Lethal Dose 50% (LD50) - AP Environmental Science

A toxin's $LD_{50}$ in rats is $250\ \text{mg/kg}$ . A lab rat weighs $0.4\ \text{kg}$ . The $LD_{50}$ dose for this rat is:
Answer: $100\ \text{mg}$ To calculate the LD50 dose for a specific animal, multiply the LD50 value by the animal's weight. The calculation is: 250 mg/kg × 0.4 kg = 100 mg. This means that 100 milligrams of the toxin would correspond to the LD50 dose for a 0.4 kg rat. At this dose level, approximately 50% of rats of this weight would be expected to die from acute exposure.
A pesticide label reports an acute oral $LD_{50}$ in mice of $5\ \text{mg/kg}$ . Approximately what dose would be expected to kill 50% of a group of $0.030\ \text{kg}$ mice (30 g each), assuming similar sensitivity?
Answer: $0.15\ \text{mg}$ To find the actual dose that would kill 50% of mice, we multiply the LD50 value by the body weight of the mice. The LD50 is 5 mg/kg, and each mouse weighs 0.030 kg (30 grams). The calculation is: 5 mg/kg × 0.030 kg = 0.15 mg. This means that a dose of 0.15 mg of the pesticide would be expected to kill 50% of a group of 30-gram mice. The LD50 concept assumes similar sensitivity across individuals of the same species with similar body weights. Answer A correctly shows this calculation result of 0.15 mg.
A toxicologist determines that Chemical J has $LD_{50}=2.5\ \text{mg/kg}$ and Chemical L has $LD_{50}=25\ \text{mg/kg}$ . If both are tested under the same conditions, which is true?
Answer: Chemical J is 10 times more toxic than Chemical L. To compare the relative toxicity of chemicals, divide the higher LD50 by the lower LD50. Chemical J has LD50 = 2.5 mg/kg and Chemical L has LD50 = 25 mg/kg. The calculation is: 25 ÷ 2.5 = 10. This means Chemical J is 10 times more toxic than Chemical L because it requires 10 times less substance per kg of body weight to kill 50% of the population. Lower LD50 values always indicate higher toxicity.
A student reads that Compound P has $LD_{50}=100\ \text{mg/kg}$ . The student concludes that 100 mg will kill 50% of test animals. What is wrong with this conclusion?
Answer: The $LD_{50}$ is given per kilogram of body mass, not as a fixed mass for all animals. The student's conclusion is incorrect because LD50 is expressed per kilogram of body weight, not as a fixed total dose. The value 100 mg/kg means that 100 milligrams per kilogram of body weight kills 50% of test animals. The actual amount needed depends on the animal's weight - a 1 kg animal would need 100 mg total, while a 2 kg animal would need 200 mg total. The LD50 accounts for body weight differences to provide a standardized toxicity measure.
A dose-response study reports: at $10\ \text{mg/kg}$ , 10% mortality; at $20\ \text{mg/kg}$ , 40% mortality; at $30\ \text{mg/kg}$ , 60% mortality. Based on this information, the $LD_{50}$ is closest to:
Answer: $25\ \text{mg/kg}$ LD50 is determined from dose-response data by finding the dose that produces 50% mortality. Looking at the given data: 10 mg/kg causes 10% mortality, 20 mg/kg causes 40% mortality, and 30 mg/kg causes 60% mortality. The LD50 (50% mortality) falls between 20 and 30 mg/kg. Using interpolation, since 40% to 60% mortality spans from 20 to 30 mg/kg, the 50% point would be at 25 mg/kg, which is closest to option B.
A rodenticide has an $LD_{50}$ of $0.5\ \text{mg/kg}$ in mice. Approximately what mass of rodenticide corresponds to the $LD_{50}$ dose for a $20\ \text{g}$ mouse?
Answer: $0.01\ \text{mg}$ To calculate the LD50 dose for a specific animal, multiply the LD50 value by the animal's weight. First, convert the mouse weight to kg: 20 g = 0.02 kg. Then calculate: 0.5 mg/kg × 0.02 kg = 0.01 mg. This means that 0.01 milligrams of rodenticide would correspond to the LD50 dose for a 20-gram mouse, representing the amount expected to kill 50% of mice of this weight.
A chemical's $LD_{50}$ is $2\ \text{mg/kg}$ . Which dose is most likely to produce less than 50% mortality (all else equal)?
