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50% LETHAL DOSE

Lethal Dose 50%
\(\text{LD}_{50}\)

Understanding dose-response relationships and the standard measure of acute toxicity used in environmental science and toxicology.

AP Environmental Science

What Is Toxicology?

Toxicology is the scientific study of the adverse effects that chemical, physical, or biological agents have on living organisms. At its core lies a fundamental principle attributed to Paracelsus (1493 - 1541):

In environmental science, toxicology helps us evaluate how pollutants, pesticides, and industrial chemicals affect ecosystems and human health.

Defining \(\text{LD}_{50}\)

The Lethal Dose 50% (\(\text{LD}_{50}\)) is the dose of a substance that kills 50% of a test population within a specified time period (usually 24 - 96 hours).

LD
Stands for Lethal Dose: the amount of substance administered
50
The percentage of the test population that dies: 50% mortality

The Dose-Response Curve

0% 50% 100% % Mortality Dose (mg/kg)
\(\text{LD}_{50}\)
 Sigmoid curve

How \(\text{LD}_{50}\) Is Determined

Historically, \(\text{LD}_{50}\) values were determined through animal testing. Groups of test organisms receive increasing doses, and mortality is recorded.

1
Divide subjects into groups. Each group receives a different dose of the substance.
2
Administer the substance (oral, dermal, or inhalation) and observe for a set period (24 - 96 hours).
3
Record mortality at each dose level and plot the dose-response curve.
4
Determine the \(\text{LD}_{50}\) by finding the dose corresponding to 50% mortality on the fitted curve.

Units and Interpretation

\(\text{LD}_{50}\) is expressed in milligrams of substance per kilogram of body weight (\(\text{mg/kg}\)). This normalization allows comparison across species of different sizes.

More Toxic
Low \(\text{LD}_{50}\)
 Less Toxic
High \(\text{LD}_{50}\)
 Botulinum 0.001 Dioxin 0.02 Nicotine 50 Caffeine 192 Sugar 29,700
\(\text{LD}_{50}\) values in mg/kg (oral, rat)

\(\text{LD}_{50}\) vs. Related Measures

Measure What It Measures Units Context
\(\text{LD}_{50}\) Dose killing 50% mg/kg Oral / dermal exposure
\(\text{LC}_{50}\) Concentration killing 50% ppm or mg/L Inhalation / aquatic
\(\text{ED}_{50}\) Dose producing an effect in 50% mg/kg Therapeutic / sublethal
\(\text{TD}_{50}\) Dose that is toxic to 50% mg/kg Non-lethal toxicity

Acute vs. Chronic Toxicity

Acute Toxicity
Short-term, high-dose exposure. Effects appear within hours or days. \(\text{LD}_{50}\) is a measure of acute toxicity.
Chronic Toxicity
Long-term, low-dose exposure over weeks, months, or years. May cause cancer, organ damage, or reproductive harm.

Threshold Dose and NOAEL

Not all exposures cause harm. Toxicologists identify threshold levels below which no adverse effects are observed.

NOAEL
No Observed Adverse Effect Level: the highest dose at which no harmful effects are detected
LOAEL
Lowest Observed Adverse Effect Level: the lowest dose at which harmful effects are first observed

How to Interpret \(\text{LD}_{50}\) Values

1
Identify the substance and its \(\text{LD}_{50}\) value in mg/kg.
2
Note the test species (usually rat, oral route). Values differ between species and exposure routes.
3
Compare values: a smaller number means more toxic, a larger number means less toxic.
4
Apply the toxicity scale: \(\lt 1\) mg/kg = extremely toxic; 1 - 50 = highly toxic; 50 - 500 = moderately toxic; 500 - 5,000 = slightly toxic; \(\gt 5,000\) = practically non-toxic.
5
Consider the full picture: \(\text{LD}_{50}\) only measures acute lethality. Also assess chronic effects, bioaccumulation, and environmental persistence.

Toxicity Classification Scale

Category \(\text{LD}_{50}\) (mg/kg) Example
Extremely Toxic \(\lt 1\) Botulinum toxin
Highly Toxic 1 - 50 Strychnine, nicotine
Moderately Toxic 50 - 500 DDT, aspirin
Slightly Toxic 500 - 5,000 Table salt (3,000)
Practically Non-toxic \(\gt 5,000\) Sucrose (29,700)

Example 1: Comparing Pesticides

Two pesticides are being evaluated for agricultural use:

Pesticide A
\(\text{LD}_{50} =\) 5 mg/kg
Pesticide B
\(\text{LD}_{50} =\) 200 mg/kg

Example 2: Reading a Dose-Response Graph

0% 50% 100% % Mortality Dose (mg/kg) 10 25 50 100 200
X: \(\text{LD}_{50} = 25\)
Y: \(\text{LD}_{50} = 100\)
 Substance X Substance Y

Example 3: Calculating Lethal Dose

A substance has an \(\text{LD}_{50}\) of 150 mg/kg (oral, rat). Estimate the dose that would be lethal to 50% of a population of 80 kg humans (assuming direct extrapolation).

1
Write the formula: \(\text{Lethal dose} = \text{LD}_{50} \times \text{body weight}\)
2
Substitute: \(150 \, \text{mg/kg} \times 80 \, \text{kg}\)
3
Calculate: \(12{,}000 \, \text{mg} = 12 \, \text{g}\)

Common Mistakes

✕ Higher = More Toxic
Students often think a higher \(\text{LD}_{50}\) means more toxic. It is the opposite: lower \(\text{LD}_{50}\) = more toxic.
✕ Confusing \(\text{LD}_{50}\) and \(\text{LC}_{50}\)
\(\text{LD}_{50}\) measures dose (mg/kg). \(\text{LC}_{50}\) measures concentration (ppm or mg/L). They are not interchangeable.
✕ Ignoring Chronic Effects
\(\text{LD}_{50}\) only measures acute lethality. A substance with a high \(\text{LD}_{50}\) can still be dangerous through long-term exposure.

Question 1 of 5

Substance A has an \(\text{LD}_{50}\) of 5 mg/kg and Substance B has an \(\text{LD}_{50}\) of 5,000 mg/kg. Which statement is correct?

Question 2 of 5

A pesticide has an \(\text{LD}_{50}\) of 300 mg/kg (oral, rat). For a 60 kg person, what is the estimated lethal dose that would kill 50% of a similarly exposed population?

Question 3 of 5

A researcher studying fish toxicity reports a value in mg/L. This value most likely represents which measure?

Question 4 of 5

On a dose-response curve, the \(\text{LD}_{50}\) is found at the point where:

Question 5 of 5

Lead has a relatively high \(\text{LD}_{50}\) (450 mg/kg in rats), yet it is considered one of the most dangerous environmental pollutants. Which concept best explains this?