How many grams to toothpaste to kill a rat? One of the leading toothpaste brands advertises Fluoride (NaF) at 1400ppm. And the MSDS for Sodium Fluoride says that 52mg/kg is enough to kill a rat. How would I calculate this?

1 Answer
Feb 20, 2015

You would need "37.1 g" of toothpaste to get the job done.

So, let's start with what "1400 ppm" actually means. PPM, or parts per million, is used to express really small concentrations of a substance in a solution or a mixture. Mathematically, a 1-ppm concentration has

"1 ppm" = "1 mg"/("1 kg")

Every 1 kg of solution contains 1 mg, or 10^(-3) grams, of your substance of interest. In this case, the concentration of "NaF" is 1400 ppm, which means that 1 kg of toothpaste contains 1400 mg of "NaF".

All you have to do now is set up a simple conversion factor to see how much toothpaste contains 52 mg of "NaF"

"52 mg NaF" * ("1 kg toothpaste")/("1400 mg NaF") = "0.0371 kg toothpaste"

"0.0371 kg" of toothpaste contain 52 mg of "NaF". Expressed in grams, this amount is equal to

"0.0371 kg" * ("1000 g")/("1 kg") = "37.1 g"