Math practice · Unit #13 · 8th grade · Chemistry in nature

The Tree That Ate Air

1642: van Helmont grows a willow for five years. The tree gains ~75 kg; the soil loses ~60 g. If the tree didn't come from the dirt, where did 75 kilograms of wood come from? The numbers make the argument.

skills: unit conversion ratios atom accounting energy units ≈ 35 min
Name Period Date
PART A

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.

  1. Mass gained by the tree: 76.7 − 2.3 = ___ kg

  2. Convert the soil's loss to grams, then to kg. Soil loss in kg: 60 g = ___ kg

  3. 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 ___."

  4. 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.)

PART B

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.

Atom inventory
ElementLeft side (reactants)Right side (products)Balanced?
Carbon
Hydrogen
Oxygen
  1. 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?

PART C

Calorie math

Food energy is chemistry you can eat. Walking burns about 4 kcal per minute. Labels: cookie = 220 kcal · apple = 95 kcal.

  1. Minutes of walking to burn the cookie? The apple?

  2. 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?)

  3. 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.)

PART D

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).

  1. Carbon fraction of CO₂: 12 ÷ 44 ≈ 0.27. As a percent?

  2. CO₂ needed to deliver 250 kg of carbon: 250 ÷ 0.27 ≈ ___ kg

  3. 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

  1. 74.4 kg
  2. 0.06 kg
  3. ≈1,240× — "…the tree is mostly NOT made of soil."
  4. Air (carbon dioxide — invisible, unweighable by his tools).

Part B

C: 6 = 6 ✓ · H: 12 = 12 ✓ · O: 12 + 6 = 18 = 6 + 12 ✓

  1. C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O. Photosynthesis banks the sun's energy into sugar; respiration spends it — one ledger, two directions.

Part C

  1. Cookie: 55 min · apple: ≈24 min
  2. Butter: 20 × 9 = 180 kcal; sugar: 20 × 4 = 80 kcal. Fat packs more C–H bonds per gram — denser chemical storage.
  3. 1,600 ÷ 4 = 400 g of glucose-equivalent per rest day.

Part D

  1. ≈27%
  2. ≈926 kg (accept ~900–930)
  3. The tree's carbon was weighed and traced to CO₂ — "made of air" is not poetry, it's the mass balance.