50% kill (LD50) for rats is 192 mg/kg. MSDS sheets state that the lethal dose of caffeine is 25 mg. How many cups of tea (assuming each tea bag contains 25 mg of caffeine) would a 700 g rat need to drink to consume an average lethal dose? [2]
The Correct Answer and Explanation is:
To calculate how many cups of tea a 700 g rat would need to drink to consume an average lethal dose of caffeine, we need to break down the problem step by step.
Step 1: Determine the lethal dose of caffeine for a rat
The LD50 (lethal dose for 50% of subjects) is given as 192 mg/kg for rats. This means that for each kilogram of body weight, the lethal dose is 192 mg of caffeine.
For a rat weighing 700 g, we first convert the weight to kilograms: 700 g=0.7 kg700 \, \text{g} = 0.7 \, \text{kg}700g=0.7kg
Next, multiply the rat’s weight in kilograms by the lethal dose per kilogram: Lethal dose=192 mg/kg×0.7 kg=134.4 mg\text{Lethal dose} = 192 \, \text{mg/kg} \times 0.7 \, \text{kg} = 134.4 \, \text{mg}Lethal dose=192mg/kg×0.7kg=134.4mg
So, the lethal dose of caffeine for a 700 g rat is 134.4 mg.
Step 2: Calculate how many cups of tea this corresponds to
Each tea bag contains 25 mg of caffeine. To find out how many cups of tea are needed to reach the lethal dose, divide the lethal dose by the amount of caffeine per tea bag: Number of cups=134.4 mg25 mg/cup=5.376\text{Number of cups} = \frac{134.4 \, \text{mg}}{25 \, \text{mg/cup}} = 5.376Number of cups=25mg/cup134.4mg=5.376
Since the rat cannot drink a fraction of a cup in this context, we round this to the nearest whole number. Therefore, the rat would need to drink 5 cups of tea to consume a lethal dose of caffeine.
Conclusion:
A 700 g rat would need to drink 5 cups of tea (each containing 25 mg of caffeine) to consume an average lethal dose of caffeine.
