Using hypochlorite dilution to measure pool volume

[chem geek]

Welcome to the forum!

What I am about to say is still controversial, but here are some things to consider. This linked thread has some more details of what I summarize below.

First, with regard to the concentration of chlorine in bleach, the Material Safety Data Sheet (MSDS) for Clorox Regular Bleach says 6.15% while Ultra Clorox Regular Bleach says 6-7.35%. Such concentrations in an MSDS refer to the weight percentage (i.e. percent of the weight of the ingredient out of the total weight). The density is listed as approximately 1.1 (g/ml) as compared to your pool water which has a density closer to 1.0 (g/ml).

Second, the ppm of chlorine in pool water is for the disinfecting form of chlorine, namely HOCl, which has a molecular weight of 52.46 g/mole. However, the molecular weight of sodium hypochlorite is 74.4424 g/mole. This means that a weight of 74 units of sodium hypochlorite results in a weight of 52 units of chlorine in the pool.

So, in my opinion, the proper formula for calculating ppm from a volume of liquid chlorine is as follows:

(PoolVol) = (Bleach Frac. Conc.) * (Bleach Vol) * (Density in g/ml = kg/liter) * (1,000,000 mg/kg) * (52.46 g/mole HOCl) / (ppm = mg/liter) / (74.4424 g/mole NaOCl)

Using some of your numbers I get the following:

PoolVol = 0.0615 * 5.4375 * 1.1 * 1,000,000 * 52.46 / 11.5 / 74.4424 = 22,541 gallons.

If I use 7.35% for the high-end of Ultra Clorox Bleach then I get 26,939 gallons.

Since this is quite a ways off from your dimensional estimation then either something is wrong with my analysis or with the measurements or assumptions (concentration). I have a very accurate estimate of my pool volume since I measured all the dimensions when the pool had not yet filled with water so I should try a similar experiment to what you have done and see what happens. One problem is that I use the more concentrated 12.5% chlorinating liquid (from my local pool store) and it might be less accurate in its concentration measurement than Clorox Regular bleach.

[EDIT] It may be that the convention for ppm of Chlorine in a pool uses the "standard" of 100% being the amount of chlorine from chlorine gas (Cl2) in which case the molecular weight is 70.9064 g/mole for Cl2 and that is pretty close to 74.4424. If we use that instead, then for the 6.15% we get closer to what you got or namely 30,467 gallons. I will continue to investigate this, but if your measurements and estimates are correct, then this would imply that the ppm Chlorine number indeed refers to the chlorine gas as the "reference". [END-EDIT] [SECOND-EDIT] I found a source that says that indeed the ppm FC is indeed measured relative to Cl2 so the 30,467 gallon number is the right one and your calculations are quite close to the "accurate" way of doing it. The density and molecular weight ratio somewhat cancel each other out which makes your calculation and mine very similar. [END-EDIT]

Richard