Math practice · Unit #10 · 8th grade · Physical & chemical changes

The Green Skin

The Statue of Liberty arrived penny-brown and turned green in ~30 years. New color = new substance. But how much copper is even up there? Estimate it — then track mass as it changes identity.

skills: Fermi estimation percent change volume · density ≈ 35 min
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Name Period Date
PART A

How much copper is the statue wearing?

The copper skin is 2.4 mm thick (about two pennies). The statue's surface area is roughly 4,000 m². Copper's density is 8,960 kg/m³. Work the chain: thickness → volume → mass.

  1. Convert the thickness to meters: 2.4 mm = ___ m. (You'll need this — volume wants meters all the way through.)

  2. Volume of the skin = area × thickness = 4,000 m² × your answer. Volume?

  3. Mass = volume × density = your volume × 8,960 kg/m³. Mass in kg? In metric tonnes (÷ 1,000)?

  4. The published figure is about 80 tonnes. How close was your estimate, in percent error? What makes an estimate like this still useful even when it's off by a few percent?

PART B

Rust GAINS mass

Iron rusts into iron oxide (Fe₂O₃): the oxygen joins the metal. Start with 100 g of pure iron; let it rust completely.

  1. Rust is iron + oxygen: every 112 g of iron grabs 48 g of oxygen. So 100 g of iron becomes about 143 g of rust. Mass gained?

  2. Percent increase = gain ÷ original × 100. Compute it.

  3. Where did the extra 43 g come from — was matter created? One sentence, using the word oxygen. (Is rusting physical or chemical? The mass change is your evidence.)

PART C

Where does the candle go?

A 350 g candle burns down until 12 g of wax remain. A student says "338 g of matter was destroyed." The conservation law disagrees.

  1. Mass of wax that burned: 350 − 12 = ___

  2. Burning wax + oxygen → carbon dioxide + water vapor (both gases, both invisible). If the books must balance, the missing 338 g is… where? Finish the sentence: "The candle didn't disappear — it ___."

  3. Bonus thinking: the gases actually weigh more than 338 g. What joined the wax from the air? (Preview of the next unit's favorite trick.)

PART D

Evidence scorecard

Score each change: color change +2 · gas produced +3 · new smell +2 · temperature change on its own +3 · just changed shape/state +0. 5+ points = call it chemical. Defend your two closest calls.

  1. Ice melting into water. Score: ___ Verdict: ___

  2. A nail rusting on the fence. Score: ___ Verdict: ___

  3. Crackling alka-seltzer dropped in water. Score: ___ Verdict: ___

  4. Your two closest calls — what evidence would you collect to be SURE? (Think like the measurement unit: what could you measure before and after?)

Answer key — teachers

Part A

  1. 0.0024 m
  2. 4,000 × 0.0024 = 9.6 m³
  3. 9.6 × 8,960 = 86,016 kg ≈ 86 tonnes
  4. |86 − 80| ÷ 80 ≈ 7.5% — an estimate within 10% settles real questions (can the frame hold it? how much did it cost?) without exact blueprints.

Part B

  1. 43 g gained
  2. 43 ÷ 100 = 43%
  3. No matter created — oxygen from the air bonded into the rust; new substance = chemical change, and the scale proves it.

Part C

  1. 338 g
  2. "…it left as invisible gases (CO₂ and water vapor)."
  3. Oxygen from the air — so the gases outweigh the lost wax.

Part D

  1. Melting: 0 → physical (same substance, new state).
  2. Rust: +2 color (and arguably more) → chemical.
  3. Alka-seltzer: +3 gas → chemical.
  4. Look for mass-before/after tricks, gas collection, or properties of the products vs. the reactants.