PPM Calculations

[sixhotdogneck]

Working through the math of PPM calculations for the various brewing salts (adding 1g/gal of each salt):

Molecular weights of various elements and ions:

Ca = 40.078 g/mol
Cl = 35.453 g/mol
SO4 = 96.06 g/mol
Na = 22.989769 g/mol
Mg = 24.305 g/mol
H = 1.00794 g/mol
O = 15.999 g/mol
HCO3 = 61.0168 g/mol
CO3 = 60.01 g/mol
OH = 17.008 g/mol
H2O = 18.01528 g/mol

General Formula:

X = ion addition in units of mg/L
Y = molecular weight of element in g/mol
Z = total molecular weight of ion in g/mol
W = resulting mg/L

X mg/L * (Y g/mol / Z g/mol) = W mg/L

Determine mg/L of a 1g/gal addition of each salt:

1mg/L = 1ppm
3.78541 L/gal
1g/3.78541L = 0.26417217685798896288645087322113 g/L * 1000 mg/g = 264.17217685798896288645087322113 mg/L = ppm

PPM Calculations:

Calcium Sulfate Dihydrate (Gypsum)
CaSO4 + 2(H2O) = 172.16856 g/mol

Ca = 264.17217685798896288645087322113 mg/L * (40.078 g/mol / 172.16856 g/mol) = 61.5 mg/L (ppm)
SO4 = 264.17217685798896288645087322113 mg/L * (96.06 g/mol / 172.16856 g/mol) = 147.39 mg/L (ppm)

Calcium Chloride
CaCl(2) = 110.984 g/mol

Ca = 264.17217685798896288645087322113 mg/L * (40.078 g/mol / 110.984 g/mol) = 95.4 mg/L (ppm)
Cl = 264.17217685798896288645087322113 mg/L * (70.906 g/mol / 110.984 g/mol) = 168.8 mg/L (ppm)

Magnesium Sulfate Heptahydrate (Epsom Salts)
MgSO4 + 7(H2O) = 246.47196 g/mol

Mg = 264.17217685798896288645087322113 mg/L * (24.305 g/mol / 246.47196 g/mol) = 26.05 mg/L (ppm)
SO4 = 264.17217685798896288645087322113 mg/L * (96.06 g/mol / 246.47196 g/mol) = 102.96 mg/L (ppm)

Magnesium Chloride Hexahydrate
MgCl(2) + 6(H2O) = 203.30268 g/mol

Mg = 264.17217685798896288645087322113 mg/L * (24.305 g/mol / 203.30268 g/mol) = 31.58 mg/L (ppm)
Cl = 264.17217685798896288645087322113 mg/L * (70.906 g/mol / 203.30268 g/mol) = 92.135 mg/L (ppm)

Sodium Chloride (Salt)
NaCl = 58.44 g/mol

Na = 264.17217685798896288645087322113 mg/L * (22.989769 g/mol / 58.44 g/mol) = 103.9229 mg/L (ppm)
Cl = 264.17217685798896288645087322113 mg/L * (35.453 g/mol / 58.44 g/mol) = 160.2617 mg/L (ppm)

Sodium Bicarbonate (Baking Soda)
NaHCO3 = 84.007 g/mol

Na = 264.17217685798896288645087322113 mg/L * (22.989769 g/mol / 84.007 g/mol) = 72.294 mg/L (ppm)
HCO3 = 264.17217685798896288645087322113 mg/L * (61.0168 g/mol / 84.007 g/mol) = 191.876 mg/L (ppm)

Calcium Carbonate (Chalk)
CaCO3 = 100.0869 g/mol

Ca = 264.17217685798896288645087322113 mg/L * (40.078 g/mol / 100.0869 g/mol) = 105.782 mg/L (ppm)
HCO3 = 264.17217685798896288645087322113 mg/L * (61.0168 g/mol / 100.0869 g/mol) * 2 = 322.0989 mg/L (ppm) (terms of bicarbonate)

Calcium Hydroxide (Pickling Lime)
Ca(OH)2 = 74.093 g/mol

Ca = 264.17217685798896288645087322113 mg/L * (40.078 g/mol / 74.093 g/mol) = 142.894 mg/L (ppm)
HCO3 = 264.17217685798896288645087322113 mg/L * (61.0168 g/mol / 74.093 g/mol) * 2 = 435.100 mg/L (ppm) (terms of bicarbonate)

Several questions arise:

1.) Is the bicarbonate equivalent of the carbonate done correctly? (i.e. Multiply by 2)
2.) Would spreadsheet makers consider changing their sheets such that instead of supplying the concentration of the salt in question (and guessing at the concentration to attain a certain ppm) one could specify the desired ppm and the spreadsheet would solve for the needed concentration/weight?

