Density
Why a huge log floats and a tiny coin sinks — it's not about size, it's about how tightly matter is packed.
⏱️ About 12 min
A massive tree trunk floats down a river while a small steel bolt drops straight to the bottom. Size clearly isn't the deciding factor. What matters is how much mass each object packs into its volume — its density — and comparing that to the water around it.
💡
The big idea: Density is how much mass is packed into a given volume: d = m/V. It's a property of the material itself, not of how big the piece is — a gold ring and a gold bar have the same density. Compare an object's density to the fluid around it and you can predict whether it floats or sinks.
Mass packed into a volume
Density answers a simple question: how much matter is crammed into a given space? Pack more mass into the same volume and the density goes up. It's why a small lead fishing weight feels surprisingly heavy while a big foam cushion feels like almost nothing.
Density is defined as mass divided by volume:
\[ d = \frac{m}{V} \]
Density = mass ÷ volume. Common units: g/cm³ or g/mL for solids and liquids (note 1 cm³ = 1 mL), and g/L for gases.
🔑 Density belongs to the material, not the piece
Cut a bar of aluminium in half and each half has half the mass and half the volume — so the density is unchanged. Density is an intensive property: it doesn't depend on how much you have. Every piece of pure aluminium has a density of about 2.70 g/cm³, whether it's a foil scrap or an engine block.
Rearranging the formula
The single relationship d = m/V rearranges to give whatever you're missing. If you know any two of the three quantities, you can find the third:
\[ d = \frac{m}{V} \qquad\Longleftrightarrow\qquad m = d\,V \qquad\Longleftrightarrow\qquad V = \frac{m}{d} \]
Solve for mass by multiplying, or for volume by dividing. Same relationship, three views.
✨ Floating and sinking, explained
An object sinks in a fluid if it's denser than the fluid, and floats if it's less dense. Water is about 1.00 g/mL, so anything denser than 1.00 g/mL sinks in it and anything less dense floats. Wood (≈ 0.5 g/cm³) floats; a steel bolt (≈ 7.9 g/cm³) sinks — regardless of size.
📝 Worked example: A 50.0 g sample of cooking oil fills a graduated cylinder to 40.0 mL. Find its density, and decide whether it floats on water (water = 1.00 g/mL).
- Use d = m/V with m = 50.0 g and V = 40.0 mL.
- d = 50.0 g ÷ 40.0 mL = 1.25 g/mL.
- Wait — check against experience: oil actually floats on water, so its density should be less than 1.00 g/mL. Our number, 1.25, is larger, which would mean it sinks.
- So for a liquid that really floats on water (like most cooking oils, ≈ 0.92 g/mL) the measured density must come out below 1.00 g/mL. With the numbers given here (50.0 g in 40.0 mL), the sample is denser than water and would sink.
✓ d = 1.25 g/mL. Since 1.25 > 1.00, this sample is denser than water and would sink.
✏️ Practice: A metal block has a mass of 24 g and a volume of 3.0 cm³. What is its density?
g/cm³
Solution
- Use d = m/V.
- d = 24 g ÷ 3.0 cm³.
- = 8.0 g/cm³. (Close to iron, ≈ 7.9 g/cm³ — so this block would sink in water.)
✏️ Practice: Aluminium has a density of 2.70 g/cm³. What volume does a 54.0 g piece of aluminium occupy?
cm³
Solution
- Rearrange d = m/V to V = m/d.
- V = 54.0 g ÷ 2.70 g/cm³.
- = 20.0 cm³.
Check your understanding
1. You saw a solid aluminium bar exactly in half. What happens to the density of each half?
Each half has half the mass and half the volume, so m/V is unchanged. Density is an intensive property — it depends on the material, not on how big the piece is. A common misconception is that a bigger object is automatically denser.
2. Object A has density 0.8 g/cm³ and object B has density 1.3 g/cm³. Placed in water (1.0 g/cm³):
Compare each to water's 1.0 g/cm³. A (0.8) is less dense, so it floats; B (1.3) is denser, so it sinks. Whether something floats depends on density relative to the fluid, not on its mass or size.
3. A liquid has mass 30.0 g and volume 25.0 mL. What is its density?
d = m/V = 30.0 g ÷ 25.0 mL = 1.2 g/mL. Since that's greater than 1.0 g/mL, this liquid would sink beneath water rather than float on it.
✅ Key takeaways
- Density = mass ÷ volume (d = m/V), usually in g/cm³ or g/mL for solids and liquids.
- The formula rearranges to m = dV and V = m/d, so any two quantities give the third.
- Density is intensive: it depends on the material, not on the amount you have.
- An object floats if it's less dense than the fluid and sinks if it's denser.
- Water is about 1.00 g/mL — the benchmark for whether things float or sink in it.
➡️ Density, units, and significant figures are the measuring tools every chemist carries. With the toolkit in hand, you're ready to look inside matter itself — starting with the atom.
Want to test yourself on this?
Try the Chemistry practice test →