converting weight to volume and pool math

[smackdab]

Calcium Chloride Dihydrate has a density of 1.85 g/cm3 so 1 gallon (128 fluid ounces) of Calcium Chloride Dihydrate should weigh 15.44 lbs (247.04 oz weight).

So 1 ounce (weight) of calcium chloride dihydrate should be 1.93 fluid ounces volume. 247.04/128=1.93

My calculation must not be correct because I see in Pool Math 10,000 gallons for a 500 ppm increase in CH it shows "981 oz weight = 1126 oz volume" whereas my calculation would be 981 oz weight = 1893 oz volume. 981 x 1.93 = 1893.

What am I missing?

 

[chem geek]

You are forgetting that the units of measurement for items like FC, TA, and CH are NOT in the weight units of the products that get added. Calcium Hardness (CH) in particular is measured as parts-per-million (ppm) or equivalently milligrams per liter (mg/L) of calcium carbonate (CaCO₃), NOT calcium chloride dihydrate that you assumed.

Also, you are using a SOLID density for calcium chloride dihydrate but you aren't buying a block of solid but rather should be using the BULK density which is around 0.835 g/cm³ (for calcium chloride anhydrous, the bulk density is around 1.2 g/cm³).

So a 500 ppm CH increase would be (500 mg/L CaCO₃) * (147.0154 g/mole CaCl₂•2H₂O) / (100.0892 g/mole CaCO₃) = 734.422 mg/L so in 10,000 gallons which is 37854 liters this is (734.422 mg/L) * (37,854 L) / (1000 mg/g) = 27800 g or 27.8 kg which is 980.6 ounces so 981 in PoolMath is correct.

(27,800 g) / (0.835 g/ml) = 33293 ml or 1125.8 ounces so 1126 in PoolMath is correct.

Similarly, chlorine is in ppm Cl₂ units (i.e. molecular chlorine) with a molecular weight of 70.906 g/mole while TA is in the same CaCO₃ calcium carbonate units as CH, BUT carbonate counts twice towards TA compared to bicarbonate so there's a factor of 2 that needs to be taken into account (i.e. you divide your bicarbonate computation by 2 for equivalent carbonate).

 

[smackdab]

Ok thanks. I left out alot of things. I see where the calculation comes from now.

It appears Calcium Chloride Dihydrate bulk density can vary somewhat from manufacturer to manufacturer. Is there any certain place you get the bulk densities from or did you just average out several msds sheets for Ice Melters?

Also looking at the msds sheets it appears Dowflake Xtra, Dowflake, Peladow is just a lower percentage of anhydrous calcium chloride instead of being dihydrate. CAS#10043-52-4

 

[chem geek]

For bulk density I just used an average from several sources.

Peladow is 90% Calcium Chloride Anhydrous, but older Dowflake is 96% Calcium Chloride Dihydrate so equivalent to 72% Calcium Chloride Anhydrous. However, I can't find that Dowflake anymore.

See Peladow with >90% calcium chloride and 58-66 lb/ft³ which is 0.929-1.057 g/ml (I must have gotten 1.2 from other sources). See Dowflake Xtra with >83% calcium chloride with no listed bulk density and this does seem to be mostly calcium chloride anhydrous -- perhaps some water but this is not calcium chloride dihydrate nor even what they call "conventional 77-80% calcium chloride flake". See Dowflake with 77-80% Calcium Chloride with 51-60 lb/ft³ which is 0.817-0.961 g/ml (my 0.835 is in between but also from other sources). This seems to be in between monohydrate and dihydrate.