You are missing the point that the FC measurement itself is in ppm Cl
2 units and that chlorine gas is defined as 100% Available Chlorine even though only ONE of its two chlorine atoms results in chlorine in the pool. This is why Trichlor can be around 90% Available Chlorine (99% purity of 91.5% Available Chlorine) where it only has half that or 45% chlorine atoms by weight in that molecule. The same is true for sodium hypochlorite where the chlorine atom is only 35.453/74.442 = 47.6% but in terms of the DEFINITION of Weight % Available Chlorine you have to multiply this by a factor of 2 to get 95.2% that is the Weight % Available Chlorine of pure sodium hypochlorite (that doesn't exist, but for the purposes of this discussion).
I know that this somewhat arbitrary definition of Weight % Available Chlorine being 100% for molecular chlorine in spite of only one of its two chlorine producing hypochlorous acid in water is confusing, but that's how the industry defined it. You are stuck on the Weight % Available Chlorine being the weight of chlorine atoms when it is not. It is the weight of chlorine gas equivalent added to the pool and as shown below only HALF its weight becomes chlorine in hypochlorous acid in the pool.
Cl
2(g) + H
2O ---> HOCl + H
+ + Cl
-
Chlorine Gas + Water ---> Hypochlorous Acid + Hydrogen Ion + Chloride Ion
That is, half of chlorine gas with water becomes hypochlorous acid while the other half becomes hydrochloric acid. Or put another way, 100% Available Chlorine as represented by chlorine gas has 200% chlorine atoms in it (i.e. 2 chlorine atoms per 1 chlorine that becomes hypochlorous acid). The industry decided to standardize its weight percent around chlorine gas and unfortunately only half of that weight is the type of chlorine that we care about.
But as long as this ~ 50% error is built into all FC calculations, that's fine. Perhaps my "3" ppm FC (Taylor's pink reagent, or the common yellow stuff) is always referenced to the trade %, while it has always been about a true 1.5 all along? OK with me.
Any analytical (non-pool) chemists around these parts who can take 1 ml of my 12.5% and assay the real chlorine content? I am predicting it will be close to 60 mg, while the trade will say it's 125 mg. No bets, though!
You are correct that the FC test is standardized/defined to return FC in ppm Cl
2 units which means converting the molar concentration of hypochlorous acid into chlorine gas by multiplying moles/liter by ((70.906 g/mole Cl
2)/(74.442 g/mole NaOCl)) * (1000 mg/g) to get milligrams/liter of Cl
2 equivalent. This works because after dissolving in water only one of the Cl in Cl
2 is chlorine at the +1 oxidation state (in HOCl) while the other is at the -1 oxidation state (in chloride, Cl
-).
1 ml of your 12.5% that I assume to be Trade % means that it contains 0.125 g of Cl
2 equivalent so 125 mg. This is because
(Weight % Available Chlorine) * (Weight of Sample) = (Weight of Cl
2 equivalent)
((12.5 Volume % Available Chlorine)/Density) * ((volume of 1 ml)*Density) = (12.5 Volume % Available Chlorine) * (volume of 1 ml)
So you see that the density cancels out (yes, I know this is confusing, but it's the way it is by definition of what Volume % Available Chlorine means). If you were to add this to 1 liter of water, then this would be 125 mg/L or ppm FC.
Now the question is what do you mean by "the real chlorine content"? If you want that measured in a weight then you need to DEFINE the equivalent molecule you want the measurement to be referenced against. It's 125 milligrams of Cl
2 gas in terms of its effect in the water where, again, only half of that chlorine gas weight becomes the chlorine of interest in the water (hypochlorous acid). In terms of sodium hypochlorite, it's 125*(74.442/70.906) = 131 grams while in terms of hypochlorous acid it's 125*(52.46/70.906) = 92.5 grams while in terms of chlorine atom it's 125*(35.453/70.906) = 62.5 grams (again, not counting chlorine atoms that are part of chloride salt since that is also present in chlorinating liquid and bleach).
Salt Test
By the way, ALL of the analytical tests we deal with regarding concentration (ppm) have this same issue where you need to know the molecule you are referencing against. For example, the Taylor K-1766 salt test analytically measures chloride ion because it titrates using silver nitrate to precipitate silver chloride until all the chloride is precipitated at which point the excess silver reacts with the chromate indicator dye to form the red/brown silver chromate. In spite of analytically measuring chloride ion, the result is reported in ppm sodium chloride regardless of whether there is any sodium present and it is instead all potassium or something else.
Total Alkalinity (TA) Test
Another test that is even more confusing than the salt test because it has a factor of 2 that will drive one nuts is the Total Alkalinity (TA) test. This analytically measures all ions that can accept a hydrogen ion down to a pH of around 4.5 which is the transition point in the test. Bicarbonate ion gets counted once because it can accept one hydrogen ion, carbonate ion gets counted twice, cyanurate ion gets counted once (though doubly and triply deprotonated cyanurate ions would get counted more but they are too small in concentration to worry about), borate ion will be counted once (though most boron will be in boric acid and not counted). This test reports in ppm calcium carbonate (CaCO
3) and as I just noted carbonate counts twice towards TA compared to bicarbonate. What this means is that if you were to add a known weight of sodium bicarbonate to the water and then thought "well, I'll just multiply by the molecular weight of calcium carbonate of 100.0869 g/mole and divide by the molecular weight of sodium bicarbonate of 84.0066 g/mole" you would be off by a factor of 2. The TA will be half this calculated amount because it would take half as much calcium carbonate on a mole per mole (or molecule per molecule) basis as it would take sodium bicarbonate to produce that TA.
Calcium Hardness (CH) and Cyanuric Acid (CYA) Tests
Fortunately the Calcium Hardness (CH) and Cyanuric Acid (CYA) tests don't have any factors, but the CH is still in ppm calcium carbonate and not in the calcium chloride that is normally added to the water. The CYA is most direct in that it is in the same ppm Cyanuric Acid units that is the same as pure CYA that is added to the water.