Now that you've removed most of the alkalinity from all of your water, it's time to treat the mash water to hit a target pH. Let's start by estimating your distilled water mash pH. Based on more of my mash experiments, trends from Kai Troester's website and product specifications from Weyermann Specialty Malts, you can assume the following:
-Roasted malts will lower mash pH by 0.028 for each 1% they comprise of the total grainbill.
-Acidulated malts will lower mash pH by 0.1 for each 1% they comprise of the total grainbill.
-Pale malted wheat will raise mash pH by 0.003 for each 1% it comprises of the total grainbill.
-All other malts will lower mash pH by 0.00027 per degree Lovibond in excess of Pilsner malt for each 1% they comprise of the total grainbill.
-Pilsner malt has an average color of 1.8 degrees Lovibond.
-Decoction mashing will lower mash pH by about 0.1.
If you want to brew a beer with 9 lbs 6 oz of pale ale malt (3L), 8 oz of caramel 60L and 2 oz of chocolate malt (10 lbs total), the pH drops from each grain can be estimated as follows:
pH Drop, Pale Ale Malt = 0.00027 x (3 - 1.8) x (100 x (9 + 6/16)/10) = 0.03
pH Drop, Caramel 60L = 0.00027 x (60 - 1.8) x (100 x (8/16)/10) = 0.079
pH Drop, Chocolate Malt = 0.028 x (100 x (2/16)/10) = 0.035
Using 5.65 as your distilled water mash pH for Pilsner malt, the distilled water mash pH for your grainbill will be 5.65 - 0.03 - 0.079 - 0.035 = 5.51. If your target pH is 5.4, you wouldn't have very far to go if the residual alkalinity of your water was near zero. Unfortunately, that's not the case for Madison city water.
Remember Kohlbach's formula for how residual alkalinity affects wort pH, and how the 0.084 number would have to change for mashes of varying thickness? To figure out the replacement multipliers, I manipulated the data from Kai's mash pH experiments and created the following chart:
It would be possible to create a two-variable equation to calculate the pH shift from a given residual alkalinity and water-to-grist ratio, but a more elegant solution is to plot the pH shifts against total mEq of residual alkalinity per pound of grist:
That nice linear relationship means that each mEq of alkalinity will result in a constant pH increase per pound of grain. The same value will apply to each mEq of acidity as well, but the shift will be in the opposite direction. The pH shift, determined in an experiment I performed at home, is 0.059 per mEq of acid per pound of grain. If you accept my experiment as the gospel truth, you can determine your target residual alkalinity with the following equation:
Target RA = (Target pH - pHd) x Grist Weight / 0.059 / Mash Water Volume + 0.05
In the equation, pHd is the distilled water mash pH for a given grainbill, grist weight is in lbs, and mash water volume is in liters. If your mash water volume is 14.2 L, your target residual alkalinity will be (5.4 - 5.51) x 10 / 0.059 / 14.2 + 0.05 = -1.263 mEq/L.
Now that you know the target RA of your mash water, let's assume you're starting with the lime-treated water from Part IV:
Calcium = 3.302 mEq/L
Magnesium = 3.702 mEq/L
Chloride = 158 mg/L
Sulfate = 95 mg/L
Total Alkalinity = 1 mEq/L
RA = 1 - 3.302/3.5 - 3.702/7 = -0.472
Calculating the acidity required to lower your mash pH is similar to the previous calculation for total water volume:
Required Acidity = Water RA - Target RA = -0.472 - -1.263 = 0.791 mEq/L
Because the pH of your mash will be lower than the pH of your sparge water, a smaller percentage of lactic acid molecules will dissociate in your mash. Here's how to estimate what will happen:
Dissociation = 100 x (1 - 1 / (1 + 10^(Target Mash pH - 3.83))) = 100 x (1 - 1 / (1 + 10^(5.4 - 3.83))) = 97.4%
...here's how to calculate how much acidity your lactic acid will contribute to your mash:
Acidity = 1000 x (Acid Strength / 100) x (Dissociation / 100) / 90.09 / ((Acid Strength / 100) / 1.2+(1 - Acid Strength / 100)) = 1000 x (88 / 100) x (97.4 / 100) / 90.09 / ((88 / 100) / 1.2+(1 - 88 / 100)) = 11.149 mEq/L
...and here's how to determine your required volume of lactic acid:
Lactic Acid = Required Acidity x Water Volume / 11.722 = 0.791 x 14.2 / 11.149 = 1.0 mL
If you need to raise the alkalinity of your mash water, here's an equation that will tell you how much calcium carbonate to add in grams:
CaCO3 = (Target RA - Water RA) x Water Volume / 14.27
If your target RA is 0.5 mEq/L, you'll want to add (0.5 - -0.472) x 14.2 / 14.27 = 1 g of calcium carbonate. I'd add it directly to your mash because it won't dissolve in non-acidified water. That said, Kai's experiments suggest that mash additions are only effective when the total alkalinity of the water (after adding CaCO3) is around 5 mEq/L or less. You should never need that much alkalinity, so don't lose sleep over the solubility of calcium carbonate.
That brings us to the end of this series on water chemistry. Whether you crunch the numbers or use the simplified treatments from Part II, you should be rewarded with improved brewhouse efficiencies and cleaner-tasting beer. If you'd like to use the detailed calculations but don't want to do the math every time you brew, my water treatment spreadsheet (located here) will do the work for you. The file name is Water_Gallons.xlsx, and the same calculations are embedded in the Recipe_Gallons.xlsx file. You can return to the beginning of this series here.