Reference:

Alkalinity Conversions

 

[ajdelange]

Rather imprecise!

That was a joke (OK, a weak one).

On a more serious note, calculation of calcium and chloride from CaCl2 is a simple matter of dividing CaCl2 weight by the molecular weight of CaCl2 to determine the number of moles. of CaCl2 corresponding to the mass. The number of moles of calcium is clearly 1 per mole of CaCl2 and the number of moles of Cl is clearly twice the number of moles of CaCl2. The weights of the ions are then found by multiplying the moles of the ions by the atomic weights of the ions (realizing that you'll be off by the electrons gained or lost which would show up in numbers calculated to the precision you've shown.

Carbonates and bicarbonates are an entirely different matter and there are volumes of information here on how to handle them. See the Sticky here and come back with questions.

 

[sixhotdogneck]

Rather imprecise!

That was a joke (OK, a weak one).

Nice The power of calculators/computers. Of course unless special data types are used (not float/double precision) the imprecision really does add up.

On a more serious note, calculation of calcium and chloride from CaCl2 is a simple matter of dividing CaCl2 weight by the molecular weight of CaCl2 to determine the number of moles. of CaCl2 corresponding to the mass. The number of moles of calcium is clearly 1 per mole of CaCl2 and the number of moles of Cl is clearly twice the number of moles of CaCl2. The weights of the ions are then found by multiplying the moles of the ions by the atomic weights of the ions (realizing that you'll be off by the electrons gained or lost which would show up in numbers calculated to the precision you've shown.

I see what you're saying:

1g of CaCl2 / 110.984 g/mol = 0.00901030779211417862034167087148 mol / g

40.078 g/mol * 0.00901030779211417862034167087148 mol / g = 0.36111511569235205074605348518718 g of Ca
70.906 g/mol * 0.00901030779211417862034167087148 mol / g = 0.63888488430764794925394651481316 g of Cl

Carbonates and bicarbonates are an entirely different matter and there are volumes of information here on how to handle them. See the Sticky here and come back with questions.

I'll take a look at it.

 

[ajdelange]

I was in a hurry when I wrote No. 2 and so was rather terse. If you add 1 mmole of sodium bicarbonate to a liter of deionized (DI) water 0.98 mmol stays as bicarbonate, 1% converts to carbonic acid and 1% converts to carbonate. If the water has any alkalinity and the pH is lower than 8.38 the acid in it (HCO3- ion) will pull the pH of the mix lower and more of the bicarbonate will convert to carbonic.

If you add calcium carbonate to water very little happens as it is essentially insoluble. I, however, the water is acidified, then some CaCO3 does dissolve and some of the carbonate ion converts to bicarbonate and carbonic. In order to determine what happens when carbonate or bicarbonate is added to water one has to consider a system of 5 simultaneous equations. To someone just getting started on this it must appear totally bewildering. But there is a lot of material on it here.

 

[kilda011]

2.) Would spreadsheet makers consider changing their sheets such that instead of supplying the concentration of the salt in question (and guessing at the concentration to attain a certain ppm) one could specify the desired ppm and the spreadsheet would solve for the needed concentration/weight?

I just downloaded the EZ Water Calculator and had the same thought. I added a target ppm row and used the solver function to do the math for me. As long as you set proper constraints and set a meaningful objective, it will crank out what you need. See picture for example. Note, I also changed their Lime salt to NaCl and added Alkalinity as a target.

https://drive.google.com/open?id=1ycl8qTa9dLCqLgDFrjrNTQqfz8V7-tmZ

 

[An Ankoù]

I know this is old, but I was using the OPs data for my own calculations. Had a right head-scratcher with the CaCl2 caalculation as it didn't seem to tie in with other people's figures while the other calculations work fine. It turns out that the CaCl2 commonly bought over here is the dihydrate and not anhydrous calcium chloride. Adding that extra 36 g M-1 tallies fine with the others' calculations.

