Van Helmont's numbers
Start: a 2.3 kg willow sapling in 90.8 kg of dried soil. Five years of nothing but water. End: a 76.7 kg tree — and the soil has lost just 0.06 kg.
Mass gained by the tree: 76.7 − 2.3 = ___ kg
Convert the soil's loss to grams, then to kg. Soil loss in kg: 60 g = ___ kg
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The ratio that ends the argument: tree gain ÷ soil loss = 74.4 ÷ 0.06 = ___. Finish the sentence: "The tree gained about ___ times more mass than the soil lost — so the tree is mostly NOT made of ___."
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Van Helmont concluded it was all the water. He was half right — he couldn't weigh the other ingredient because it's invisible. What is it? (You met it in the steel wool.)
Prove the books close: photosynthesis
6 CO₂ + 6 H₂O → C₆H₁₂O₆ + 6 O₂
Trees rearrange air and water into sugar. Count every atom on both sides —
the conservation law says the inventory must match exactly.
| Element | Left side (reactants) | Right side (products) | Balanced? |
|---|---|---|---|
| Carbon | |||
| Hydrogen | |||
| Oxygen |
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Respiration (you, right now) runs the exact same equation backwards. Write it flipped: glucose + oxygen → ___ + ___. What does it mean that life and air run the same books in opposite directions?
Calorie math
Food energy is chemistry you can eat. Walking burns about 4 kcal per minute. Labels: cookie = 220 kcal · apple = 95 kcal.
Minutes of walking to burn the cookie? The apple?
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Fat stores 9 kcal per gram; carbohydrate stores 4 kcal per gram. A 20 g pat of butter vs. 20 g of sugar — energy of each? Why does the same mass of fat hold more than double the energy? (Which one is the denser storage, chemically?)
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Your body is burning glucose all day just to stay alive — roughly 1,600 kcal before you move a muscle. At 4 kcal/g of carbohydrate, how many grams of glucose is a rest day? (Real bodies mix fuels — this is the simplified version.)
How much air is a tree?
A big tree's dry mass is about 500 kg, and dry plant matter is about half carbon — call it 250 kg of carbon. All of it pulled from CO₂ in the air. CO₂ is 12/44 carbon by mass (C = 12, O₂ = 32, total 44).
Carbon fraction of CO₂: 12 ÷ 44 ≈ 0.27. As a percent?
CO₂ needed to deliver 250 kg of carbon: 250 ÷ 0.27 ≈ ___ kg
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So one tree pulled ~900 kg of CO₂ out of the air. One sentence for the bridge to biology: why does "a tree is made of air" turn out to be literally, weighably true?
Answer key — teachers
Part A
- 74.4 kg
- 0.06 kg
- ≈1,240× — "…the tree is mostly NOT made of soil."
- Air (carbon dioxide — invisible, unweighable by his tools).
Part B
C: 6 = 6 ✓ · H: 12 = 12 ✓ · O: 12 + 6 = 18 = 6 + 12 ✓
- C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O. Photosynthesis banks the sun's energy into sugar; respiration spends it — one ledger, two directions.
Part C
- Cookie: 55 min · apple: ≈24 min
- Butter: 20 × 9 = 180 kcal; sugar: 20 × 4 = 80 kcal. Fat packs more C–H bonds per gram — denser chemical storage.
- 1,600 ÷ 4 = 400 g of glucose-equivalent per rest day.
Part D
- ≈27%
- ≈926 kg (accept ~900–930)
- The tree's carbon was weighed and traced to CO₂ — "made of air" is not poetry, it's the mass balance.