KH reference info and calculations
First, I meant to post this when Loop's "Simple DIY Drop Checker" post was current, but life intervened and I forgot about it until I needed to change my CO2 bottle. Second, I apologize if this post is a little long, but I want to include enough detail that others can avoid encountering some of the problems I have. If you are confident that your DIY KH reference solution is more accurate than your test kit, you can ignore this post; or better yet proof read it and make sure I haven't made any mistakes or miscalculations. The last thing I want to do is add more confusion to this subject.
When I first saw the DIY drop checker thread, I didn't even know what one was. I knew about the pH, KH, CO2 relationship, but had long ago discovered that it was useless for my tank due to the high GH, pH, and dissolved Calcium Carbonate in Kansas tap water. Once I read about how they worked, and saw how easy a drop checker was to build; I immediately began hunting for suitable materials to build one. I quickly put together a prototype to test using an old salt shaker, some tubing, a suction cup and a zip tie. Now all I needed was a known KH solution.
I searched the web expecting to find a commercial product that I could purchase. Instead I found dozens of links on how to make your own using baking soda and water. My first thought was "Great, now I don't have to pay shipping and wait a week." Then I began reading through the various instructions. I can't ever recall encountering so much confusing, conflicting, missing, and just plain incorrect information; even for the internet. I felt like I was reading recipes for Gumbo or Vegetable Soup as opposed to a technical procedure. Even different threads from this site had conflicting information regarding the ratio of baking soda to water, which was rather surprising.
Unfortunately, most of the instructions didn't include any technical info, assumptions, or example calculations, so I had no way to know which recipe to trust. I knew some of the instructions had to be correct, but which ones? To make matters even more frustrating, most of the instructions required weighing out minute amounts of baking soda accurate to within milligrams. While that is fine for some people (chemist, pharmacists, people who reload their own ammo, meth dealers, etc.); most people don't have a properly calibrated lab grade scale sitting on their kitchen counter. I really wanted to start with a known, easy to measure VOLUME of baking soda; say 1/4 or 1/8 teaspoon; and then calculate the necessary amount of water to add for a given KH. It's pretty easy to measure a volume of water with standard kitchen items.
Most good Pyrex measuring cups have graduations of 25 ml. Combine that with a syringe, marinade needle, turkey baster, or even measuring spoons and it's not too difficult to get within +/- 5-10ml. I decided the best course of action was to start with the basic chemistry, grind through the calculations, and then compare my results with some of the more detailed threads on the internet. Since I wasn't concerned about too much CO2, I decided to start with a 30dKH solution and dilute that down to 3dKH for the drop checker (30dKH also easily dilutes to 6,5, or 2 dKH, and 4dKH isn't much more work).
*Note: remember that to dilute 30dkH to 3dKH you need a 9:1 ratio of distilled water to KH solution, NOT a 10:1 ratio (just remember that 9+1=10, and 30/10 = 3).
Naturally, my first batch was a complete failure. I ended up with a solution that tested 14dKH as opposed to 30dKH (it was actually closer to 12dKH). In the process of trying to figure out where I had screwed up I learned a few very useful pieces of information.
First, as most of you already know, test kits expire quite rapidly compared to how often you normally use them. I knew the reagents would degrade over time, but I figured the box would contain an expiration/use by date if the product was likely to go bad before being used. While trying to find the expiration date of my KH test kit I stumbled upon an e-mail from API regarding this exact subject. The reason they don't put a use by date on the box is because the majority of their large customers (distributors and large retailers) specifically request that this information NOT be printed on the packaging. Essentially, they don't want customers to know the test kit they just purchased is only good for another 3-6 months. For example, not only was my test kit well past the suggested use by date, the GH test kit that came packaged with it was already over 2 years old when I bought the kit (which explains why I could never get it to change colors).
To add insult to injury, the nearest pet store(s) likely to stock a KH test kit were 90 miles away; which meant it was going to be at least a week before I could get a new one. Even with an expired test kit, I knew that something else had gone wrong. I was almost certain it had to due with my mass to volume conversion for the baking soda, but all of my math checked out fine. I decided to purchase a fresh, unopened box of baking soda and a new jug of distilled water; and then try again when I got a new test kit. When I purchased the baking soda I made sure it said "Active Ingredient: Sodium Bicarbonate 100%." Later I began to wonder if there was perhaps an inactive ingredient in baking soda from the grocery store. There's not, but the last line of the fine print read: "616mg Sodium per 1/2 teaspoon of baking soda."
I realized I could use that to calculate an exact density of Arm & Hammer baking soda. I ended up with a density of 913.9mg/cm^3; which was no where near the listed density for sodium bicarbonate (2.196g/cm^3). At this point I realized my monumentally stupid mistake. Chemically, baking soda is 100% sodium bicarbonate, but physically it is a powder, not a solid; meaning it contains a significant amount of air. The exact amount will depend upon how fine the powder is ground, and how much it has been compacted. Luckily backing soda doesn't compact much under its own weight unless you're dealing with huge quantities. Once I substituted this value into my calculations I got a theoretical value of 12.5 dKH for my original batch; which matched the results of my new test kit.
Anyway, after all of my blabbering, here is a sample calculation along with necessary chemical information and conversion factors.
Chemical formula for Sodium Bicarbonate (baking soda) --> NaHCO3
Sodium content of Arm & Hammer (A&H) baking soda --> 616mg/.5 tsp
NaHCO3 --> 84.01 g/mole
CO3 --> 60.01 g/mole (this is the carbonate ion)
Na --> 22.99g/mole
1dKH = 17.857ppm (part per million; by weight)
1ppm = 1mg/L of H20 (this will vary somewhat with temperature)
1cm^3 (cc) = .203 tsp (teaspoons, NOT tablespoons)
Keep in mind that KH is a measure of the concentration of carbonate ions (CO3), so the sodium and hydrogen atoms present in baking soda do not contribute to the KH value.
Sample Calculation for a 30dKH solution:
17.857ppm/1dKH X 30dKH = 535.71ppm --> 535.71mg CO3/L of H20
535.71mg CO3/(L of H20) X (84.01 g/mole NaHCO3)/(60.01 g/mole CO3) = 749.96 mg NaHCO3/(L of H2O)
For those of you wanting a 40dKH solution this equals 1.000g baking soda per L of water.
Density of A&H baking soda:
616mg Na/.5 tsp X (.203tsp/cm^3) X (84.01 g/mole NaHco3/22.99 g/mole Na) = 913.9mg/cm^3
749.96mg NaHCo3/(L of H20) X (1 cm^3/913.9mg) X (.203 tsp/cm^3) = .166 tsp NaHCO3/(L of H20)
.166 tsp/(1 L of H2O) = .125 tsp/(? L of H20); ? = .7504 L of H20
Therefore 1/8 tsp of A&H baking soda dissolved into 750.4 ml of H20 yields a 30dKH solution. (For a 40dKH solution this works out to 1/4 tsp per 1.126 L of H20).
I mixed up a batch using this ratio and tested it with a fresh KH test kit. At 29 drops the solution turned from blue to green. At 30 drops the solution turned bright yellow. Adding additional drops didn't have any noticeable affect on the color. Considering that reading a drop checker relies on color matching, this formula should be more than accurate enough. Personally, I plan on using my 30dKH solution to verify my test kit as it gets older.
I hope this information is useful to some of you out there, and that my calculations made sense. I'll gladly answer any questions to the best of my ability, but I'm a mechanical engineer NOT a chemical engineer.