The lethal dose (LD50) for caffeine is 200 mg/kg and each cup of coffee contains 90 mg caffeine. a) How many cups of coffee should a person of 80 kg should drink at once to reach the lethal dose? b) If the person were to drink one cup of coffee per day for this number of days (calculated in 1) a)), would s/he be likely to die from an overdose of caffeine? c) If the person could drink exactly the number of cups of coffee you calculated in a) all at one sitting, would the person be guranteed to die? Why or why not?
The Correct Answer and Explanation is:
) How many cups of coffee should an 80 kg person drink at once to reach the lethal dose?
The lethal dose (LD50) of caffeine is 200 mg per kg of body weight.
- First, calculate the total lethal dose for an 80 kg person: Lethal dose=200 mg/kg×80 kg=16,000 mg\text{Lethal dose} = 200 \, \text{mg/kg} \times 80 \, \text{kg} = 16,000 \, \text{mg}Lethal dose=200mg/kg×80kg=16,000mg
- Each cup of coffee contains 90 mg of caffeine. To find the number of cups required to reach the lethal dose: Number of cups=Lethal doseCaffeine per cup=16,000 mg90 mg/cup≈177.8 cups\text{Number of cups} = \frac{\text{Lethal dose}}{\text{Caffeine per cup}} = \frac{16,000 \, \text{mg}}{90 \, \text{mg/cup}} \approx 177.8 \, \text{cups}Number of cups=Caffeine per cupLethal dose=90mg/cup16,000mg≈177.8cups
So, the person would need to drink approximately 178 cups of coffee to reach the lethal dose of caffeine.
b) Would the person be likely to die from an overdose of caffeine if they drink one cup of coffee per day for this number of days?
The number of days it would take for the person to drink this amount of caffeine, drinking one cup per day, is:Number of days=178 cups\text{Number of days} = 178 \, \text{cups}Number of days=178cups
This means that it would take 178 days to consume the lethal dose by drinking one cup of coffee each day.
The lethal dose of caffeine is the amount that, when consumed all at once, has a 50% probability of causing death. Drinking 1 cup per day over 178 days is not likely to result in an overdose because the body metabolizes caffeine over time, and daily intake at such a low rate is typically not dangerous. Most individuals would likely be able to tolerate the daily caffeine dose without experiencing toxic effects.
c) If the person could drink exactly the number of cups of coffee (178) all at once, would they be guaranteed to die?
No, drinking 178 cups of coffee all at once would not guarantee death. Here’s why:
- The LD50 value represents the amount of caffeine required to kill 50% of individuals, not all individuals. This means that there is a 50% chance of surviving an overdose of this magnitude.
- Individuals have different sensitivities to caffeine, and factors like general health, age, tolerance to caffeine, and other metabolic factors influence how caffeine affects the body. For example, an individual with a high tolerance to caffeine may survive a larger dose than someone who rarely consumes caffeine.
Therefore, while it’s highly dangerous and could result in fatal symptoms such as seizures, heart arrhythmia, or organ failure, it would not be guaranteed that the person would die immediately after consuming 178 cups in one sitting.
