Question

How many grams of toothpaste are required 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?

Answer 1

In the above question, we have found the amount of toothpaste that needs to kill a rat. The concentration of NaF is given in ppm so we have to first convert it into a number of mg/kg. From this, we can find out the amount of NaF present in 1kg of toothpaste. And then we have to see how much toothpaste will contain 52mg and hence, the result obtained will be the amount required to kill the rat.

Complete step by step solution:
In the above question, the amount of NaF is given as 1440ppm.
1 ppm can be defined as 1 mg of substance present in 1 kg of the solution.
Mathematically, it can be written as:
1 ppm = $\dfrac{{{\text{1 mg}}}}{{{\text{1 kg}}}}$
In the above question, it is given that the amount of NaF present is 1400ppm which implies that in the toothpaste, the amount of NaF present is $\dfrac{{{\text{1400 mg}}}}{{{\text{1 kg}}}}$ .
It is given that 52mg/kg is sufficient to kill the rat.
We obtain that 1400 mg is present in 1 kg of toothpaste.
So, 52mg is present in $\dfrac{{{\text{52}}}}{{{\text{1400}}}}{\text{ = 0}}{\text{.037}}$ kg of toothpaste.
Hence, 37 gram of toothpaste is sufficient to kill the rat.

Note:
The parts per million is usually used to measure the amount of contamination and sediments in soil. It is also used to measure the pollutants present in air.