Lethal Dose 50% (LD50)
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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:
Above the $LD_{50}$, so mortality should exceed 50%.
Below the $LD_{50}$, so mortality should be less than 50%.
Unrelated to $LD_{50}$ because the dose is in mg, not mg/kg.
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?
$72\ \text{mg}$
$45\ \text{mg}$
$4.5\ \text{mg}$
$0.72\ \text{mg}$
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:
$50\ \text{mg/kg}$
$15\ \text{mg/kg}$
$5\ \text{mg/kg}$
$25\ \text{mg/kg}$
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 insecticide is more toxic because $0.003\ \text{g/kg}$ is smaller than $3\ \text{mg/kg}$.
The second is less toxic because it is reported in grams.
The first is more toxic because mg/kg is always more toxic than g/kg.
They have the same toxicity because $0.003\ \text{g/kg}=3\ \text{mg/kg}$.
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 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.
The second 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?
Compound Q would require a higher dose to kill 50% than a compound with $LD_{50}=50\ \text{mg/kg}$.
The $LD_{50}$ indicates the dose that kills 50% of cells, not organisms.
Compound Q is more toxic than a compound with $LD_{50}=50\ \text{mg/kg}$.
Compound Q is less toxic 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?
$25\ \text{mg/kg}$
$2.5\ \text{mg/kg}$
$250\ \text{mg/kg}$
$2500\ \text{mg/kg}$
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 correct; higher $LD_{50}$ means higher toxicity.
The student is incorrect; $LD_{50}$ measures chronic toxicity only.
The student is correct because both values are in mg/kg.
The student is incorrect; lower $LD_{50}$ indicates higher toxicity.
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.