Density and States of Matter
Density and States of Matter
All matter is made up of particles. The arrangement, movement, and spacing of these particles determine whether a substance is a solid, liquid, or gas. Density links the mass of a substance to its volume.
The Three States of Matter
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Particle arrangement | Regular, closely packed pattern | Close together, random arrangement | Far apart, random |
| Particle movement | Vibrate about fixed positions | Move around each other (flow) | Move rapidly in all directions |
| Particle spacing | Very close | Close (slightly more than solid) | Very far apart |
| Shape | Fixed | Takes shape of container | Fills container |
| Volume | Fixed | Fixed | Expands to fill container |
| Can be compressed? | No | Almost no | Yes (large gaps between particles) |
| Density | High | Medium-high | Low |
Changes of State
Changes of state are physical changes — they are reversible and do not create new substances. The particles themselves do not change; only their arrangement and energy change.
- Melting — solid to liquid (particles gain energy, vibrate more, overcome some bonds)
- Boiling/evaporation — liquid to gas (particles gain enough energy to escape attractive forces)
- Freezing — liquid to solid (particles lose energy, form a regular pattern)
- Condensing — gas to liquid (particles lose energy, attractive forces pull them together)
- Sublimation — solid directly to gas (e.g. dry ice, CO2)
During a change of state, the temperature stays constant even though energy is being supplied. This energy is used to break or form bonds between particles, not to increase their kinetic energy.
Conservation of mass applies: when a substance changes state in a closed system, the mass stays the same because no particles are added or removed.
Density
Density is defined as mass per unit volume:
density = mass / volume
rho = m / V
Where:
- rho (the Greek letter rho) = density (kg/m cubed, or g/cm cubed)
- m = mass (kg or g)
- V = volume (m cubed or cm cubed)
Typical densities:
| Material | Density (kg/m cubed) |
|---|---|
| Air | 1.2 |
| Water | 1,000 |
| Ice | 920 |
| Aluminium | 2,700 |
| Iron | 7,900 |
| Gold | 19,300 |
Notice that ice is less dense than water — this is unusual and is why ice floats.
Required Practical: Measuring Density
For a regular solid (e.g. a metal block):
1. Measure the mass using a balance
2. Measure the dimensions (length, width, height) using a ruler or vernier callipers
3. Calculate the volume (e.g. for a cuboid: V = l x w x h; for a cylinder: V = pi x r squared x h)
4. Calculate density using rho = m / V
For an irregular solid (e.g. a pebble):
1. Measure the mass using a balance
2. Fill a eureka can (displacement can) with water until it overflows from the spout
3. Gently lower the object into the water
4. Collect the displaced water in a measuring cylinder
5. The volume of displaced water = the volume of the object
6. Calculate density using rho = m / V
For a liquid:
1. Place an empty measuring cylinder on a balance and record the mass
2. Pour the liquid into the measuring cylinder and record the new mass
3. Mass of liquid = new mass - mass of empty cylinder
4. Read the volume from the measuring cylinder (read from the bottom of the meniscus)
5. Calculate density using rho = m / V
Unit Conversions
- 1 m cubed = 1,000,000 cm cubed (10 to the power 6)
- 1 kg = 1,000 g
- To convert g/cm cubed to kg/m cubed, multiply by 1,000
Example: A block of metal has a mass of 540 g and dimensions 10 cm x 5 cm x 4 cm.
Volume = 10 x 5 x 4 = 200 cm cubed
Density = 540 / 200 = 2.7 g/cm cubed = 2,700 kg/m cubed (this is aluminium)
Exam Tips
- Always give units with your density answer — and make sure the units are consistent (do not mix kg with cm cubed)
- In the required practical, explain how using a displacement can avoids errors from estimating the volume of irregular shapes
- Questions about changes of state often ask why mass is conserved — state that no particles are lost or gained