P1: Matter

What you'll learn

This topic covers the fundamental structure and behaviour of matter at GCSE level. You'll explore how the particle model explains the three states of matter, calculate density using direct measurements, and understand how energy transfers affect temperature and changes of state. These principles underpin much of Physics and Chemistry at GCSE level.

Key terms and definitions

Density — the mass per unit volume of a substance, measured in kg/m³ or g/cm³

Particle model — a scientific representation of matter as tiny, discrete particles (atoms, molecules or ions) with spaces between them

State of matter — the physical form a substance takes: solid, liquid or gas, determined by particle arrangement and energy

Internal energy — the total kinetic and potential energy of all particles in a system

Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1°C, measured in J/kg°C

Specific latent heat — the energy required to change the state of 1 kg of a substance without changing its temperature, measured in J/kg

Sublimation — the direct change of state from solid to gas without passing through the liquid state

Brownian motion — the random movement of particles suspended in a fluid, caused by collisions with fast-moving fluid molecules

Core concepts

The particle model and states of matter

All matter consists of particles in constant, random motion. The arrangement, separation and energy of these particles determine which state the substance is in.

Solids:

• Particles arranged in regular, fixed positions
• Strong forces of attraction hold particles close together
• Particles vibrate about fixed positions but cannot move from place to place
• Fixed shape and volume
• High density (particles tightly packed)

Liquids:

• Particles close together but can move past each other
• Moderate forces of attraction between particles
• Particles move randomly at varying speeds
• Fixed volume but take the shape of their container
• Generally high density, slightly lower than solids

Gases:

• Particles far apart with weak forces between them
• Particles move rapidly and randomly in all directions
• Fill the entire volume of their container
• No fixed shape or volume
• Low density (particles widely separated)

The particle model explains observable properties but has limitations. It assumes particles are solid spheres with no forces between them, which isn't accurate for all substances. Real particles have complex shapes and interactions.

Density and its measurement

Density relates the mass of a substance to its volume:

ρ = m/V

where ρ (Greek letter rho) is density, m is mass, and V is volume.

Measuring density of regular solids:

1. Measure mass using a balance (in kg or g)
2. Measure dimensions using a ruler or callipers (length, width, height)
3. Calculate volume (e.g., for a cube: V = l × w × h)
4. Apply the density equation

Measuring density of irregular solids:

1. Measure mass using a balance
2. Fill a displacement (eureka) can with water to the spout
3. Submerge the object completely
4. Collect displaced water in a measuring cylinder
5. Volume of object equals volume of water displaced
6. Calculate density using ρ = m/V

Measuring density of liquids:

1. Measure mass of empty measuring cylinder
2. Pour liquid into cylinder and record volume
3. Measure total mass (cylinder + liquid)
4. Subtract to find mass of liquid only
5. Calculate density

Typical densities to know:

• Solids: iron ≈ 7900 kg/m³, aluminium ≈ 2700 kg/m³
• Liquids: water = 1000 kg/m³, oil ≈ 900 kg/m³
• Gases: air ≈ 1.2 kg/m³

Changes of state and energy

When substances change state, they absorb or release energy without changing temperature. The energy goes into breaking or forming bonds between particles, changing their potential energy rather than kinetic energy.

Heating curve for a pure substance:

• Temperature rises as substance is heated (kinetic energy increases)
• Temperature remains constant during melting (solid → liquid)
• Temperature rises again as liquid is heated
• Temperature remains constant during boiling (liquid → gas)
• Flat sections represent changes of state where energy changes potential energy

Changes of state:

• Melting: solid → liquid (energy absorbed)
• Freezing: liquid → solid (energy released)
• Boiling/evaporation: liquid → gas (energy absorbed)
• Condensation: gas → liquid (energy released)
• Sublimation: solid → gas (energy absorbed)

During changes of state, particle arrangement and separation change but the particles themselves remain the same. This explains why mass is conserved.

Internal energy and temperature

Internal energy is the sum of:

• Kinetic energy of particles (due to their motion)
• Potential energy of particles (due to their positions and interactions)

Temperature is directly proportional to the average kinetic energy of particles. When you heat a substance:

• If temperature rises: internal energy increases due to increased kinetic energy
• During a change of state: internal energy increases due to increased potential energy, but temperature stays constant

This distinction is crucial. Adding energy doesn't always increase temperature.

Specific heat capacity

Different substances require different amounts of energy to change temperature. This is quantified by specific heat capacity (c).

Energy equation: ΔE = m × c × Δθ

where:

• ΔE = change in thermal energy (J)
• m = mass (kg)
• c = specific heat capacity (J/kg°C)
• Δθ = change in temperature (°C)

Materials with high specific heat capacity (like water, c = 4200 J/kg°C) require much energy to change temperature. This explains why:

• Coastal areas have moderated climates (water heats/cools slowly)
• Water is used in cooling systems
• Sand heats up quickly on sunny days (low specific heat capacity)

Investigating specific heat capacity:

1. Measure mass of material (e.g., metal block)
2. Insert heater and thermometer into block
3. Record initial temperature
4. Heat for measured time at known power
5. Record final temperature
6. Calculate energy supplied: E = power × time
7. Use ΔE = mcΔθ to find c

To improve accuracy: insulate the block to reduce energy losses to surroundings.

