Red #40 has an acute oral LD50 of roughly 5000 mg dye/1 kg body weight. This means if you had a mass of 1 kg, ingesting 5000 mg of Red #40 will have a 50% of killing you. Determine the amount of dye a 70 kg person would need to eat to reach his or her LD50. How many moles of dye would that be? The molar mass of Red #40 is 496.42 g/mol. Using the calculated concentration of Red #40 dye in the sports drink, how many of liters of sports drink would it take to reach this LD50?

350 g dye

0.705 mol

2.9 * 10⁴ L

Explanation:

The lethal dose 50 (LD50) for the dye is 5000 mg dye / 1 kg body weight. The amount of dye that would be needed to reach the LD50 of a 70 kg person is:

70 kg body weight * (5000 mg dye / 1 kg body weight) = 3.5 * 10⁵ mg dye = 350 g dye

The molar mass of the dye is 496.42 g/mol. The moles represented by 350 g are:

350 g * (1 mol / 496.42 g) = 0.705 mol

The concentration of Red #40 dye in a sports drink is around 12 mg/L. The volume of drink required to achieve this mass of the dye is:

3.5 * 10⁵ mg * (1 L / 12 mg) = 2.9 * 10⁴ L