## Friday, February 18, 2011

### Five Gallons At A Time: Water Chemistry, Part IV

According to A.J. deLange, slaked lime can remove total alkalinity to about 1 mEq/L (50 mg/L as CaCO3) if sufficient calcium is present. For all of my batches, I like to treat my mash and sparge water (usually as one bulk volume to reduce measurement errors) to that level before I worry about mash pH. That way, the pH rise during sparging will be minimized regardless of what I'm brewing. Today, I'm going to show you how to do so with either lactic acid or slaked lime.

Acids, which contribute hydrogen ions, lower the alkalinity of water via the following reaction (simplified from A.J. deLange's Alkalinity II article):

H + HCO3 -> H2O + CO2

Note that both the free hydrogen ion and the bicarbonate ion cease to exist. The late brewing scientist Jean De Clerck seems to have made a mistake by claiming that acids counteract carbonates without eliminating them (I say "seems" because I've heard this attributed to him as an argument against using acids, but I haven't read it in the original source).

Diving into the math, let's start with the same source water profile as Part III:

Calcium = 3.992 mEq/L
Magnesium = 3.702 mEq/L
Chloride = 1.016 mEq/L
Sulfate = 0.354 mEq/L
TA = 6.78 mEq/LRA = 6.78 - 3.992/3.5 - 3.702/7 = 5.111 mEq/L

Let's also assume your total water volume is 35.6 L (9.4 gallons). To calculate the required acidity, all you need to do is replace your desired total alkalinity drop with an equivalent mEq/L of hydrogen ions:

Required Acidity = TA Drop1 = Water TA - Target TA = 6.78 - 1 = 5.78 mEq/L

From there, acid chemistry can be complex because the number of hydrogen ions released by a mole of weak acid (such as lactic acid) will decrease as the pH of the environment drops. Luckily for us, each molecule of lactic acid only has one hydrogen ion to keep track of. For lactic acid in Madison water, it's fair to assume that 99.5% of the acid's hydrogen ions will be released at any given time. For 88% lactic acid, which is the most common strength sold at homebrew shops, 99.5% dissociation means that each mL of acid will contribute 11.39 mEq of acidity. Therefore, the amount of lactic acid to add can be calculated as follows:

Lactic Acid = Required Acidity x Water Volume / 11.722 = 5.78 x 35.6 / 11.39 = 18.1 mL

Slaked lime additions are more difficult to calculate than lactic acid calculations. For starters, Madison city water doesn't have enough calcium for slaked lime to reduce its total alkalinity to the desired level. Calcium chloride and/or calcium sulfate will need to be added, and my starting point is usually 250 mg/L of calcium chloride and 150 mg/L of calcium sulfate. To figure out the weights of your salt additions, multiply the concentrations of your additions by the volume of water to be treated:

Salt Weight = Concentration x Water Volume / 1000
Calcium Chloride Weight = 250 x 35.6 / 1000 = 9 g
Calcium Sulfate Weight = 150 x 35.6 / 1000 = 5 g

To calculate how your salt additions will affect your ion concentrations, you can use the following formula:

Ion Shift (mg/L) = 1000 x Ions per Salt Molecule x Salt Weight x Ion Molecular Mass / Salt Molecular Mass / Water Volume

Here are the molecular masses of the compounds you'll be dealing with:

Calcium (Ca++) = 40.08 g/mol
Chloride (Cl-) = 35.45 g/mol
Sulfate (SO4--) = 96.06 g/mol
Calcium Chloride (CaCl2*2H2O) = 147.02 g/mol
Calcium Sulfate (CaCO4*2H2O) = 172.17 g/mol

Therefore, the salts will add the following ion concentrations to your water:

Calcium Shift = [1000 x 1 x 9 x 40.08 / 147.02 / 35.6] + [1000 x 1 x 5 x 40.08 / 172.17 / 35.6] = 69 + 33 = 102 mg/L
Chloride Shift = 1000 x 2 x 9 x 35.45 / 147.02 / 35.6 = 122 mq/L
Sulfate Shift = 1000 x 1 x 5 x 96.06 / 172.17 / 35.6 = 78 mg/L

