Questions: If the caffeine concentration in a particular brand of soda is 2.09 mg / oz, drinking how many cans of soda is lethal? Assume that 10.0 g of caffeine is a lethal dose, and there are 12 oz in a can.

Solution Steps

To determine how many cans of soda would be lethal, we need to calculate the total amount of caffeine in one can and then find out how many such cans would sum up to the lethal dose.

1. Calculate the amount of caffeine in one can of soda.
2. Divide the lethal dose by the amount of caffeine per can to find the number of cans.

Given that the lethal dose of caffeine is \(10.0 \, \text{g}\), we convert this to milligrams: \[ 10.0 \, \text{g} \times 1000 \, \frac{\text{mg}}{\text{g}} = 10000 \, \text{mg} \]

The caffeine concentration in the soda is \(2.09 \, \text{mg/oz}\) and each can contains \(12 \, \text{oz}\). Therefore, the amount of caffeine in one can is: \[ 2.09 \, \frac{\text{mg}}{\text{oz}} \times 12 \, \text{oz} = 25.08 \, \text{mg} \]

To find the number of cans that would result in a lethal dose, we divide the lethal dose by the amount of caffeine per can: \[ \frac{10000 \, \text{mg}}{25.08 \, \text{mg/can}} \approx 398.7 \, \text{cans} \]

Final Answer