Chemical math formula for borates (boron)

[easttn]

What is the "chemical" formula for figuring ppm for borates as far as a chemistry perspecitve?
I understand they are equivalent or measured in borons, such as on a test strip but I cant figure out where the numbers are coming from.

Here is an example (calcium hardness) of what Im looking for which shows where the numbers are coming from:
Calcium Carbonate (CaCO3) = 100.0869 g/mol
Calcium Chloride (CaCl) = 110.98 g/mol

100.0869 / 110.98 = 0.901846278608
(CaCO3gmol / CaClgmol = 100% Calcium Chloride Product is 90.18% Calcium Carbonate)

0.901846278608 x 0.95 = 0.85675396
(answer from above x 95% Calcium Chloride Product = 85.67% Calcium Carbonate)

8.3333333333333333 / 0.85675396 = 9.7266353 LBS to raise CH 1ppm per 1,000,000 gallons (for 95% product)
(weight of water in lbs / answer from above = LBS to raise CH 1ppm per 1,000 gallons (for 95% product))



This information fits into a similar equation somehow:

Boron
Sodium Tetraborate Decahydrate (Molar Mass: 381.38 g/mol)
Sodium Tetraborate Pentahydrate (Molar Mass: 291.29 g/mol)
Boric Acid (Molar Mass: 61.83 g/mol)

 

[JasonLion]

Borate is measured in ppm of Boron. You also need to remember that Sodium Tetraborate contains more than one boron.

 

[easttn]

I didnt think of that.

Sodium Tetraborate Decahydrate: Na2B4O7·10H2O
Sodium Tetraborate Pentahydrate: Na2B4O7·5H2O
Boric Acid: H3BO3

Sodium Tetraborates contain 4 borons while Boric Acid only conatains 1.
Boron has a molar mass of 10.811 g/mol.

So in the case of Boric Acid, it is 17% boron by weight (for a 100% boric acid product).
10.811 / 61.83 = 0.17485
8.3333333333333333 / 0.17485 = 47.6598 LBS to raise Borates 1ppm per 1,000,000 gallons (for 100% product)

That looks right to me, is it?
I'll have to come back later to try to calculate the other two which look more difficult.

 

[JasonLion]

That looks right, and matches Pool Math (given the rounding it does).

 

[easttn]

I calculated STD like this which also matches. It wasnt any harder than the other one.

Sodium Tetraborate Decahydrate (has 4 borons)
4 x 10.811 = 43.244 (4 Borons are 43.244 g/mol)
43.244 / 381.38 = 0.1133882217211 ( 100% STD Product is 11% boron by weight )
8.3333333333333333 / 0.1133882217211 = 73.49381 LBS to raise Borates 1ppm per 1,000,000 gallons (for 100% Product)

Sodium Tetraborate Pentahydrate would be the same formula but enter STP's g/mol instead of STD.

Thanks Jason. Sometimes you need a push in the right direction.