AP® Environmental Science review sheet from Aim for Five (aimforfive.com/enviro/units/8/8-12)
Unit 8 · Topic 8.12
8.12 Lethal Dose 50% (LD50)
LD50 is the dose of a substance that kills half of the animals in a test group. It is the standard way to compare how toxic different substances are: the lower the LD50, the less it takes to kill, so the more toxic the substance.
Key terms
- LD50
- toxicity
- dose
- test population
- mg/kg of body weight
What LD50 means
LD50 stands for lethal dose 50%. Researchers give groups of test animals, usually rats or mice, different doses of a substance and record how many die. The LD50 is the dose at which half of the test population dies.
Toxicity is how harmful a substance is to living things. Every substance is toxic at some dose; even water and table salt can kill in large enough amounts. LD50 puts toxicity on a common scale so substances can be compared. A toxicant is any substance that causes harm at some dose.
Units: mg per kg of body weight
LD50 is usually given in milligrams of substance per kilogram of body weight (mg/kg). Dividing by body weight lets you compare organisms of different sizes. A larger animal needs a larger total dose to reach the same mg/kg level.
To find a total dose, multiply the LD50 by the body mass: total dose (mg) = LD50 (mg/kg) × body mass (kg).
Lower LD50 means more toxic
This is the point students most often get backward. If Substance A has an LD50 of 5 mg/kg and Substance B has an LD50 of 500 mg/kg, it takes 100 times less of A to kill half the test animals. A is 100 times more toxic.
| Substance | LD50 (mg/kg) | Toxicity |
|---|---|---|
| A | 5 | Most toxic (smallest dose kills half) |
| C | 50 | Moderately toxic |
| B | 500 | Least toxic of the three |
How LD50 is used
Regulators use LD50 values to sort chemicals into toxicity categories and set labels and handling rules. For example, US pesticide labels carry a signal word based largely on how acutely toxic the product is: DANGER for the most toxic, then WARNING, then CAUTION for the least toxic. Comparing LD50 values also helps scientists choose less toxic alternatives, such as a pesticide that kills the target insect but has a much higher LD50 for birds and mammals.
Limits of LD50
- It only measures death, not other harm like cancer, birth defects or hormone disruption, which can happen at much lower doses.
- It usually measures acute (single, short-term) exposure, not chronic (long-term, low-level) exposure.
- Results from rats or mice may not match humans exactly, because species differ in how they absorb and break down chemicals.
- It requires killing test animals, which raises ethical concerns, and many labs now use alternative methods that use fewer animals.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Total dose from an LD50
A pesticide has an LD50 of 20 mg/kg in rats. What total dose would be expected to kill half of a group of rats that each weigh 0.25 kg? Give your answer in mg and in grams.
Show the solutionHide the solution
- Step 1: Total dose = LD50 × body mass = 20 mg/kg × 0.25 kg = 5 mg.
- Step 2: Convert to grams: 5 mg ÷ 1,000 mg/g = 0.005 g.
Answer: 5 mg (0.005 g) per rat.
- Example 2Calculator allowed
Trap: the bigger number is less toxic
Chemical X has an LD50 of 1,200 mg/kg. Chemical Y has an LD50 of 3 mg/kg. A student says X is more dangerous because its number is bigger. Correct the student and say how many times more toxic the more toxic chemical is.
Show the solutionHide the solution
- Step 1: LD50 is the dose needed to kill half the population. A smaller dose needed means a more toxic substance.
- Step 2: Y kills half the population at only 3 mg/kg, while X needs 1,200 mg/kg. So Y is more toxic.
- Step 3: Ratio = 1,200 ÷ 3 = 400.
Answer: Y is more toxic, about 400 times more toxic than X, because its LD50 is 400 times smaller.
- Example 3Calculator allowed
Scaling to a human (with caution)
A substance has an LD50 of 2.5 mg/kg in rats. Estimate the dose that would correspond to the LD50 for a 70 kg adult, and give one reason the estimate might be wrong.
Show the solutionHide the solution
- Step 1: Total dose = 2.5 mg/kg × 70 kg = 175 mg.
- Step 2: This assumes people respond the same way as rats per kilogram of body weight, which may not be true.
- Step 3: Humans and rats can differ in how they absorb, store and break down a substance, so the true human lethal dose could be higher or lower.
Answer: About 175 mg. The estimate may be off because humans and rats process substances differently.
Common mistakes
- Thinking a higher LD50 means more toxic. Lower LD50 means more toxic.
- Forgetting to multiply by body mass when asked for a total dose.
- Assuming a dose below the LD50 is safe. Half the population dies at the LD50, some die below it, and non-lethal harm can occur at much lower doses.
On the exam
- Expect to compare two or more LD50 values and identify the most toxic substance, or to calculate a total dose from mg/kg and body weight.
- Write units at every step; mg/kg × kg = mg.
Connected topics
Videos
Check yourself
4 questions on 8.12 Lethal Dose 50% (LD50). Pick an answer to see if you got it, and why.
A chemical has an LD50 of 200 mg/kg in rats. If the same LD50 applied to a 60 kg adult, what dose would be expected to be lethal to half of a group of such adults?
| Chemical | Oral LD50 in rats (mg/kg of body weight) |
|---|---|
| W | 2,000 |
| X | 5 |
| Y | 300 |
| Z | 50 |
Hypothetical data
Which list ranks the chemicals from most toxic to least toxic?
Chemical Z is proposed as a crop pesticide, and tiny traces of it would remain on food. Which additional information would matter most before judging whether those traces are safe to eat?
| Dose (mg/kg body weight) | Mice that died (%) |
|---|---|
| 0 | 0 |
| 10 | 0 |
| 20 | 5 |
| 40 | 25 |
| 60 | 50 |
| 80 | 80 |
| 100 | 95 |
Hypothetical data from a toxicity test on groups of 40 mice
Based on the data, what is the LD50 of the chemical for these mice?
0 of 4 answered