqueous systems in a very analytically correct way (addresses activities). It is called PHREEQC and is available for most computer formats and has a web version (webPHREEQC).

I used the program to run a simulation of aquarium water at low and high alkalinities (4dKH and 7dKH) and looked at the resulting pH and dissolved CO2 levels when various amounts of CO2 are added to the system. Since the system takes into account activity, the concentrations of ALL ions in the system are important. I took my local water utility report and general planted tank parameters for ions as a starting point for the low dKH system. For the high dKH system I assumed most ions would be present at higher levels as well (liquid rock).

I made the assumption that the units for dKH are based on CaCO3 (all of my references seem to state this, though Chris evidently found one that said CaO).

Here are the results:

dKH = 4:
pH CO2 (ppm)
6.0 120
6.2 75
6.4 47
6.6 29
6.8 18
7.0 12
7.2 7.2
7.4 4.5
7.6 2.8
7.8 1.8
8.0 1.1

dKH = 7:
pH CO2(ppm)
6.0 197
6.2 124
6.4 78
6.6 49
6.8 31
7.0 19
7.2 12
7.4 7.5
7.6 4.7
7.8 3.0
8.0 1.9


Now the important part: the comparison to Chuck Gadd's online calculator (CG 4 represents his prediction at an alkalinity of 4):
pH CG 4 %err(4) CG 7 %err(7)
6.0 120 0.0 210 6.5
6.2 75 -0.1 133 7.1
6.4 48 2.1 84 8.3
6.6 30 1.9 53 7.9
6.8 19 3.1 34 9.8
7.0 12 4.0 21 9.7
7.2 7.6 5.2 13 8.3
7.4 4.8 6.1 8.4 11.6
7.6 3 5.9 5.3 11.2
7.8 1.9 7.2 3.4 13.1
8.0 1.2 8.1 2.1 13.1

As you can see above (I hope), the error comes close to 10% (overestimated by CG's method) for typical planted aquaria desired CO2 levels at the higher dKH value. I will agree that the error in this case seems unimportant for all CO2 levels at the low dKH value. This is not too surprising - the solubility of gases does decrease as the ionic strength (total conc of all dissolved ions) increases, so if this is not taken into account the CO2 level will be overestimated.

FYI, here are my parameters:

low alkalinity:
units ppm
pH 8
pe 4
density 0.995
temp 25
Ca 40
Mg 12
Na 30
K 10
Cl 70
Alkalinity 86 as HCO3-
S(6) 29
Fe(2) 5
N(5) 10

high alkalinity:
units ppm
pH 8
pe 4
density 0.995
temp 25
Ca 120
Mg 30
Na 300
K 10
Cl 550
Alkalinity 150 as HCO3-
S(6) 70
Fe(2) 5
N(5) 10

It is possible using this program to generate the entire pH-kH-CO2 table, but it is tedious. The above alone took me over an hour (not counting the couple of hours learning to use the program).

I now return you to your regularly scheduled program

Kevin

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72g bowfront planted, CO2, 4x - T5HO, Eheim 2213 and 2217, 2 angels, pristella tetras, blue tetras, betta, albino bristlenose pleco, albino cories. Sword, vals, hygros, ludwigias, java moss and fern, anubias

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post #2 of 5 (permalink) Old 09-07-2004, 11:07 PM
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it should be pretty easy to modify the existing excel spreadsheet.
I can't do it though... -sorry, I slept half way reading...

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post #3 of 5 (permalink) Old 09-08-2004, 01:11 AM
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I don't want to throw water on all your fine work Kevin but with current test kits for kH and pH that most of us use the error factor is much larger than the difference between Chuck's chart and your findings.
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post #4 of 5 (permalink) Old 09-08-2004, 02:22 AM
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Glad to see this topic be expanded. My knowledge became limited in working with ionic strength for solutions and just decided to quit while I was ahead. Very nice though to see everything pull together. Good job!

It is at least nice to know the real numbers. Using the false equations are only compounding our errors. But yeah the error is not that huge though.

Here's a good link that shows 1 dKH is equal to 10 mg/l CaO. http://www.thekrib.com/Plants/CO2/ha...arryfrank.html I cannot fully trust it though since I've found many aquariums sites teaching chemistry to be quite poor. I want to hear Kevin, about the sources that say dKH is in CaCO3. Anyway, CaO works consistently with the math/chemistry that finds the 17.8 factor to convert dKH into ppm CaCO3. They also found the same molarity of HCO3- that 1 dKH causes as we found in the other thread. I hope this doesn't mean everything above is wrong now.

Could you just use a TDS meter as a way to cover all the bases with ionic activity?

Last edited by Rolo; 09-08-2004 at 06:28 AM.
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post #5 of 5 (permalink) Old 09-08-2004, 12:16 PM Thread Starter
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Quote:
Originally Posted by Rolo
It is at least nice to know the real numbers. Using the false equations are only compounding our errors. But yeah the error is not that huge though.

Here's a good link that shows 1 dKH is equal to 10 mg/l CaO. http://www.thekrib.com/Plants/CO2/ha...arryfrank.html I cannot fully trust it though since I've found many aquariums sites teaching chemistry to be quite poor. I want to hear Kevin, about the sources that say dKH is in CaCO3. Anyway, CaO works consistently with the math/chemistry that finds the 17.8 factor to convert dKH into ppm CaCO3. They also found the same molarity of HCO3- that 1 dKH causes as we found in the other thread. I hope this doesn't mean everything above is wrong now.
That makes sense now: 10mg/l CaO * (1mol CaO/56.0g) * (1mol CaCO3/1mol CaO) * (100.0g CaCO3/1mol CaCO3) = 17.9mg/l CaCO3

Again, this is the chemistry equivalent of reporting dollars as euros, etc.

Quote:
Originally Posted by Rolo
Could you just use a TDS meter as a way to cover all the bases with ionic activity?
Since the TDS does not speciate the ions, it would be difficult to still use the PHREEQC program - it asks for the concentration of each individually.

Also, Rex pointed out that the errors in our test kits are greater than this. I would add that usually we would overestimate dkH (since you are going for a color change - sometimes you might not need a whole drop). This would make the CO2 level from the table high to start with - then add the up to 10% error inherent in the mistake and you are pretty far off. You might think you have 11ppm CO2 (6.0dkH, 7.2pH), but with the two errors you might only have 8 or 9ppm.

Online sources for dKH as CaCO3: Lamotte, Advanced Aquarist (near the end under "units of alkalinity")

Kevin

Kevin

72g bowfront planted, CO2, 4x - T5HO, Eheim 2213 and 2217, 2 angels, pristella tetras, blue tetras, betta, albino bristlenose pleco, albino cories. Sword, vals, hygros, ludwigias, java moss and fern, anubias

2g Mac-quarium. Clown gravel, fluorescent plastic plants, and 2 guppies.
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