Calcium2 = 80 + 102 = 182 mg/L -> 182 x 2 / 40.08 = 9.082 mEq/L
Magnesium = 3.702 mEq/L
Chloride2 = 36 + 122 = 158 mg/L
Sulfate2 = 17 + 78 = 95 mg/L
TA2 = TA1 = 6.78 mEq/L
RA2 = 6.78 - 9.082/3.5 - 3.702/7 = 3.656 mEq/L

I usually like to keep chloride below 250 mg/L and sulfate below 150 mg/L, and your ion concentrations are still well within those ranges. I also like to have at least 1 mEq/L of calcium for yeast nutrition, which is currently the case but may not be after a lime treatment. Here's how much calcium your water will need to ensure that enough will remain after adding slaked lime:

Required Calcium = TA Drop1 + Minimum Calcium = 5.78 + 1 = 6.78 mEq/L

At 9.082 mEq/L, you'll have plenty of calcium. Next, you'll need to know your water pH. 7.5 is common for Madison city water, so we'll go with that. Now for the fun stuff: determining the molar concentrations of bicarbonate and carbonic acid in your water supply. The calculations, taken from Understanding Alkalinity and Hardness - Part I by A.J. deLange, are as follows (brackets designate millimoles of a substance):

[HCO3-] / [H2CO3] = 10^(Water pH - 6.48) = 10^(7.5 - 6.48) = 10.471
[CO3--] / [HCO3-] = 10^(Water pH - 10.33) = 10^(7.5 - 10.33) = 0.00148
Bicarbonate (HCO3-) = Total Alkalinity / (1 + 2 x [CO3--] / [HCO3-]) = 6.78 / (1 + 2 x 0.00148) = 6.76 mM/L.
Carbonic Acid (H2CO3) = Bicarbonate / ([HCO3-] / [H2CO3]) = 6.76 / 10.471 = 0.646 mM/L.

Understanding carbonate chemistry is important because the activity of slaked lime (Ca(OH)2) in the presence of calcium and a carbonate buffer system is governed by two chemical reactions (from Understanding Alkalinity and Hardness - Part II by A.J. deLange):

1. Ca++ + Ca(OH)2 + 2HCO3- -> 2CaCO3 + 2H2O (2CaCO3 drops out of solution as a solid)
2. Ca(OH)2 + 2H2CO3 -> Ca++ + 2HCO3- + 2H2O

The first reaction describes the precipitation of calcium carbonate, which removes calcium and bicarbonate from the water and results in a lower residual alkalinity. The second reaction describes the conversion of carbonic acid to bicarbonate, which adds calcium and bicarbonate to the water and results in a higher residual alkalinity. The first reaction has a far greater impact than the second, but the second reaction is significant enough that we need to account for it. For mathematical simplicity, you can assume that carbonic acid is converted to bicarbonate before calcium carbonate is precipitated.  Knowing your concentration of carbonic acid, you can calculate the impact of reaction 2 as follows:

Calcium3 = Calcium2 + Ionic Charge x (Carbonic Acid / 2) = 9.082 + 2 x (0.646 / 2) = 9.728 mEq/L
TA3 = Initial Total Alkalinity + Carbonic Acid = 6.78 + 0.646 = 7.426 mEq/L
RA3 = 7.426 - 9.728/3.5 - 3.702/7 = 4.118 mEq/L

Finally, here's how to calculate the amount of slaked lime to add:

TA Drop2 = TA3 - Target TA = 7.426 - 1 = 6.426 mEq/L
Slaked Lime = 0.037 x TA Drop x Water Volume = 0.037 x 6.426 x 35.6 = 8 g

...and here's what your water will look like after the treatment:

Calcium4 = Calcium3 - TA Drop2 = 9.728 - 6.426 = 3.302 mEq/L
Magnesium = 3.702 mEq/L
Chloride4 = Chloride2 = 158 mg/L
Sulfate4 = Sulfate2 = 95 mg/L
TA4 = Target TA = 1 mEq/L
RA4 = 1 - 3.302/3.5 - 3.702/7 = -0.472

In the next post, I'll discuss how to treat your mash water to achieve an appropriate pH.

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