 

[VikeMan]

I know this is old, but I was using the OPs data for my own calculations. Had a right head-scratcher with the CaCl2 caalculation as it didn't seem to tie in with other people's figures while the other calculations work fine. It turns out that the CaCl2 commonly bought over here is the dihydrate and not anhydrous calcium chloride. Adding that extra 36 g M-1 tallies fine with the others' calculations.

Nobody buys anhydrous CaCl2 for brewing, at least not in the USA. It's too expensive and it's not even available from brewing suppliers. And even if a brewer sourced some, it wouldn't stay anhydrous for long after opening.

 

[An Ankoù]

Nobody buys anhydrous CaCl2 for brewing, at least not in the USA. It's too expensive and it's not even available from brewing suppliers. And even if a brewer sourced some, it wouldn't stay anhydrous for long after opening.

That's what I thought and that's why I posted.

Calcium Chloride
CaCl(2) = 110.984 g/mol

Would be better as
CaCl2.2H20 = 111+36 = 147 g/mol

It makes around 1/3 difference to the salt addition.

 

[Silver_Is_Money]

From testing it, I'm taking the firm position that CaCl2 generally comes from the unopened container as about 94%-96% pure CaCl2, and that you can't ever buy it as specifically the dihydride. 94% to 96% is much closer to anhydrous than it is to dihydride. When it is down to about 75.5% purity it is at the dihydride state. But it doesn't stop adsorbing water at that juncture. It continues until it turns into a mush water/salt goo. I think it impossible to sell CaCl2 in the dihydride state.

The very simple way to test the purity percentage of your CaCl2 prills is to add 25 grams to DI water and make it up to a total of 250 mL (or use 5 grams made up to 50 mL if you really trust your scales accuracy plus your ability to accurately assess that you have 50 mL). Stir to fully dissolve and then let all of the rather appreciable heat this causes cool back down to room temperature. Then take an SG reading. If it reads 1.081 SG it is Anhydrous. If it reads say 1.077 instead, it is right close to 95%.

SG's For various ~percents (weight by volume) for CaCl2 solutions made up as above (admittedly rather loosely rounded):
------------------------
100% = 1.081 SG
99% = 1.080 SG
97.5% = 1.079 SG
96% = 1.078 SG
95% = 1.077 SG
94% = 1.076 SG
92.5% = 1.075 SG
91% = 1.074 SG
90% = 1.073 SG
87.5% = 1.071 SG
85% = 1.069 SG
82.5% = 1.067 SG
80% = 1.065 SG
76% = 1.062 SG
73% = 1.060 SG
70% = 1.052 SG
60% = 1.049 SG
50% = 1.041 SG
40% = 1.033 SG
30% = 1.025 SG

If any fine white powder hazes it up and eventually drops out of solution at any juncture of storage, that is a calcium carbonate contaminant. If the pH of your test solution is above 7 it certifiably has CaCO3 contamination at some level. And of course that will throw off the SG's by some measure, but only to the degree that CaCO3 is soluble. Solids suspended in solutions do not impact SG. Calcium Carbonate will assuredly foul up the mash pH lowering ability of CaCl2's calcium ion. Unfortunately, due to poor quality control, the budget level (as in already only 94% to 96% pure) CaCl2 offered by LHBS's almost inevitably contains some measure of calcium carbonate contaminant. This may be a reason as to why the common presumption is for dihydrate CaCl2, but it is a very poor reason, rooted in presumption as opposed to science.

 

[An Ankoù]

You're right, it's a minefeld. One supplier (Braumarkt) sells "pearls" at 94-97% pure (Im not sure whether they mean 94-97% of calcium chloride dihydrate with some neutral adulterant or anhydrous with some small degree of hydration) and another (Malt Miller) specifies the dihydrate. I've got the latter so I know where I stand with that. The anhydrous is so hygroscopic that I'd have to do the SG measure you kindly suggest above. Thanks for all your help.