Matter · 7.1
Matter, Mass & Volume
Matter has mass and occupies space. Its particles are always moving, but their spacing and freedom of motion distinguish solids, liquids, and gases.
Build the model
Connect the measurement to the mechanism.
The particle model links what cannot be seen directly to measurable behaviour. Solids keep shape and volume, liquids keep volume but flow, and gases spread to fill their container. Mass measures inertia; volume measures occupied three-dimensional space.
- Simple definition
- Matter is anything that has mass and occupies space; volume is the amount of space it occupies.
- Example
- An ice cube is matter because it has mass and takes up a measurable volume in a glass.
The space inside a box: multiply its three sides, after putting them all in the same unit.
Use one consistent length unit before multiplying
A centimetre is a hundredth of a metre, so a cubic centimetre is a hundredth cubed — a millionth of a cubic metre.
Three powers of the length conversion are required
A litre is a 10 cm cube; a thousand litres fill one cubic metre, and one millilitre is exactly one cubic centimetre.
Therefore 1 mL = 1 cm³
Solid
Particles are close and usually ordered. They vibrate about equilibrium positions, giving a fixed shape and volume.
Liquid
Particles remain close but can rearrange. A liquid flows to match its container while keeping nearly fixed volume.
Gas
Particles are far apart and move rapidly in random directions. A gas has no fixed shape or volume and is compressible.
Change one variable at a time
Make the relationship visible.
Choose a state
The motion control represents kinetic energy qualitatively; it does not change the number or size of particles.
Shapefixed
Volumefixed
Particle spacingclose, often ordered
Particle motionvibrate about positions
Catch the common trap
Explain before calculating.
Which state keeps a fixed volume but takes the shape of its container?
Choose an answer to test the model.
Worked examples
Choose the reference, calculate, then check.
EasyA rectangular tank measures 40 cm × 25 cm × 20 cm. Find its volume in litres.
- V = 40 × 25 × 20 = 20 000 cm³.
- 1 L = 1000 cm³ → V = 20 L.
AnswerV = 20 L
MediumA block measures 20 cm × 10 cm × 5.0 cm. Find its volume in cm³, litres, and m³.
- V = 20 × 10 × 5.0 = 1000 cm³.
- Since 1000 cm³ = 1 L, the volume is 1.0 L.
- Multiply by 10⁻⁶ m³ per cm³: 1000 × 10⁻⁶ = 1.0 × 10⁻³ m³.
AnswerV = 1000 cm³ = 1.0 L = 1.0 × 10⁻³ m³
HardA measuring cylinder holds 120 cm³ of water; a stone is lowered in and the level reads 165 cm³. The stone's mass is 117 g. Find the stone's volume and density.
- Volume by displacement: 165 − 120 = 45 cm³.
- ρ = m/V = 117 ÷ 45.
- ρ = 2.6 g/cm³ = 2600 kg/m³.
AnswerV = 45 cm³; ρ = 2.6 g/cm³
ChallengingSteam occupies about 1600× the volume of the water that made it. Use the particle model to explain, and estimate the average particle spacing ratio.
- Same number of particles fills 1600× the volume — particle spacing, not particle size, changes.
- Spacing scales with the cube root of volume per particle: 1600^(1/3) ≈ 11.7.
- Gas molecules sit roughly 12 molecular diameters apart, which is why gases compress and liquids barely do.
AnswerSpacing grows by ∛1600 ≈ 12×; the particles themselves are unchanged