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?

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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?

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Answer 1 · 2015-02-20T18:54:43

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

So, let's start with what $1400 ppm$ $"1400 ppm"$ 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

$1 ppm = \frac{1 mg}{1 kg}$ $"1 ppm" = "1 mg"/("1 kg")$

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

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

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

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

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

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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?

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