Hydrogen Cyanide from Apple Seeds — Lethal Dose Calculations

Key data

• Seed mass: $m_{ ext{seed}} = 33.3\ ext{mg} = 0.0333\ ext{g}$
• Hydrogen cyanide (HCN) yield per gram of crushed seeds: $Y = 0.162\ \frac{\text{mg}}{\text{g}}$
• Human body weight: $M = 84.6\ \text{kg}$
• Lethal dose for HCN: $\text{LD}_{\text{per kg}} = 1.52\ \frac{\text{mg}}{\text{kg}}$

Per-seed HCN yield

• HCN produced per seed (assuming seeds crushed and ingested):
  $\text{HCN per seed} = m_{ ext{seed}} \times Y = 0.0333 \ times 0.162 \approx 0.0053946\ \text{mg}$

Lethal dose calculation

• Total lethal dose for the 84.6 kg person:
  $\text{LD} = (1.52\ \frac{\text{mg}}{\text{kg}}) \times 84.6\ \text{kg} = 128.592\ \text{mg}$

Seeds required to reach lethal dose

• Number of seeds needed:
  $N_{ ext{seeds}} = \frac{\text{LD}}{\text{HCN per seed}} = \frac{128.592}{0.0053946} \approx 2.3837 \times 10^4$
• Rounded: about (2.38 \times 10^4) seeds (roughly 23,800 seeds).

Apples required (average seeds per apple = 9)

• If each apple contains ~9 seeds:
  $N<em>{ ext{apples}} = \frac{N</em>{ ext{seeds}}}{9} = \frac{2.3837 \times 10^4}{9} \approx 2.649 \times 10^3$
• Rounded: about (2.65 \times 10^3) apples (approximately 2,650 apples).

Step-by-step summary

• Convert seed mass to grams to combine with the given mg/g yield: (m_{ ext{seed}} = 0.0333\text{ g}).
• Compute HCN per seed using the given yield: $\text{HCN per seed} = m_{ ext{seed}} \times 0.162 = 0.0333 \times 0.162 \approx 0.00539\ \text{mg}.$
• Compute the lethal dose for the individual: $\text{LD} = 1.52 \ \frac{\text{mg}}{\text{kg}} \times 84.6\ \text{kg} = 128.592\ \text{mg}.$
• Determine seeds required to reach this dose: $N_{ ext{seeds}} = \frac{128.592}{0.0053946} \approx 2.3837 \times 10^4.$
• Translate seeds to apples: with 9 seeds per apple, apples needed ≈ (2.3837 \times 10^4 / 9 \approx 2.649 \times 10^3).

Important considerations and context

• The data describe a hypothetical lethal dose using a linear model and average values; actual toxicity varies with metabolism, absorption, and efficiency of amygdalin hydrolysis.
• Amygdalin releases hydrogen cyanide primarily when the seed is crushed or chewed, not typically from intact seeds.
• Real-world ingestion of tens of thousands of seeds or thousands of apples is impractical, underscoring the concept of dose magnitude rather than a realistic scenario.
• This example illustrates dose, mass units, and unit conversions in toxicology calculations.

Connections to foundational principles

• Dose–response concept: toxicity scales with absorbed dose; here, mg of HCN per body weight (mg/kg).
• Unit consistency: converting between mg and g, and applying weight-based dosing.
• Real-world relevance: cyanide poisoning risk from plant compounds and the importance of food processing (crushing vs. chewing) on toxin release.

Potential extensions or variations

• Explore how varying body weight (e.g., 70 kg vs 90 kg) changes the lethal-dose seeds.
• Examine sensitivity to the HCN yield per gram (e.g., if yield varies to 0.10–0.25 mg/g).
• Consider non-linearities in dose–response and LD50 concepts in toxicology.

Key formulas (LaTeX)

• Seed mass to grams: $m_{ ext{seed}} = 0.0333\ \text{g}$
• HCN per seed: $\text{HCN per seed} = m_{ ext{seed}} \times 0.162 = 0.0333 \times 0.162 \approx 0.0053946\ \text{mg}$
• Lethal dose: $\text{LD} = 1.52\ \frac{\text{mg}}{\text{kg}} \times 84.6\ \text{kg} = 128.592\ \text{mg}$
• Seeds needed: $N_{ ext{seeds}} = \frac{128.592}{0.0053946} \approx 2.3837 \times 10^4$
• Apples needed: $N<em>{ ext{apples}} = \frac{N</em>{ ext{seeds}}}{9} \approx 2.649 \times 10^3$