Overview
You should be able to:
- Describe the arrangement and motion of particles in solids, liquids and gases.
- Explain Brownian motion and what it tells us about particles.
- Use and rearrange density ρ = m / V.
- Use and understand pressure = force / area and p = h ρ g for liquids.
- Interpret gas behaviour with the particle model and use p₁V₁ = p₂V₂ and p₁/T₁ = p₂/T₂ (T in kelvin).
- Explain absolute zero and the link between temperature and average kinetic energy.
Most marks here are for clear explanations and diagrams, not horrible maths.
1. Particle Model of Solids, Liquids & Gases
Arrangements & Motion
- Solid
- Particles very close together, in a regular pattern.
- Strong forces between particles.
- Particles vibrate about fixed positions.
- Solids have a fixed shape and fixed volume.
- Liquid
- Particles still close together but irregular, can move/slide past each other.
- Forces still quite strong but particles can change places.
- Liquids have a fixed volume but no fixed shape (they flow).
- Gas
- Particles far apart, random arrangement.
- Almost no forces between particles (except during collisions).
- Move quickly in all directions.
- Gases can be compressed and fill any container.
Visualising the Three States
Brownian Motion
Random, zig-zag motion of tiny particles (e.g. smoke in air or pollen in water) is evidence that gas or liquid particles are constantly moving and colliding.
2. Density
Definition & Formula
Density tells you how much mass there is in a given volume. Closely packed particles → higher density.
ρ = m / V
Units: mass in kg, volume in m³, density in kg/m³ (sometimes g/cm³ in lab questions).
Common mistake: mixing units – if mass is in g and volume in cm³, convert to kg and m³ before using the formula, or clearly state g/cm³.
Finding Density in the Lab
- Regular solid – measure mass with a balance, find volume from dimensions (e.g. L × W × H), then ρ = m / V.
- Irregular solid – use a measuring cylinder or displacement can to find volume of water displaced.
- Liquid – measure mass of empty beaker, then with liquid; mass of liquid = difference, volume from measuring cylinder.
Visualising Density
Quick Check
Q1. A cube of metal has mass 0.80 kg and side length 0.10 m. What is its density?
Show answer
Volume = 0.10 × 0.10 × 0.10 = 0.001 m³.
ρ = m / V = 0.80 / 0.001 = 800 kg/m³.
3. Pressure in Solids, Liquids & Gases
Pressure in Solids
p = F / A
Units: force in newtons (N), area in m², pressure in pascals (Pa = N/m²).
Large area → lower pressure (e.g. snowshoes). Small area → higher pressure (e.g. drawing pin, knife blade).
Pressure in Liquids (and Gases)
Liquids and gases exert pressure because particles are moving randomly and collide with surfaces and each other.
In a liquid of density ρ at depth h, the pressure due to the liquid is:
p = h ρ g
Pressure increases with depth and with density of the liquid.
Quick Check
Q2. A 500 N box stands on a base of area 0.25 m². What pressure does it exert on the floor?
Show answer
p = F / A = 500 / 0.25 = 2 000 Pa.
Q3. Sea water has density about 1 025 kg/m³. Estimate the pressure 10 m below the surface (take g = 10 N/kg).
Show answer
p = h ρ g ≈ 10 × 1 025 × 10 ≈ 102 500 Pa (≈ 1.0 × 105 Pa).
4. Gas Behaviour & Gas Laws
Particles & Temperature
- In gases, particles move randomly and collide with container walls – this causes pressure.
- When gas is heated, particles move faster on average.
- Absolute temperature in kelvin (K) is proportional to average kinetic energy of the particles.
Common mistake: using °C instead of K in gas law equations. Always convert: 20 °C → 293 K, −10 °C → 263 K, etc.
Gas in a Cylinder – Visual
Gas Law Relationships (fixed mass of gas)
Pressure & Volume (constant temperature)
If a gas is kept at constant temperature, increasing volume gives particles more space, so they hit the walls less often → pressure decreases.
Pressure is inversely proportional to volume: p ∝ 1 / V.
Pressure & Temperature (constant volume)
If volume is fixed and temperature increases, particles move faster and collide more often and harder → pressure increases.
Quick Check
Q4. A gas has pressure 200 kPa in a 3.0 m³ container at constant temperature. The volume is reduced to 1.5 m³. What is the new pressure?
Show answer
p₁V₁ = p₂V₂ → 200 × 3.0 = p₂ × 1.5 → 600 = 1.5 p₂ → p₂ = 400 kPa.
Q5. A gas at 300 K has pressure 100 kPa. It is heated at constant volume to 450 K. What is the new pressure?
Show answer
p₁ / T₁ = p₂ / T₂ → 100 / 300 = p₂ / 450 → p₂ = 450 × (100 / 300) = 150 kPa.
5. Putting It All Together
Most “Solids, liquids & gases” questions are really asking:
- What are the particles doing? (draw or describe their motion and spacing)
- How does that change density / pressure / temperature?
- Can you use a simple formula correctly? (ρ = m/V, p = F/A, p = hρg, gas laws)
When you get stuck, close your eyes and imagine the particles. Are they close together or far apart? Still or fast? Colliding often or rarely? Your explanation usually falls out of that picture.
Checklist Before the Exam
- Can you draw neat particle diagrams for solids, liquids and gases?
- Can you rearrange ρ = m/V to find any of ρ, m or V?
- Can you explain why pressure increases with depth in a liquid?
- Can you convert between °C and K and use the gas equations safely?
- Have you done at least 5–10 past-paper questions from this topic?