Specific latent heat

Energy required to change state without changing temperature is given by:

E = m × L

where:

• E = energy (J)
• m = mass (kg)
• L = specific latent heat (J/kg)

There are two types:

• Specific latent heat of fusion (melting/freezing)
• Specific latent heat of vaporisation (boiling/condensing)

Latent heat of vaporisation is always greater than latent heat of fusion for the same substance because particles must be separated much further when forming a gas compared to a liquid.

For water:

• Latent heat of fusion ≈ 334,000 J/kg
• Latent heat of vaporisation ≈ 2,260,000 J/kg

This explains why steam burns are more severe than boiling water burns — steam releases enormous energy when condensing on skin.

Gas pressure and the particle model

Gas pressure results from particles colliding with container walls. Each collision exerts a tiny force; billions of collisions per second create measurable pressure.

Increasing temperature:

• Particles gain kinetic energy and move faster
• More frequent and more forceful collisions with walls
• Pressure increases (if volume is constant)

Decreasing volume:

• Same number of particles in smaller space
• More collisions per second with walls
• Pressure increases (if temperature is constant)

Brownian motion provides evidence for the particle model. When smoke particles are observed through a microscope, they move randomly. This happens because:

• Fast-moving air molecules collide with larger smoke particles
• Collisions are unbalanced (more molecules hitting one side than another)
• Smoke particle changes direction randomly
• We cannot see air molecules directly, only their effect

This observation supports the idea that matter consists of moving particles too small to see.

Worked examples

Example 1: Density calculation

Question: A student measures an aluminium cube with sides of 2.0 cm. The mass is 21.6 g. Calculate the density of aluminium in g/cm³. [3 marks]

Solution:

• Volume = length × width × height = 2.0 × 2.0 × 2.0 = 8.0 cm³ [1 mark]
• ρ = m/V [1 mark]
• ρ = 21.6/8.0 = 2.7 g/cm³ [1 mark]

Example 2: Specific heat capacity

Question: A kettle supplies 462,000 J of energy to 1.5 kg of water. The temperature rises from 20°C to 93°C. Calculate the specific heat capacity of water. The specific heat capacity of water is 4200 J/kg°C. [4 marks]

Solution:

• ΔE = mcΔθ [1 mark]
• Rearrange: c = ΔE/(m × Δθ) [1 mark]
• Δθ = 93 - 20 = 73°C [1 mark]
• c = 462,000/(1.5 × 73) = 4219 J/kg°C ≈ 4200 J/kg°C [1 mark]

(Note: Small difference due to rounding and energy losses)

Example 3: Latent heat

Question: How much energy is needed to boil 0.50 kg of water at 100°C? The specific latent heat of vaporisation of water is 2,260,000 J/kg. [2 marks]

Solution:

• E = mL [1 mark]
• E = 0.50 × 2,260,000 = 1,130,000 J (or 1.13 MJ) [1 mark]

Example 4: Explaining changes of state

Question: Explain, in terms of particles and energy, what happens when ice melts. [3 marks]

Solution:

• Energy is absorbed by the ice [1 mark]
• This energy weakens/breaks bonds between particles [1 mark]
• Particles gain enough energy to move past each other, forming liquid water, but temperature remains constant during melting [1 mark]

Common mistakes and how to avoid them

• Confusing mass and volume — Remember: density = mass ÷ volume. Make sure you identify which value is which in questions. Mass is measured in kg or g, volume in m³, cm³ or dm³.

• Unit conversion errors — Always check units match the equation. Convert cm to m if using kg/m³, or use g/cm³ consistently. 1 m³ = 1,000,000 cm³ (not 100).

• Thinking temperature rises during changes of state — Temperature stays constant when substances melt or boil. Energy changes potential energy (breaking bonds) not kinetic energy (movement).

• Mixing up latent heat types — Fusion relates to melting/freezing (solid ↔ liquid). Vaporisation relates to boiling/condensing (liquid ↔ gas). Vaporisation values are always larger.

• Describing particle behaviour incorrectly — Particles in solids vibrate but don't move position. Particles don't change size or disappear when substances change state — only arrangement changes.

• Forgetting to show working — In calculations, always show the formula, substitution and answer with units. This ensures method marks even if your final answer is wrong.

Exam technique for "P1: Matter"

• Command words matter: "Calculate" requires numerical working and units. "Explain" needs because/therefore reasoning linking cause and effect. "Describe" needs observable changes stated clearly without necessarily explaining why.

• Use particle language precisely — State whether particles move, vibrate, are close together or far apart. Avoid vague terms like "expand" without explaining particles move further apart.

• Show calculation steps — Write formula, substitute values with units, calculate answer. This typically earns 1 mark per step even if arithmetic contains errors.

• Check unit consistency — If energy is in J, mass in kg and you're using specific heat capacity, it must be in J/kg°C. Convert at the start to avoid errors.

Quick revision summary

Matter exists in three states determined by particle arrangement and energy. Density (ρ = m/V) compares mass to volume. Internal energy is the sum of kinetic and potential energy of particles. Heating substances increases internal energy, raising temperature or causing changes of state. Specific heat capacity (ΔE = mcΔθ) quantifies energy needed for temperature changes. Specific latent heat (E = mL) quantifies energy for state changes at constant temperature. Gas pressure results from particle collisions with container walls. Brownian motion provides evidence for moving particles.