Answer: $0.5\ \text{mg/kg}$ LD50 represents the dose that causes 50% mortality, so doses below this value would be expected to cause less than 50% mortality. The chemical has LD50 = 2 mg/kg, meaning this dose kills 50% of the population. Among the options, 0.5 mg/kg is the only dose lower than 2 mg/kg. Since it's below the LD50, this dose would most likely produce less than 50% mortality in a test population.
A dose-response study indicates the $LD_{50}$ for Chemical K is $40\ \text{mg/kg}$ . Which statement best describes what happens at $40\ \text{mg/kg}$ ?
Answer: 50% of the population dies. LD50 represents the specific dose at which 50% mortality occurs in a test population. When Chemical K has an LD50 of 40 mg/kg, this means that at exactly this dose level, approximately 50% of the population dies from acute exposure. This is the fundamental definition of LD50 - the lethal dose for 50% of the population. It's important to note that saying 50% survives is equivalent to saying 50% die.
Two chemicals are tested for acute toxicity in fish. Chemical X has $LD_{50}=4\ \text{mg/kg}$ and Chemical Y has $LD_{50}=0.4\ \text{mg/kg}$ . Which interpretation is correct?
Answer: Chemical Y is 10 times more toxic than Chemical X. LD50 measures acute toxicity, where lower values indicate higher toxicity. Chemical X has an LD50 of 4 mg/kg while Chemical Y has an LD50 of 0.4 mg/kg. Since Chemical Y requires only 0.4 mg per kg of body weight to kill 50% of fish compared to Chemical X's 4 mg/kg, Chemical Y is more toxic. To determine how many times more toxic, divide 4 by 0.4, which equals 10. Therefore, Chemical Y is 10 times more toxic than Chemical X.
A chemical has $LD_{50}=0.25\ \text{g/kg}$ . Which of the following is the correct conversion to mg/kg?
Answer: $250\ \text{mg/kg}$ To convert from g/kg to mg/kg, multiply by 1000 since there are 1000 milligrams in one gram. The calculation is: 0.25 g/kg × 1000 mg/g = 250 mg/kg. This conversion maintains the same toxicity value but expresses it in different units. Both 0.25 g/kg and 250 mg/kg represent the same LD50 value for the chemical.
Chemicals C and D have $LD_{50}$ values of $900\ \text{mg/kg}$ and $0.9\ \text{g/kg}$ , respectively, in the same species. Which conclusion is correct?
Answer: They have the same toxicity based on $LD_{50}$ . To compare chemicals with LD50 values in different units, convert to the same units first. Chemical C has LD50 = 900 mg/kg, while Chemical D has LD50 = 0.9 g/kg. Converting Chemical D: 0.9 g/kg × 1000 mg/g = 900 mg/kg. Both chemicals have identical LD50 values when expressed in the same units (900 mg/kg), indicating they have the same acute toxicity in the test species.
In a dose-response test, Chemical S has $LD_{50}=75\ \text{mg/kg}$ . Which dose would most likely result in more than 50% mortality (all else equal)?
Answer: $150\ \text{mg/kg}$ LD50 represents the dose that causes 50% mortality in a test population. Chemical S has LD50 = 75 mg/kg, meaning this dose results in approximately 50% mortality. Doses higher than the LD50 would be expected to cause more than 50% mortality, while doses lower than the LD50 would cause less than 50% mortality. Among the options, 150 mg/kg is the only dose higher than 75 mg/kg, so it would most likely result in more than 50% mortality.
A dose–response curve for two substances (tested in the same organism and conditions) shows that Substance R reaches 50% mortality at a lower dose than Substance S. What can be concluded about their $LD_{50}$ values and relative toxicity?
Answer: Substance R has a lower $LD_{50}$ and is more toxic than Substance S. A dose-response curve plots the relationship between dose and the percentage of organisms affected (in this case, mortality). The LD50 is the dose at which the curve crosses the 50% mortality line. If Substance R reaches 50% mortality at a lower dose than Substance S on the same graph, this means Substance R has a lower LD50 value. Since a lower LD50 indicates higher toxicity, Substance R is more toxic than Substance S. The fact that both substances eventually reach 100% mortality at high doses is irrelevant to their LD50 values, which specifically measure the dose for 50% mortality. Answer A correctly states that Substance R has a lower LD50 and is more toxic.
A chemical has $LD_{50}=900\ \text{mg/kg}$ . Which statement is correct about a chemical with $LD_{50}=90\ \text{mg/kg}$ (same species/route)?
