User blog:EvergreenFir/How much toothpaste would it take to kill Mabel?

So we all know that Mabel at a tube of toothpaste. And hopefully we all know that's a terrible idea. But just how bad of an idea was it? How much toothpaste would it take to kill Mabel? Using math, we can get an estimate.

First, we need to know the LD50 of the most toxic substance in toothpaste: sodium fluoride (NaF in chemical symbols). The LD50 means "lethal dose 50%" and refers to the amount of a substance it takes to kill 50% of test subjects (usually mice and rats). For sodium fluoride, the LD50 is between 31 mg/kg1 and 200 mg/kg2. In other words, it would take between 3100 mg (3.1 grams) and 20000 mg (20 grams) to reach the LD50 for someone who weighed 100 kg (220 lbs).

Next we need to estimate Mabel's body mass. An average 12 year old girl weights 93 lbs.3 There are 2.2 pounds per kilogram, so 93 lbs = 41 kg.

Last, we need to know how much sodium fluoride is in a tube of toothpaste. The one in my bathroom (Colgate Total) contains 6 oz of toothpaste, 0.24% of which is sodium fluoride. So the tube has 6*0.0024=0.0144 oz of sodium fluoride. There are 28349.5 mg (28.35 grams) in an ounce, so 0.0144*28349.5 = 408.23 mg of sodium fluoride in one tube of tooth paste.

So the equation we can use is Mabel's_mass * LD50NaF / NaF_in_tube

So, the final calculations are:

LD50NaF = 31 mg
 * (41 kg * 31 mg/kg) / 408.23 mg/tube = 3.11 tubes

LD50NaF = 200 mg
 * (41 kg * 200 mg/kg) / 408.23 mg/tube = 20.1 tubes

In sum, it would take between 3 and 20 tubes of toothpaste for Mabel to reach a lethal dose for 50% of test subjects.