Thank you so much, Randy. It makes so much sense.
Question, if calcium hydroxide is 1 mole of calcium to 2 moles of alkalinity, what is the ratio of Calcium to alkalinity in the sodium hydroxide/calcium carbonate recipe, assuming one doses a 1 to 1 ratio of it, and doses it per alkalinity consumption?
I didn't design them perfectly, and know more now than I did then, but the basic recipes are close to calcium hydroxide (2:1, see bolded sentence below)
An Improved Do-it-Yourself Two-Part Calcium and Alkalinity Supplement System by Randy Holmes-Farley - Reefkeeping.com
The Design of the Calcium and Alkalinity Parts
The Dowflake material is supposed to contain 77-80% calcium chloride. From the Dow Flake website, it has a bulk density of 0.82 - 0.96 g/dry mL or 194 - 227 grams/level measuring cup. We will assume that it is 78.5% calcium chloride by weight and weighs 200 grams per level measuring cup. Because calcium comprises 36% of calcium chloride, by weight, each cup contains 200 x 0.785 x 0.36 = 56.5 grams of calcium.
Consequently, dissolving 2 ½ cups (500 g) of Dowflake per gallon = 141 grams of calcium per gallon, or 37,300 mg/L. The final concentration will vary with how much moisture was actually in the calcium chloride, and how well it packed in your measuring cup. A concentration of 37,300 ppm
calcium is equivalent to 0.93 molar.
When calcification takes place, two moles of alkalinity are lost for every one mole of calcium. So, we need to match the calcium above with 1.86 molar baking soda (sodium bicarbonate) equivalents (before or after baking, the baking doesn't change the alkalinity). As I measure it, Arm & Hammer baking soda weighs about 264 grams per level measuring cup. Because sodium bicarbonate has a molecular weight of 84 g/mole, we need to dissolve 1.86 x 84 = 156 grams/L, or about 594 grams (2 ¼ level measuring cups) of baking soda per gallon. Note that it doesn't matter how many grams the 594 grams of baking soda becomes after baking. All baking does is change the amount of carbon dioxide and water in the baking soda:
2 NaHCO3 --> Na2CO3 + H2O + CO2
More, or less, baking will only alter the pH increase upon addition to the aquarium. However, substantial under-baking may make it impossible to fully dissolve the solid material in the recipe, as sodium bicarbonate is less soluble than sodium carbonate (which is why Recipe #2 is more dilute). Overbaking with respect to time or temperature has no negative effect.
Residual Ions from the Calcium and Alkalinity Parts
Adding 1 gallon of each of these additives will result in a residue of ions remaining after calcification. These are mostly sodium and chloride, and the amounts of those two added are equal in numbers (i.e., moles), but slightly different in weight-based concentrations such as ppm because they do not weigh the same.
After adding 594 grams of baking soda (1 gallon of Recipe #1), we will have added 163 grams of sodium. In natural seawater, magnesium is present at about 12.0% of the sodium concentration (by weight). In order to match the magnesium additions to the sodium additions to leave them in a natural ratio, we need to add 12% of 163 grams, or 19.5 grams, of magnesium for every gallon of the two-part additive that we add.
Additionally, we may want to account for magnesium that is actually incorporated into the coral skeletons. For this calculation, I have assumed that the amount of magnesium incorporated is about 6.5% of the calcium level (by weight), or about 2.5% of the skeleton by weight. In the course of adding this gallon of both parts of the two part supplement, we added 141 grams of calcium, so we need to add 0.065 x 141 = 9 grams of magnesium to account for this deposition.
The magnesium parts of the recipe are designed to add enough magnesium so that it is not depleted by either of the two means described above. Because the magnesium supplement (either version) is 47,000 mg/L in magnesium, we need to add (9 +19.5) grams/47 g/L = 610 ml of the magnesium solution for each gallon of the other parts of Recipe #1.
Interestingly, the potassium present as an impurity in the Dowflake works to our advantage in this use. Recipe #1 has 1,342 ppm potassium in its calcium part. That amount puts it in the right ratio relative to other ions in the recipe (chloride, sodium, etc.) so that it is neither boosted nor depleted significantly over time based on salinity changes (see modeling below).
Residue Remaining from Recipe #1 when using Recipe #1, Part 3A
After one year of adding 8 ppm of calcium and the accompanying 0.4 meq/L (1.1 dKH) of alkalinity per day (41 mL of both parts per day or 4 gallons of both parts per year in a 50-gallon aquarium, including the effect of the magnesium part #3A, 2440 mL/year), the following residue (Table 2) would remain after calcification and adjustment for salinity (there is roughly a 32% rise in salinity over a year using this addition rate without water changes).
Note that in this recipe, all of the ions match NSW fairly closely (green), but without using Part 3A, the magnesium and sulfate are severely depleted (red).