Answer: It is more toxic. When comparing LD50 values, a lower value indicates higher toxicity. The first chemical has LD50 = 900 mg/kg, while the second has LD50 = 90 mg/kg. Since 90 mg/kg is 10 times lower than 900 mg/kg, the second chemical requires much less substance to kill 50% of the population. Therefore, a chemical with LD50 = 90 mg/kg is more toxic than one with LD50 = 900 mg/kg.
A dose-response test finds $LD_{50}=300\ \text{mg/kg}$ for Chemical H. Which chemical would be expected to be more toxic in the same species?
Answer: A chemical with $LD_{50}=0.2\ \text{g/kg}$ To identify a more toxic chemical, look for one with a lower LD50 value. Chemical H has LD50 = 300 mg/kg. Converting all options to mg/kg: A) 500 mg/kg, B) 0.4 g/kg = 400 mg/kg, C) 350 mg/kg, D) 0.2 g/kg = 200 mg/kg. Option D has the lowest LD50 at 200 mg/kg, which is less than 300 mg/kg, making it more toxic than Chemical H because it requires less substance to kill 50% of the population.
A cleaning product contains Chemical Q. In rats, the reported acute oral $LD_{50}$ is $500\ \text{mg/kg}$ . Approximately how much of Chemical Q corresponds to the $LD_{50}$ dose for a $0.250\ \text{kg}$ rat?
Answer: $125\ \text{mg}$ To calculate the actual LD50 dose for a specific animal, multiply the LD50 value (in mg/kg) by the animal's body weight (in kg). For Chemical Q with an LD50 of 500 mg/kg and a rat weighing 0.250 kg, the calculation is: 500 mg/kg × 0.250 kg = 125 mg. This means 125 mg of Chemical Q would be the dose expected to kill 50% of rats weighing 0.250 kg each. The LD50 is always expressed per unit body weight to allow for scaling across different sized organisms. Answer A correctly shows this calculated dose of 125 mg.
A researcher reports that a solvent has an $LD_{50}$ of $2\ \text{g/kg}$ in rabbits. Which statement correctly interprets this value?
Answer: A dose of $2\ \text{g/kg}$ is expected to kill 50% of exposed rabbits. LD50 represents the dose that causes 50% mortality in a test population when expressed per kilogram of body weight. The value 2 g/kg means that 2 grams of solvent per kilogram of rabbit body weight is expected to kill 50% of exposed rabbits. This is a standardized measure that accounts for body weight differences, making it applicable across different sized animals within the species. The LD50 specifically measures acute toxicity from single or short-term exposure.
A dose-response curve shows that 50% mortality occurs at $80\ \text{mg/kg}$ for Chemical R. Which is the best interpretation?
Answer: At $80\ \text{mg/kg}$ , about half the tested organisms die. LD50 represents the dose at which 50% mortality occurs in a test population. When a dose-response curve shows that 50% mortality occurs at 80 mg/kg for Chemical R, this means that at this specific dose level, approximately half of the tested organisms would die from acute exposure. This is the standard definition of LD50 - the lethal dose for 50% of the population. The curve doesn't indicate complete safety below this dose or 100% mortality at this dose.
A chemical has $LD_{50}=0.05\ \text{mg/kg}$ . Another has $LD_{50}=5\ \text{mg/kg}$ . Which statement is correct?
Answer: The first chemical is 100 times more toxic. To compare the relative toxicity of chemicals, divide the higher LD50 by the lower LD50. The first chemical has LD50 = 0.05 mg/kg and the second has LD50 = 5 mg/kg. The calculation is: 5 ÷ 0.05 = 100. This means the first chemical is 100 times more toxic than the second because it requires 100 times less substance per kg of body weight to kill 50% of the population. Lower LD50 values always indicate higher toxicity.
A chemical has $LD_{50}=500\ \text{mg/kg}$ in rats. Another has $LD_{50}=0.4\ \text{g/kg}$ in rats. Which is more toxic?
Answer: The second chemical, because $0.4\ \text{g/kg}=400\ \text{mg/kg}$ , which is lower. To compare chemicals with LD50 values in different units, convert to the same units first. The first chemical has LD50 = 500 mg/kg, while the second has LD50 = 0.4 g/kg. Converting the second: 0.4 g/kg × 1000 mg/g = 400 mg/kg. Since 400 mg/kg is lower than 500 mg/kg, the second chemical is more toxic because it requires less substance per kg of body weight to kill 50% of rats.

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