# 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?

Feb 20, 2015

You would need $\text{37.1 g}$ of toothpaste to get the job done.

So, let's start with what $\text{1400 ppm}$ 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 $\text{NaF}$ is 1400 ppm, which means that 1 kg of toothpaste contains 1400 mg of $\text{NaF}$.

All you have to do now is set up a simple conversion factor to see how much toothpaste contains 52 mg of $\text{NaF}$

$\text{52 mg NaF" * ("1 kg toothpaste")/("1400 mg NaF") = "0.0371 kg toothpaste}$

$\text{0.0371 kg}$ of toothpaste contain 52 mg of $\text{NaF}$. Expressed in grams, this amount is equal to

$\text{0.0371 kg" * ("1000 g")/("1 kg") = "37.1 g}$