Borek, please explain specifically where you find error in my reasoning. I stand by my explanation, based on the definition of normality. Furthermore, you will want to share your explanation with the Labchem folks too.
LabChem Catalog # LC13850-1
Product description: EDTA, 0.01M (0.02N), Titrant for Water Hardness, (1mL = 1mg CaCO3)
I welcome you to check out their fine product line for yourself... Again, here is the widely accepted definition of normality:
Normality = molarity x n (where n = the number of protons exchanged in a reaction).
In short, while there is a relationship between the normality of a solution and the molarity of a solution, the normality can only be determined by examining the reaction, determining the proton exchange and multiplying molarity by that number.
Returning to the question at hand, the hardness test:
We can agree that 1 mole of EDTA neutralizes 1 mole of Calcium as CaCO3 (it’s a 1:1 equivalence). Here is where normality confuses things, since EDTA molarity is not equivalent to normality in this case. It is very common to see the hardness calculation based on the normality of EDTA, even though in this instance molarity would be much more straightforward since we simply want to convert back to hardness in mg/L. In the hardness reaction each EDTA molecule exchanges two protons to chelate one divalent calcium cat ion (Ca++). So, even though there is a 1:1 molecular equivalence using molarity, the EDTA normality is, by definition, twice the molarity for the hardness test. Again, given that EDTA donates two protons per molecule in the balanced equation for hardness determination, you must multiply EDTA molarity by two to get the correct normality. For this very reason you don't see standardized EDTA available for purchase as a “normal” solution (unless specified "for hardness" as in the example I gave above). EDTA can potentially donate up to four protons, depending on the reaction. The textbook definition of “normality” means that a standardized “normal” solution of EDTA could be very misleading.
The EDTA hardness calculation using a “molar” solution is:
Hardness as CaCO3 mg/L = Vol (mL) titrant x EDTA (Mol) x 100g/mol CaCO3 x 1,000mg/g
Vol (mL) Sample
This simplifies to:
Hardness as CaCO3 mg/L = V1 x M1 X 100,000 / V2
To convert the calculation to use a “normal” solution, N/2 must be substituted for M1. Factoring out the 2 in the N/2 term with 100,000, you get:
Hardness as CaCO3 mg/L = V1 x N X 50,000 / V2