Lethal Dose 50% (LD50)
Help Questions
AP Environmental Science › Lethal Dose 50% (LD50)
A chemical has $LD_{50}=70 \text{mg/kg}$. A $0.2 \text{kg}$ lab animal receives $7 \text{mg}$. The dose is $\frac{7}{0.2}=35 \text{mg/kg}$. Relative to the $LD_{50}$, this dose is:
Unrelated to $LD_{50}$ because the dose is in mg, not mg/kg.
Below the $LD_{50}$, so mortality should be less than 50%.
Above the $LD_{50}$, so mortality should exceed 50%.
At the $LD_{50}$, so mortality should be 50%.
Explanation
To determine the relationship between the received dose and the $LD_{50}$, calculate the dose per kg of body weight and compare to the $LD_{50}$. The animal received 7 mg and weighs 0.2 kg, so the dose is $7 \div 0.2 = 35$ mg/kg. Since the chemical's $LD_{50}$ is 70 mg/kg, the received dose of 35 mg/kg is exactly half the $LD_{50}$. This dose is below the $LD_{50}$, so mortality should be less than 50%.
A chemical has $LD_{50}=18\ \text{mg/kg}$. A test animal weighs $250\ \text{g}$. What is the $LD_{50}$ dose for this animal?
$45\ \text{mg}$
$72\ \text{mg}$
$0.72\ \text{mg}$
$4.5\ \text{mg}$
Explanation
To calculate the LD50 dose for a specific animal, multiply the LD50 value by the animal's weight. First, convert the weight to kg: 250 g = 0.25 kg. Then calculate: 18 mg/kg × 0.25 kg = 4.5 mg. This means that 4.5 milligrams of the chemical would correspond to the LD50 dose for a 250-gram test animal, representing the amount expected to kill 50% of animals of this weight.
In an LD50 test on lab rats, Substance A has an $LD_{50}$ of $25\ \text{mg/kg}$ and Substance B has an $LD_{50}$ of $200\ \text{mg/kg}$. Which statement best compares their acute toxicity?
They have the same toxicity because both are measured in mg/kg.
Substance B is more toxic because it has a higher $LD_{50}$.
Substance A is less toxic because it requires a smaller dose to kill 50%.
Substance A is more toxic because it has a lower $LD_{50}$.
Explanation
LD50 is the dose that kills 50% of a test population, expressed as mg of substance per kg of body weight. A lower LD50 indicates higher toxicity because less substance is needed to cause 50% mortality. Substance A has an LD50 of 25 mg/kg, meaning it takes only 25 mg per kg of body weight to kill half the population. Substance B has an LD50 of 200 mg/kg, requiring much more substance to achieve the same lethal effect. Therefore, Substance A is more toxic because it has a lower LD50 value.
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:
$50\ \text{mg/kg}$
$5\ \text{mg/kg}$
$25\ \text{mg/kg}$
$15\ \text{mg/kg}$
Explanation
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.
An insecticide has $LD_{50}=3\ \text{mg/kg}$ (oral, rats). Another has $LD_{50}=0.003\ \text{g/kg}$ (oral, rats). Which statement is correct?
The second is less toxic because it is reported in grams.
The second insecticide is more toxic because $0.003\ \text{g/kg}$ is smaller than $3\ \text{mg/kg}$.
They have the same toxicity because $0.003\ \text{g/kg}=3\ \text{mg/kg}$.
The first is more toxic because mg/kg is always more toxic than g/kg.
Explanation
When comparing LD50 values, it's essential to ensure units are consistent. The first insecticide has LD50 = 3 mg/kg, while the second has LD50 = 0.003 g/kg. Converting the second value: 0.003 g/kg = 3 mg/kg (since 1 g = 1000 mg). Both substances have identical LD50 values when expressed in the same units, meaning they have the same acute toxicity in rats when administered orally.
A chemical has $LD_{50}=0.05\ \text{mg/kg}$. Another has $LD_{50}=5\ \text{mg/kg}$. Which statement is correct?
The second chemical is 100 times more toxic.
The first chemical is 10 times more toxic.
They have the same toxicity because both are in mg/kg.
The first chemical is 100 times more toxic.
Explanation
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 toxin has $LD_{50}=6\ \text{mg/kg}$ in a frog species. Which dose is most likely to be near the threshold for 50% mortality?
$6\ \text{mg/kg}$
$600\ \text{mg/kg}$
$0.6\ \text{mg/kg}$
$60\ \text{mg/kg}$
Explanation
The LD50 represents the dose that produces exactly 50% mortality. A toxin with LD50 = 6 mg/kg means that 6 mg/kg is the dose most likely to be near the threshold for 50% mortality in frogs. This is the defining characteristic of LD50 - it identifies the specific dose level where approximately half the population dies from acute exposure. The other doses would produce mortality rates either significantly above or below 50%.
A lab report lists $LD_{50}=5\ \text{mg/kg}$ for Compound Q in guinea pigs. Which statement is correct?
The $LD_{50}$ indicates the dose that kills 50% of cells, not organisms.
Compound Q is less toxic than a compound with $LD_{50}=50\ \text{mg/kg}$.
Compound Q is more toxic than a compound with $LD_{50}=50\ \text{mg/kg}$.
Compound Q would require a higher dose to kill 50% than a compound with $LD_{50}=50\ \text{mg/kg}$.
Explanation
LD50 measures acute toxicity, with lower values indicating higher toxicity. Compound Q has an LD50 of 5 mg/kg, which means it takes only 5 mg per kg of body weight to kill 50% of guinea pigs. A compound with LD50 = 50 mg/kg would require 10 times more substance (50 mg/kg) to achieve the same lethal effect. Therefore, Compound Q is more toxic than a compound with LD50 = 50 mg/kg because it needs less substance to cause the same mortality rate.
A chemical has $LD_{50}=0.25\ \text{g/kg}$. Which of the following is the correct conversion to mg/kg?
$250\ \text{mg/kg}$
$25\ \text{mg/kg}$
$2.5\ \text{mg/kg}$
$2500\ \text{mg/kg}$
Explanation
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.
A student claims that a chemical with $LD_{50}=400\ \text{mg/kg}$ is more toxic than one with $LD_{50}=40\ \text{mg/kg}$. Which correction is accurate?
The student is incorrect; lower $LD_{50}$ indicates higher toxicity.
The student is correct because both values are in mg/kg.
The student is correct; higher $LD_{50}$ means higher toxicity.
The student is incorrect; $LD_{50}$ measures chronic toxicity only.
Explanation
The student's understanding of LD50 is incorrect. LD50 measures acute toxicity, where lower values indicate higher toxicity, not higher values. A chemical with LD50 = 40 mg/kg is more toxic than one with LD50 = 400 mg/kg because it takes less substance (40 mg/kg vs 400 mg/kg) to kill 50% of the population. The student has the relationship backwards - lower LD50 means you need less of the substance to cause the same lethal effect, indicating higher toxicity.