It is actually correct. See below.
The other important part is to realize what standard you are referring to when reporting concentrations.
In Europe, and I presume Canada, degrees are converted to parts per million by 10 mg/L relative to the simple oxide of Ca or Mg (CaO). Here in the States we use the carbonate of calcium as the standard. They are equivalent:
10° x 10 mg CaO/L° = 100 mg/L as CaO. Ca/Ca+O = 71.4% x 100 ppm = 71.4 ppm Ca2+
10° x 17.8 mg CaCO3/L° = 178 mg/L as CaCO3. Ca/Ca+C+3(O) = 40% x 178 ppm = 71.4 ppm Ca2+
You're very right about going into the details. Hardness can be a little difficult to understand. I was just using the simple approah that I have used for hardness. I was basically using your formula in bold italics that was for CaCO3. James from Cali is in the US and I'm in the US; I didn't think that I needed to go into the other ones. I've been using the conversions from The Krib (Aquaria and Tropical Fish)
and my Hagen test kit. I didn't feel that these were needed. I was just a litttle lazy.
These are my conversions from the Hagen Kit:
Multiply GH or KH(mg/L CaCo3) by X 0.056 = dH° or/ou/o/gH°
Multiply GH or KH(mg/L CaCo3) par X 0.07 = Clark H°
Multiply GH or KH(mg/L CaCo3) por X 0.1 = fH°
Multiply GH or KH(mg/L CaCo3) por X 1 = hardness°
X 0.02 = mEq/L
Here's one of the many quotes from the krib. They used the same ones that I use. I believe that these are the ones most used. 1 degree of hardness equals 17.86 ppm. And 1 divided by 17.86 = 0.056. I put the formulas in bold italics and I quote it here. Water Hardness
by larry/creative.net (Larry Frank)
Date: Tue, 16 Dec 1997
After reading all the posts for hardness and alkalinity, I tried to go back through the aquarium literature that I have, and make some sense of all the different definitions, also tried to understand how all this affects CO2 addition. The following is what I came up with. My thanks to Dave (eworobe-at-cc.UManitoba.CA) for his help with understanding alkalinity. Any errors are mine not his.
All fresh water sources contain calcium and magnesium in varying quantities. These are cations with a 2+ charge. They form salts with anions which have a negative charge. The most important of these are bicarbonate (HCO3- ; carbonate CO32- ; and sulfate SO42-.
General Hardness (GH) measures the cations (+ charge); for calcium and magnesium.
Carbonate Hardness (KH) Refers to only the bicarbonate, and carbonate anions(-charge); it does not measures the sulfates and other anions.
Carbonate Hardness is a confusing term because it does refer to hardness, but rather to the alkalinity (the ability of a solution to resist a pH change with an addition of an acid.) from the carbonates and bicarbonates. Other anions (such as hydroxide, borates, silicates, and phosphates) can contribute to the alkalinity. To be absolutely correct, you should NEVER use the term 'KH'; however, this is often refered to in aquarium literature. It should be noted that it is the bicarbonate/carbonate buffering system which provides the majority of the alkalinity in aquariums plant aquariums.
KH and GH are usually are close two each other, but the GH can be the same, higher or lower to the KH depending on the Cations and Anions in the sample. For example, a large amount of NaHCO3 would raise the (KH) and not effect the (GH). A large amount of MgSO4 would raise the (GH) and not the (KH).
Usually, in fresh water most of the cations are calcium and magnesium (In a 3:1 ratio) and most of the anions are carbonates. The levels for (GH) and (KH) will often be similar.
It would make sense to measure the general hardness in # of ions/liter or molarity, but this is not used. The common units found in the literature are degrees of general hardness dGH (GH) from the German system or ppm Ca from CaCO3 . Carbonate hardness (KH) is a term which has nothing to d with hardness, rather it is the amount of carbonate or bicarbonate equivalents which effect the alklinity or acid buffering capacity. (KH) is equated to ppm CO3 from CaCO3
Converting from dGH and dKH to ppm CaCO3 can be accomplished by multiplying by 17.86
How the conversion factors were derived: (GH)
By definition, 1dGH = 10 mg/liter CaO
Atomic Weight Ca = 40, O = 16, CaO = 56
So 10 mg/liter CaO contains 40/56 *10 = 7.143 mg/liter of Ca
By definition ppm Ca is not for elemental calcium but for ppm CaCO3.
Atomic weight CaCO3 = 100
So 7.143 mg/liter of elemental Ca would be expressed as 100/40 * 7.143 = 17.8575 mg/liter(ppm)CaCO3.
1dGH = 17.86 ppm CaCO3 and 7.143 ppm Ca2+.
1 dGH is defined as 10mg/lit CaO this can be related to ppm of CaCO3 as in above. Now the definition for dKH must have come from the amount of carbonate in 17.86 ppm CaCO3 which has nothing to do with GH wich is defined by CaO! Historically GH must have been defined first in terms of CaO; hardness in terms of ppm CaCO3 second, then KH third?
