Two Part Calculations/Questions

[DeadlyMuffin]

I'm one of those people who can't leave well enough alone and wants to know how things work, so simply using the online calculators to find the amounts of Calcium/Alk to add isn't enough for me. I'd like to see the math myself.

Alkalinity: My test kit reads in KH (which is a confusing measurement) so I'm going to divide by 2.8 to get meq/L (where does this number come from? I found it here: http://www.advancedaquarist.com/issues/feb2002/chemistry.htm).

So say I have a 100L tank at 6 KH (2.143 meq/L) and I want to go to 8 KH (2.857 meq/L). Difference is .714 meq/L or, with the 100 L tank, 71.4 meq.

The alk part of my two part is using baking soda which (assuming it's pure!) is 42g/mol, so to get 71.4 meq I need .0714 mol or 3g of pure baking soda.

Is this the right way to do the calculation? Seems like the same sort of thing we did in general chemistry (or high school for that matter). Looking at it this way, is it necessary to dissolve the baking soda in water at all if you can measure it by mass? If it's dissolved you would of course have to take into account the new tank capacity, although it's probably pretty negligible for a big tank. Is it because the sodium and the bicarbonate don't separate the same if they were simply tossed into salt water as opposed to dissolved in fresh water?

Calcium is measured in ppm, which is a bit weird. Parts per million of... what exactly? I've tried to look this up, but I can't find if it's per million water molecules or by mass, which would be different in salt water than in pure water. If I know how it's being measured, I should be able to convert it to a molarity and do the same sort of calculation I did with alk.

Am I doing this right or am I off in left field here?

 

[Randy Holmes-Farley]

Calcium is measured in parts per million of calcium ion, Ca++, to total mass, not just the water, but the correction is minor.

I work through the two part calculations here:

An Improved Do-it-Yourself Two-Part Calcium and Alkalinity Supplement System
http://reefkeeping.com/issues/2006-02/rhf/index.php

from it:

http://reefkeeping.com/issues/2006-02/rhf/index.php#19

Calculation Rationale for the Recipes
The calculation rationale that follows is for Recipe #1. The rationale for Recipe #2 is the same, except that everything is divided by 2 and baking the baking soda is not required. This section is provided for those who want to know how the recipe is devised, who are concerned that there might be an error or who might want to change it slightly. It is not necessary to read the following section if all you want to do is use it.

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).

Residue Remaining from Recipe #1 when using Recipe #1, Part 3B

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 sulfate solution, 2440 mL/year), the following residue (Table 3) would remain after calcification and adjustment for salinity (there is roughly a 29% rise in salinity over a year using this addition rate without water changes):

Note that in this recipe, all of the ions except sulfate (red) match NSW fairly closely (green), but without using Part 3A, magnesium and sulfate are severely depleted (red).

In a previous article discussing water changes, I showed how the rise in sulfate shown in Table 2 is mitigated to some extent by water changes. Those data are reproduced in Figure 5 below, which shows the effect of daily water changes amounting to 7.5%, 15% and 30% on a monthly basis. Clearly, the 15% and 30% changes per month mitigate the rise in sulfate over a year by a substantial amount (reducing the increase by 54% and 74%, respectively).

 

[Randy Holmes-Farley]

The alk part of my two part is using baking soda which (assuming it's pure!) is 42g/mol, so to get 71.4 meq I need .0714 mol or 3g of pure baking soda.

That is not correct. As I indicate above, the molecular weight of sodium bicarbonate (NaHCO3) is 84 g/mole.

 

[DeadlyMuffin]

You're quite right, I got 42 using the atomic numbers rather than the atomic masses.

 

[DeadlyMuffin]

I read through your article, and it seems pretty straightforward. You want to be able to add each part in equal amounts, so your alk portion will have twice the molarity of the calcium portion.

Is the method I'm using to determine how much to add correct? (with the corrected weight I'm getting 6g of baking soda in my example).

edit: now that I think about it, if the adjustment for salt water is negligible, 1 ppm corresponds to 1 mg/L, so the calcium part is pretty simple too! Calcium is 40g/mol so .001g/L over 40g/mol gives a molarity of .000025mol/L for 1 ppm Ca++.

 

[DeadlyMuffin]

Also, can anyone show me where the factor of 2.8 to convert from dKH to meq/L comes from? I found the actual number in the article I cited, but I don't understand its origin.

Using the numbers from from the posted article (950meq/L for Alk and 18,500mg/L for Ca++ using recipe 2) I'm getting numbers that match the reef calculator, so I guess I'm doing things right.

 

[Randy Holmes-Farley]

dKH is a historical unit. Explaining why it relates to meq/L is like explaining why deg F relates to deg C. An equation is about the limit of most people's interest, although there is a true reason.

I discuss such unit of measure issues here:

The Units of Measure of Reefkeeping
http://reefkeeping.com/issues/2005-08/rhf/index.php

from it:

dKH

dKH stands for the German term “degrees of carbonate hardness.” It is a unit of alkalinity, and is equivalent to 0.36 meq/L or 17.8 ppm calcium carbonate equivalents. There are other related units that have similar names, such as Clark degrees, but they are rarely used by reef aquarists. Hardness is most often used to refer to calcium and magnesium in solution, but “carbonate hardness” evolved from the assumption that in fresh water, much of the carbonate comes from weathering of calcium and magnesium carbonates. So some units of measure (like dKH and ppm calcium carbonate equivalents) refer to the concentration with respect to the amount of calcium carbonate that would need to dissolve into the water to produce that alkalinity. An article explaining in detail what alkalinity is and what the units mean is online here. There is a calculator for converting between different alkalinity units online here. There is a calculator for determining how much of different supplements to add to boost alkalinity, as well as calcium and magnesium, online here.

 

[DeadlyMuffin]

Thank you.

I feel a lot more comfortable doing the calculation on the back of an envelope than plugging numbers into an online calculator, and now it looks like I should be able to do that pretty easily.

I appreciate the background on dKH as well, it's always interesting to see who uses different units. The units of measure article is definitely a great resource to have.

 

[Randy Holmes-Farley]

:thumbsup:

FWIW, we have checked the calculator pretty carefully.