Properties of matter (density, etc.)
The idea
Why does a pebble sink while a massive cargo ship floats? The answer is density — how much mass is packed into each unit of volume, computed as density = mass/volume. Density belongs to a family of characteristic properties, like melting point and conductivity, that identify a substance no matter how big the sample is: a gold ring and a gold bar both have a density of about 19.3 g/cm³. You already compare materials by look and feel; characteristic properties let you identify them with numbers.
On the particle level, density depends on how heavy a substance's particles are and how tightly they pack. The common trap is confusing dense with heavy. A bathtub of foam can outweigh a steel bolt, yet steel is far denser, because density compares equal volumes — one cubic centimetre against one cubic centimetre. For an irregular object, get the volume by water displacement: submerge it and the water level rises by exactly the object's volume, since 1 mL of displaced water equals 1 cm³.
Worked example
A souvenir keychain stamped 'pure aluminum' has a mass of 54 g. Dropped into a measuring cylinder holding 20.0 mL of water, it raises the level to 26.0 mL. Aluminum has a density of 2.7 g/cm³. Does the stamp tell the truth?
- Find the keychain's volume by displacement: the water rose from 20.0 mL to 26.0 mL, so the keychain occupies 26.0 − 20.0 = 6.0 mL, which is 6.0 cm³.
- Compute its density: density = mass/volume = 54 g ÷ 6.0 cm³ = 9.0 g/cm³.
- Compare with the claim: 9.0 g/cm³ is more than three times aluminum's 2.7 g/cm³, so this metal packs far more mass into the same space than aluminum can.
- Cross-check from the other direction: a genuine 6.0 cm³ aluminum keychain would have a mass of only 2.7 × 6.0 = 16.2 g, nowhere near the measured 54 g.
- Interpret: 9.0 g/cm³ sits right at copper's density (about 9.0 g/cm³), so the keychain is most likely a copper-based metal with a false stamp.
Answer. No — its density is 9.0 g/cm³, far above aluminum's 2.7 g/cm³, so the keychain is not pure aluminum and is probably copper-based.
Check your understanding
- Why can a huge steel ship float on water while a tiny steel bolt sinks straight to the bottom?
- How does measuring density let you check what a metal object is made of without damaging it?
- What would happen to your density calculation if some air bubbles clung to the object while it was underwater?
- Why is density a fair way to compare materials when mass alone is not, and what does dividing by volume actually accomplish?
Build the foundations first
Properties of matter (density, etc.) builds on these concepts. If any feel shaky, start there.