Section 1 of 6Defining Density
Density links the mass of a sample to the space it takes up.
Definition
- Density is the mass contained in each unit volume of a material, so it describes how tightly matter is packed together.
Equation
- ρ = m/V, where ρ is density in kg m⁻³, m is mass in kg and V is volume in m³.
Rearranging
- The same relationship gives m = ρV for the mass of a known volume and V = m/ρ for the volume of a known mass.
Particle link
- A solid or liquid has particles almost touching, while a gas has the same particles spread over a far larger volume.
Intensive property
- Density depends on the material, not on the size of the sample, so a small and a large piece of iron have equal density.
| Material | Typical density / kg m⁻³ |
|---|---|
| Air (room conditions) | 1.2 |
| Water | 1.0 × 10³ |
| Aluminium | 2.7 × 10³ |
| Iron | 7.9 × 10³ |
| Lead | 1.1 × 10⁴ |
Section 2 of 6Finding Volume and Mass
A density experiment needs two measurements, one for mass and one for volume.
1
Weigh the object on a balance, converting the reading to kilograms before it is used in any equation.
2
For a regular solid, measure its dimensions with a ruler, micrometer or vernier calliper, and repeat to reduce random error.
3
Calculate volume with the correct formula: cuboid lwh, cylinder πr²h, sphere ⁴⁄₃πr³.
4
For an irregular solid, lower it into a measuring cylinder of water and take the rise in water level as its volume.
5
Divide mass by volume, and quote the answer to the same number of significant figures as the least precise measurement.
Section 3 of 6Units and Conversions
Units and Conversions
Cubed factors
- Converting a length unit to a volume unit needs the conversion factor cubed, so 1 cm³ = (10⁻² m)³ = 10⁻⁶ m³.
g cm⁻³ to kg m⁻³
- Multiply by 1000, because 1 g cm⁻³ equals 10⁻³ kg divided by 10⁻⁶ m³, giving 1000 kg m⁻³.
mm to m
- Divide by 1000 for each length, so a 40 mm side is 0.040 m before multiplying the three sides.
Sense check
- Metals should come out in thousands of kg m⁻³, liquids near 10³ and gases near 1, which quickly exposes a slip.
Section 4 of 6Floating, Sinking and Mixtures
Sinking
- An object that is denser than the fluid it is in will sink, because its weight exceeds the upthrust it can receive.
Floating
- A less dense object floats with part of its volume above the surface, and the submerged fraction is ρobject/ρfluid.
Gas density
- Gas density changes greatly with pressure and temperature, so a stated value only applies under given conditions.
Alloys and mixtures
- The density of a mixture is total mass divided by total volume, not the simple average of the two densities.
Section 5 of 6Worked Example
Question
- A metal block measures 5.0 cm × 4.0 cm × 2.5 cm and has a mass of 395 g.
- Calculate its density in kg m⁻³.
- Volume = 5.0 × 4.0 × 2.5 = 50 cm³ = 50 × 10⁻⁶ m³ = 5.0 × 10⁻⁵ m³.
- Mass = 395 g = 0.395 kg.
- ρ = m/V = 0.395 / (5.0 × 10⁻⁵) = 7.9 × 10³ kg m⁻³.What the symbols mean: ρ = density (kg m−3 or g cm−3) · m = mass (kg) · V = volume (m3)
Answer ρ = 7.9 × 10³ kg m⁻³, which is consistent with iron or steel.
Section 6 of 6Exam Checklist & Tips
3.5.1 – Key Points for the Exam
- Density Mass per unit volume of a substance, measured in kg m⁻³.
- Volume The amount of three-dimensional space occupied by an object or fluid.
- Displacement method Finding the volume of an irregular solid from the volume of water it pushes aside.
- Relative density The density of a substance divided by the density of water, a ratio with no units.
Common Mistakes
- Forgetting to cube the conversion factor, for example turning cm³ into m³ by dividing by 100 instead of 10⁶.
- Mixing grams with cubic metres, which gives an answer that is wrong by a factor of 1000.
- Saying that a heavier object is always denser; density depends on both mass and volume.
- Averaging two densities to find the density of a mixture instead of dividing total mass by total volume.