A steel block measures 5.0 cm × 4.0 cm × 2.0 cm and has a mass of 316 g. What is its density?
- Volume = 5.0 × 4.0 × 2.0 = 40 cm3.
- Density = mass ÷ volume = 316 ÷ 40.
- 316 ÷ 40 = 7.9.
Answer: 7.9 g/cm3
Density and changes of state
Physics · Particle model of matter. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Density tells you how much mass is packed into each unit of volume. It depends on how heavy the particles are and how closely they are packed.
In a solid and in a liquid the particles touch each other, so the densities are high and similar. In a gas the particles are far apart with empty space between them, so the density is about 1000 times smaller.
Melting, freezing, boiling, evaporating, condensing and sublimating are changes of state. They are physical changes, not chemical ones. No new substance is made, the change can be reversed, and the mass stays the same because the number of particles does not change.
Rules to remember
- density = mass ÷ volume (ρ = m/V)
- Units: kg/m3 (mass in kg, volume in m3) or g/cm3 (mass in g, volume in cm3)
- 1 g/cm3 = 1000 kg/m3
- Regular solid: volume = length × width × height, mass from a balance
- Irregular solid: volume = volume of water it displaces (displacement can or the rise in a measuring cylinder)
- Liquid: mass = mass of cylinder with liquid − mass of empty cylinder; read the volume from the cylinder
- Mass is conserved in a change of state
Common mistake
Students use the final reading on the measuring cylinder as the volume of the object. The volume is the rise in the water level: final reading − first reading.
Worked example
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