One measure of toxicitiy of a substance is through LD50. The LD50 is the \"letha

Question

One measure of toxicitiy of a substance is through LD50. The LD50 is the "lethal dose", the concentration that causes death in 50% of the test animals. The LD50 for caffeine is 192 mg of caffeine per kg of body mass. A 180 lb person would need to consue about 80 cups of coffee before ingesting the "lethal dose" of caffeine. People with smaller body masses, like children, do not need to ingest as much of a product before they reach the LD50. How many cans of an energy drink would a 40 lb child have to drink to ingest the "lethal dose" of caffeine if there are 157 mg of caffeine per can? Is it likely this child will consume this number of cans in a day?

2.205 = 1kg

Explanation / Answer

Weight of the child in kg = 40/2.205 = 18.14 kg (2.205lb = 1 kg)

The LD50 for caffeine is given as 192mg of caffeine per kg of body mass.

So for 18.14 kg total LD50 dosage = 18.14* 192 mg = 3482.88 mg

Per can caffeine content is 157 mg. So number of cans to be consumed for lethal dosage = 3482.88 / 157 = 22.1839 cans.

Approximately 22 cans of energy drink can lead to the death of the child. It is not likely that a child will consume 22 cans of energy drink in a day.

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