Having trouble with brewing water calculations

[arringtonbp]

Today I finally got more detailed information about my water, but I'm having a difficult time with the calcium and magnesium calculations.

Calcium - Calcium hardness = 45 - 52 ppm
Magnesium = Not tested for, very low concentration
Sulphates = 40 – 42 ppm
Sodium = 12 – 15 ppm
Chlorides = 18 – 20 ppm
Carbonates = Not tested for
Alkalinity = 15 – 25 ppm

The alkalinity is measured as CaCO3. My pH range is 7.4-7.6, which I am now gathering is not a very useful piece of information when it comes to brewing.

I need to get the following mineral concentrations:

Ca+2
Mg+2
SO4-2
Na+
Cl-
HCO3-

I believe I have the sulphates, sodium, and chloride. The utility told me the magnesium concentration is too low and they don't measure it. I'm not sure if I have enough information to calculate the bicarbonates and the calcium.

 

[arringtonbp]

I am also wondering what calcium hardness means. Is this referring to the levels of CaCO3?

 

[ajdelange]

Alkalinity is measured by adding acid to the water sample until virtually all the bicarbonate and carbonate have been converted to CO2 and left the solution. Given this it is natural to represent alkalinity in units of acid measure: mEq/L. However it turns out that because the molecular weight of calcium carbonate is 100 if you dissolve 100 mg of CaCO3 in 1 liter of water using CO2 as the acid and adjust the pH to 8.3 (with CO2) you get:

CaCO3 + CO2 + H2O --> 2HCO3- + Ca++

The 1 mmol (100/100) of CaCO3 give 2 mmol of HCO3-. If you measure the alkalinity of this with hydrochloric acid

Ca++ + 2HCO3- + 2HCl --> 2CO2 + 2H2O + 2Cl- + Ca++

It's obviously going to take 2 mEq of H+ (from the acid) to convert the 2 mmol of HCO3- to CO2

Thus 100 mg/L limestone dissolved as nature would leads to alkalinity of 2 mEq/L. There are also 2 mEq/L Ca++ (1 mmol times the charge of +2). This 'hardness' would be found by titrating the solution with a calcium chelating agent of know strength as opposed to acid. 2 mEq of chelant would be required for each liter.

So 100 mg/L CaCO3 gives 2 mEq/L alkalinity and 2 mEq/L hardness. Let's just multiply those numbers by 50. This gives alkalinity of 100 mg/L "as CaCO3" and 100 mg/L hardness "as CaCO3" which is the amount of limestone we started with. How convenient! Problem is that this causes so much confusion.

Now forget about all that and just remember that if anything is expressed 'as CaCO3' you divide by 50 and that is the number of mEq/L of the substance in question. So a calcium hardness of 45 ppm as CaCO3 is 45/50 = 0.9 mEq/L. To find out how much calcium that is you multiply by the equivalent weight of calcium which is 20 which gives you 18 mg/L. For magnesium the equivalent weight is 12.15.

For bicarbonate it's a bit trickier because while bicarbonate ion has an equivalent weight of 61 not all allkalinity comes from bicarbonate. Pure water has a small alkalinity of its own and if the sample pH is high the water will contain carbonate and hydroxyl ions as well as bicarbonate ions. At lower pH it turns out some things cancel in the math and you can simply calculate 61*alkalinity_as_CaCO3/50 as an estimate of the bicarbonate. It is when pH gets into the 8ish region that this approximation falls apart. In fact you do not need to know bicarbonate content. That's why labs don't measure it (and the fact that it is difficult to do so). Alkalinity is sufficient. Unfortunately many of the popular spreadsheets' authors seem to be unaware of this and the spreadsheets seem to prefer that you enter bicarbonate content. Coupled with the fact that Ward labs had been miscalculating it for years this lead to errors in spreadsheet calculations but they were not large. Ward Labs seems to be doing it correctly now.

 

[ncbrewer]

Great post AJ. Thanks.

 

[FourSeasonAngler]

^ yep, what he said.

 

[arringtonbp]

Alkalinity is measured by adding acid to the water sample until virtually all the bicarbonate and carbonate have been converted to CO2 and left the solution. Given this it is natural to represent alkalinity in units of acid measure: mEq/L. However it turns out that because the molecular weight of calcium carbonate is 100 if you dissolve 100 mg of CaCO3 in 1 liter of water using CO2 as the acid and adjust the pH to 8.3 (with CO2) you get:

CaCO3 + CO2 + H2O --> 2HCO3- + Ca++

The 1 mmol (100/100) of CaCO3 give 2 mmol of HCO3-. If you measure the alkalinity of this with hydrochloric acid

Ca++ + 2HCO3- + 2HCl --> 2CO2 + 2H2O + 2Cl- + Ca++

It's obviously going to take 2 mEq of H+ (from the acid) to convert the 2 mmol of HCO3- to CO2

Thus 100 mg/L limestone dissolved as nature would leads to alkalinity of 2 mEq/L. There are also 2 mEq/L Ca++ (1 mmol times the charge of +2). This 'hardness' would be found by titrating the solution with a calcium chelating agent of know strength as opposed to acid. 2 mEq of chelant would be required for each liter.

So 100 mg/L CaCO3 gives 2 mEq/L alkalinity and 2 mEq/L hardness. Let's just multiply those numbers by 50. This gives alkalinity of 100 mg/L "as CaCO3" and 100 mg/L hardness "as CaCO3" which is the amount of limestone we started with. How convenient! Problem is that this causes so much confusion.

Now forget about all that and just remember that if anything is expressed 'as CaCO3' you divide by 50 and that is the number of mEq/L of the substance in question. So a calcium hardness of 45 ppm as CaCO3 is 45/50 = 0.9 mEq/L. To find out how much calcium that is you multiply by the equivalent weight of calcium which is 20 which gives you 18 mg/L. For magnesium the equivalent weight is 12.15.

For bicarbonate it's a bit trickier because while bicarbonate ion has an equivalent weight of 61 not all allkalinity comes from bicarbonate. Pure water has a small alkalinity of its own and if the sample pH is high the water will contain carbonate and hydroxyl ions as well as bicarbonate ions. At lower pH it turns out some things cancel in the math and you can simply calculate 61*alkalinity_as_CaCO3/50 as an estimate of the bicarbonate. It is when pH gets into the 8ish region that this approximation falls apart. In fact you do not need to know bicarbonate content. That's why labs don't measure it (and the fact that it is difficult to do so). Alkalinity is sufficient. Unfortunately many of the popular spreadsheets' authors seem to be unaware of this and the spreadsheets seem to prefer that you enter bicarbonate content. Coupled with the fact that Ward labs had been miscalculating it for years this lead to errors in spreadsheet calculations but they were not large. Ward Labs seems to be doing it correctly now.

Wow, thank you for the in depth information here. Based on what you have said I have a few more questions. When you say that the approximation for bicarbonates falls apart around 8 pH, is that my base water pH or the pH of my mash? I have noticed that I'm coming up short on my original gravity each time, but I think a lot of that has to do with volumes. However, sometimes I'm 3-4 points off of my target OG. Is it possible I'm sacrificing some efficiency by not adjusting my mash pH?

 

[ajdelange]

I was referring to the source water pH. It also falls apart at mash pH (the percentage error is higher at 5.2 than it is at 8.5) but at mash pH so little bicarbonate remains that the absolute error is not appreciable.

Remember that you are interested in alkalinity, not bicarbonate. This can lead to problems in spreadsheets that calculate alkalinity from bicarbonate but the errors are small even at the higher pH's (about 5% at pH 8.5).