Lesson 3 · 25 min
Density: an intensive property
Weigh an unknown metal and measure its volume by displacement, and see how the measurement uncertainty decides whether you can tell what it is.
In this lesson
- Calculate density with ρ = m/V and convert between g/cm³, g/mL and kg/m³
- Distinguish intensive from extensive properties and explain why density does not depend on sample size
- Measure the density of an irregular solid with a balance and water displacement
- Use measurement uncertainty to decide which candidate substances agree with the data
Around 2012 cunning fake gold bars appeared: real gold outside, tungsten inside. Weighing them and measuring their volume would not reveal the trick, because tungsten’s density (19.3 g/cm³) is almost identical to gold’s (19.28 g/cm³). Density is one of the oldest and cheapest ways to identify a substance — but it has limits: when two densities differ by less than the measurement uncertainty, it cannot tell them apart. This lesson teaches you to measure density, and to judge what the number can and cannot tell you.
Predict first
A 10 g iron nail and a 1 kg iron bar: which has the greater density?
Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.
What density is
- density (Greek rho)
- mass, from a balance
- volume; for an irregular solid by displacement: V = V₂ − V₁
Densities of solids and liquids are usually quoted in g/cm³ (= g/mL); the SI unit is kg/m³, a factor of 1000 different. Water at 20 °C is about 0.998 g/mL — slightly below 1 and temperature dependent, which is why a precise density must state its temperature.
For an irregular lump of metal the easiest volume measurement is displacement: read the water in a cylinder, , submerge the sample and read again, ; the sample’s volume is . That is a difference of two readings — and, as the last lesson showed, subtraction inflates the relative uncertainty, so the smaller the sample, the less reliable its density.
| Metal | ρ / (g/cm³) | Metal | ρ / (g/cm³) |
|---|---|---|---|
| Magnesium | 1.74 | Nickel | 8.912 |
| Aluminium | 2.70 | Copper | 8.933 |
| Titanium | 4.5 | Silver | 10.501 |
| Zinc | 7.134 | Lead | 11.342 |
| Tin | 7.287 | Tungsten | 19.3 |
| Iron | 7.874 | Gold | 19.282 |
Worked example
What is this metal?
A grey metal piece weighs 45.20 g. Dropped into a 25 mL cylinder holding 11.2 mL of water, it raises the level to 17.6 mL. Each reading is uncertain by ±0.1 mL, the balance by ±0.01 g. What could the metal be?
Concept check
Liquid mercury has a density of about 13.5 g/cm³. Which of these metals sinks in it?
Try the calculation
What volume does 100.0 g of copper occupy? (Take copper’s density as 8.933 g/cm³.)
Key takeaways
- Density ρ = m/V is intensive — independent of sample size; 1 g/cm³ = 1 g/mL = 1000 kg/m³.
- The volume of an irregular solid comes from displacement, V = V₂ − V₁; subtracting two readings magnifies the relative uncertainty.
- Only candidates within about 2u of the measured value agree with the data; if several do, density alone cannot identify the substance.
- Density, not mass, decides whether something floats.
Data and references
- PubChem Periodic Table of Elements, National Center for Biotechnology Information (densities), accessed 2026-09.
- CRC Handbook of Chemistry and Physics, 97th ed., “Density of Solids” and “Properties of Water”.
- D. C. Harris, Quantitative Chemical Analysis, 9th ed., Ch. 3 (propagation of uncertainty).
- Vitruvius, De Architectura, Book IX (the Archimedes story).