# Calculation of mass from mmol/L

Sorry I understand this looks like a "homework question", (I'm actually a 46yr old dentist looking to see what amount of calcium phosphate should be effective in a proprietary toothpaste!). However, if the actual question below can not be worked out can you let me know what the process of the calculation would be to determine mass of a salt to add to gain a mmol/L concentration?

Original Question: I wonder if you can help on this? I want to calculate how much calcium phosphate to add to 1g of toothpaste to have between 18mmol/L to 1.5mmol/L of calcium and phosphate on the tooth surface? Also if you are able to work this out can you let me know what assumptions you have made in this calculation?

• If you need a concentration of Calcium phosphate on the surface of a tooth, we need to know how thick this layer is and what the surface area of teeth are. What is the volume of 1g of toothpaste? Should we assume that 1g of toothpaste will cover the entire surface of the teeth? – user137 Jul 31 '14 at 22:16

There are several calcium phosphates. I'll assume you mean monocalcium posphate, $\ce{Ca(H2PO4)2}$, because the others are not nearly soluble enough in water to allow even a 1.5 mmol/L solution. (I assume the toothbase's most abundant ingredient is water.)
Multiplying 1.5mmol/L by 0.9mL gives you 1.35 micro moles (1.35$\times 10^{-6}$ moles). Since 1 mole is 234 grams (formula weight), this means 316 micrograms or 0.315 mg. The same calculation with 18mmol/L gives 3.79 mg.