WANTED: Intuition for Dry Powder Calculations

[NeveroddoreveN]

There's a common pattern in DIY reefing: (1) I buy dry powder to dose some ion/anion, usually from LoudWolf. (2) I need to dilute it to make a solution. (3) I dose some amount of the solution.

Give a man a fish
I usually search and find some rule of thumb Randy has said (see attachment) and then monkey with the proportions, cross multiply a couple things, get confused and finally get a (maybe correct) answer.


...vs Teach a man to fish
How do I calculate it just with basic info about the molecule? For example, how do I calculate that trisodium phosphate is "about 58% phosphate"? And then, given the density, calculate how much water to make the solution, the size of each dose of that solution, and the estimated effect on my tank?

For example, let's use Na3PO4:
[given basic info/molar mass/density of Na3PO4]
Tank volume = 123.45 liters
Dry Powder volume = p ml
... Diluted with w ml of distilled water
... will increase my phosphate by x ppm if I dose d ml of my solution.

In general, what's the correct way to solve for one variable given the others?

 

[chipmunkofdoom2]

How do I calculate it just with basic info about the molecule? For example, how do I calculate that trisodium phosphate is "about 58% phosphate"? And then, given the density, calculate how much water to make the solution, the size of each dose of that solution, and the estimated effect on my tank?

For example, let's use Na3PO4:
[given basic info/molar mass/density of Na3PO4]
Tank volume = 123.45 liters
Dry Powder volume = p ml
... Diluted with w ml of distilled water
... will increase my phosphate by x ppm if I dose d ml of my solution.

In general, what's the correct way to solve for one variable given the others?

Here's how to calculate the percentage a substance is of another substance by weight. Let's use Na3PO4 as an example:

1. Find the molecular weight of the substance you have. You can usually find this by searching for something like "trisodium phosphate molecular weight." For Na3PO4, its 163.94 g/mol.
2. Find the molecular weight of the substance of interest. In this case, that's phosphate. The weight of phosphate is 94.97 g/mol.
3. Divide 2 by 1. This gives you the percentage PO4 of Na3PO4 by weight. In this case, it's 57.9%.

Here's how to calculate solution concentration. Let's use Na3PO4 as an example:

1. Weigh out an amount of the substance you want to add. For Na3PO4, let's use an amount like 1.88 grams.
2. Na3PO4 is about 57.9% PO4 by weight. That means we have1.088 grams of PO4 (0.579 * 1.88g Na3PO4)
2. Add the substance to a known quantity of water. Let's say in this case we have 1 liter.
3. We have added 1.088 grams PO4 to one liter of water. PPM is roughly equivalent to mg/kg. One liter of water weighs roughly 1 kg. So, ppm is roughly mg/l. So, our solution is roughly equivalent to 1,088 ppm PO4 (1.088 grams = 1,088 mg).

For calculating how much solution to add, that's a bit more tricky. The final solution of a concentration, ignoring precipitation, can be defined as:

Where:

Tv = Tank volume
Tc = Tank concentration
Sv = Solution volume
Sc = Solution concentration
C = final concentration
Tv+Sv != 0

I did not find the above very useful, so I refactored the equation to tell me how much to dose if I knew the solution and tank concentration:

Where:

Tv = tank volume
Tc = tank concentration
Sv = volume of solution dosed
Sc = solution concentration
Dc = desired concentration
Dc-Sc != 0

 

[NeveroddoreveN]

Thanks so much!!

How did you make the fancy equation thumbnails?

I like math just fine. But when making these calculations I know should be simple, I always get so confused by when to use mass and when to use volume! Technically, does ppm go by mass or volume?

Also, if Na3PO4 has a density of 1.62 g/cm³, could I use 0.67cm³ instead of 1.088g?

I know this precision is overkill for our purposes, I'm just trying to actually know how it's calculated instead of rules of thumb.

 

[ReefBeta]

Thanks so much!!

How did you make the fancy equation thumbnails?

I like math just fine. But when making these calculations I know should be simple, I always get so confused by when to use mass and when to use volume! Technically, does ppm go by mass or volume?

Also, if Na3PO4 has a density of 1.62 g/cm³, could I use 0.67cm³ instead of 1.088g?

I know this precision is overkill for our purposes, I'm just trying to actually know how it's calculated instead of rules of thumb.

It's almost always easier to use weight than volume in chemistry calculation. Weight don't change, 1 gram plus 1 grams is always 2 grams. Volume on the other hand is not. 1 liter + 1 liter different solution not always give you 2 liter solution. Also it's easier to measure accurate weight with scale. I don't know what's the accurate to measure powder volume.

 

[Randy Holmes-Farley]

Thanks so much!!

How did you make the fancy equation thumbnails?

I like math just fine. But when making these calculations I know should be simple, I always get so confused by when to use mass and when to use volume! Technically, does ppm go by mass or volume?

Also, if Na3PO4 has a density of 1.62 g/cm³, could I use 0.67cm³ instead of 1.088g?

I know this precision is overkill for our purposes, I'm just trying to actually know how it's calculated instead of rules of thumb.

ppm is neither mass nor volume. It is "parts per million parts". Could be per million parts by volume or mass or number, or even something else. For seawater ion concentrations, it is mass per mass of seawater.

Density MUST be the bulk powder density, not the crystal density, for volume to mass conversions.

 

[chipmunkofdoom2]

I like math just fine. But when making these calculations I know should be simple, I always get so confused by when to use mass and when to use volume! Technically, does ppm go by mass or volume?

As Randy said, ppm for our purposes measures mass per mass. If you wanted to measure your dry powders by volume and convert it to mass I'm sure you could, but that step seems unnecessary.

The equation thumbnails came from Google Docs. I have a document with all my formulas and equations. I used the built-in equation editor to create the equations, then I selected the equation with the Snipping Tool in Windows and pasted it into the post.

 

[NeveroddoreveN]

ppm is neither mass nor volume. It is "parts per million parts". Could be per million parts by volume or mass or number, or even something else. For seawater ion concentrations, it is mass per mass of seawater.

Density MUST be the bulk powder density, not the crystal density, for volume to mass conversions.

Would there be any advantage to using water displacement to measure volume? Would that be more accurate than bulk density?

 

[Randy Holmes-Farley]

Would there be any advantage to using water displacement to measure volume? Would that be more accurate than bulk density?

No. Bulk density is accurate enough for reef purposes.

Displacement can only work if:

1,. You know the exact density of the solids (rarely will you since no suppliers tells you the crystal form)
2. You displace liquid that it is completely insoluble in. Oil? Gasoline?

It seems overly complicated to me.

Way harder than weighing, or using bulk density and volume.

 

[taricha]

ppm = mg/kg = mg/L is a slightly wrong but close way to shortcut some math when close enough is okay. (1L of water isn't actually = 1kg)

echoing what's said earlier, use scales and mass rather than volume for solids.

 

[NeveroddoreveN]

Ok I just bought a scale.

Why did I not do this sooner! It's so cheap and solves such a fundamental issue