1dKH = 17.86 ppm CaCO3
From above; 1dKH = 17.8575 mg/liter CaCO3. 7.143 mg/liter of this is Ca, the rest ;(17.8575-7.143)= 10.7145mg/liter CO3
1dKH = 10.7145 ppm CO3
CaCO3 forms Ca(HCO3)2 in water at pH less than 10.25 . (Two bicarbonates are formed from each carbonate ion):
CaCO3 + H20 + CO2 ---> Ca(HCO3)2
CO3 mw = 60
HCO3 mw = 61
Therefore 10.7145mg/liter CO3 from CaCO3 (each CO3 carbonate anion forms two HCO3 bicarbonate anions; 61/60*2 *10.7=21.8 mg/liter HCO3
Another way to calculate this is using molarity:
1dKH = 17.86 mg/liter CaCO3
mw CaCO3 = 100
17.86 mg/liter CaCO3 = .179 m Mole CaCO3
This will form 2* .179 m Mole = .358 m Mole
Multipling moles *mw will give mg:
0.358*61(mwHCO3) = 21.8 mg/liter HCO3
1dKH = 21.8 ppm HCO3
How to use these conversion factors:
If you have alkalinity in ppm or hardness in ppm divide by 17.86 to get degrees. If you want to raise the alkalinity by 1dKH using CaCO3: use 17.86 mg CaCO3
If you want to raise the alkalinity by 1dKH using NaHCO3:
mw Na = 23
mw HCO3= 61
mw NaHCO3= 84
1dKH= 21.8 ppm HCO3
21.8 *84/61=30 mg/liter of NaHCO3
0.358 mMoles * 84(mwNaHCO3) = 30 mg/liter of NaHCO3
CO2, pH And Alkalinity from Carbonates
CO2, pH and carbonates are all related by the following three equations:
1. CO2 + H20 <------> H2CO2 (Carbonic Acid)
2. H2CO2 <------> H+ + HCO3- (Bicarbonate)
3. HCO3- <------> H+ + CO32- (Carbonate)
Example of how increasing carbonates will either raise the pH or need counterbalancing CO2 added to maintain the pH level.
If NaHCO2 is added to aquarium water the additional carbonate ions will cause a shift to the left side of equation (2). This will form more carbonic acid extracting a H+ ion and thus raising the pH. The additional carbonic acid will drive equation (1) to the left creating CO2 which will dissapate out of solution bringing equalibrium at a higher pH. In order to maintain equalibrium at the original pH equations (1) and (2) must be shifted back t the right. This can be accomplished with the addition of more CO2 into the aquarium. (Equation (3) becomes important as pH approches 10.25)
These relationships are expressed in the familliar Chart with KH/pH and the amount of CO2 needed in solution to maintain a specific pH. The higher the amount of carbonates/bicarbonates in the aquarium, the more CO2 is needed to maintain a specific pH.
pH 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 7.8 8.0
0.5 | 15 9.3 5.9 3.7 2.4 1.5 .93 .59 .37 .24 .15
1.0 | 30 18.6 11.8 7.4 4.7 3.0 1.7 1.2 .74 .47 .30
1.5 | 44 28 17.6 11.1 7.0 4.4 2.8 1.8 1.11 .70 .44
2.0 | 59 37 24 14.8 9.4 5.9 3.7 2.4 1.48 .94 .59
2.5 | 73 46 30 18.5 11.8 7.3 4.6 3.0 1.85 1.18 .73
3.0 | 87 56 35 22 14.0 8.7 5.6 3.5 2.2 1.40 .87
3.5 | 103 65 41 26 16.4 10.3 6.5 4.1 2.6 1.64 1.03
4.0 | 118 75 47 30 18.7 11.8 7.5 4.7 3.0 1.87 1.18
5.0 | 147 93 59 37 23 14.7 9.3 5.9 3.7 2.3 1.47
6.0 | 177 112 71 45 28 17.7 11.2 7.1 4.5 2.8 1.77
8.0 | 240 149 94 59 37 24 14.9 9.4 5.9 3.7 2.4
10. | 300 186 118 74 47 30 18.6 11.8 7.4 4.7 3.0
15. | 440 280 176 111 70 44 28 17.6 11.1 7.0 4.4
20. | 590 370 240 148 94 59 37 24 14.8 9.4 5.9
CO2 in excess of 40mg/liter is harmful to fish. Using this chart the alkalinity of the water from bicarbonates is balanced against a desired pH using CO2 to control the pH, making sure a unhealthy amount of CO2 is not called for.
by George Booth <booth/hpmtlgb1.lvld.hp.com>
Date: Wed, 17 Dec 1997
Great summary, Larry. I would only like to add the following for those who don't read between the lines:
The pH/KH/CO2 table is based solely on "carbonate hardness".
All KH test kits that I know of measure alkalinity, not true KH.
The CO2 value you get from the table will NOT be accurate if there are other sources of alkalinity in your water besides bicarbonate.
Even CO2 test kits are not accurate in the presence of other sources of alkalinity (phosphates, for sure).
Up to CO2 Plants The Krib This page was last updated 29 October 1998"