P9: States of Matter and Changes of State
The particle model and changes of state
📋 Key Definitions
Density: The mass per unit volume of a substance, measured in kg/m³. Density tells us how compact a substance is.
Internal energy: The total kinetic energy and potential energy of all the particles in a substance.
Specific latent heat: The amount of energy required to change the state of 1 kg of a substance without changing its temperature.
Specific latent heat of fusion: The energy required to change 1 kg of a substance from solid to liquid (melt) at its melting point.
Specific latent heat of vaporisation: The energy required to change 1 kg of a substance from liquid to gas (boil) at its boiling point.
🔬 The Three States of Matter
Matter can exist in three states: solid, liquid and gas. The behaviour of particles differs in each state.
| Property | Solid | Liquid | Gas |
|---|---|---|---|
| Arrangement | Regular, close together | Random, close together | Random, far apart |
| Movement | Vibrate about fixed positions | Move around each other | Move rapidly in all directions |
| Shape | Fixed shape | Takes shape of container | Fills container |
| Volume | Fixed volume | Fixed volume | Fills container (no fixed volume) |
| Compressibility | Cannot be compressed | Cannot be compressed | Can be compressed |
| Energy of particles | Lowest | Medium | Highest |
Particle model: In all three states, particles are in constant motion. In solids, particles vibrate about fixed positions. In liquids, particles can move past each other. In gases, particles move freely and rapidly.
📏 Density
Density is a measure of how much mass is packed into a given volume. A dense material has a lot of mass in a small volume.
ρ = m / V
ρ = density (kg/m³), m = mass (kg), V = volume (m³)
Units: Density is measured in kg/m³. You may also see g/cm³. To convert: 1 g/cm³ = 1000 kg/m³. Water has a density of 1 g/cm³ = 1000 kg/m³.
Worked Example 1: Calculating density
A block of aluminium has a mass of 5.4 kg and a volume of 0.002 m³. Calculate its density.
ρ = m / V = 5.4 / 0.002 = 2700 kg/m³
Worked Example 2: Finding mass from density
The density of iron is 7874 kg/m³. What is the mass of 0.05 m³ of iron?
m = ρ × V = 7874 × 0.05 = 393.7 kg
🧪 Measuring Density — Required Practical
Regular objects
- Measure the dimensions (length, width, height) using a ruler, vernier calliper or micrometer
- Calculate volume using the appropriate formula (e.g. V = l × w × h for a cuboid)
- Measure mass using a balance
- Calculate density: ρ = m / V
Irregular objects (displacement method)
- Measure the mass using a balance
- Fill a measuring cylinder or Eureka can with water
- Lower the object into the water
- Record the volume of water displaced — this equals the volume of the object
- Calculate density: ρ = m / V
Eureka can: A container with a spout. Fill it until water just starts to drip from the spout, then lower the object in. Collect the water that overflows — this volume equals the object's volume.
Worked Example 3: Displacement method
An irregular stone has a mass of 120 g. When lowered into a measuring cylinder, the water level rises from 45 cm³ to 90 cm³. Calculate the density.
V = 90 − 45 = 45 cm³
ρ = m / V = 120 / 45 = 2.67 g/cm³
In kg/m³: 2.67 × 1000 = 2670 kg/m³
🔥 Internal Energy
Every substance has internal energy, which is the total energy stored by all the particles. Internal energy has two parts:
| Component | Description | Related to |
|---|---|---|
| Kinetic energy of particles | Energy due to the motion of particles | Temperature |
| Potential energy of particles | Energy due to the positions and interactions between particles (bonds) | State of substance |
Heating a substance increases its internal energy. When the substance is not changing state, the energy increases kinetic energy (temperature rises). When the substance IS changing state, the energy increases potential energy (temperature stays constant).
🔄 Changes of State
When a substance changes state, the arrangement and energy of its particles change. The substance is still the same material — no new substance is formed (this is a physical change, not a chemical change).
| Change of state | Process | Direction |
|---|---|---|
| Melting | Solid → Liquid | Energy absorbed |
| Boiling / Evaporation | Liquid → Gas | Energy absorbed |
| Condensation | Gas → Liquid | Energy released |
| Freezing | Liquid → Solid | Energy released |
| Sublimation | Solid → Gas (without becoming liquid) | Energy absorbed |
Temperature does NOT change during a change of state. The energy supplied goes into breaking or weakening intermolecular bonds (potential energy increases), not increasing the kinetic energy of particles. This is why a graph of temperature against time has flat sections during changes of state.
🌡️ Heating and Cooling Curves
A heating curve shows how the temperature of a substance changes as it is heated at a constant rate:
- Slope up: Solid heats up — kinetic energy increases, temperature rises
- Flat section: Melting — energy breaks bonds, temperature stays at melting point
- Slope up: Liquid heats up — kinetic energy increases, temperature rises
- Flat section: Boiling — energy breaks bonds, temperature stays at boiling point
- Slope up: Gas heats up — kinetic energy increases, temperature rises
A cooling curve is the reverse: the substance cools, condenses (flat section), cools further, freezes (flat section), then cools as a solid.
The flat sections on a heating or cooling curve correspond to changes of state. The temperature at which a substance melts or boils is a characteristic property that can be used to identify the substance.
⚡ Specific Latent Heat
Specific latent heat is the energy needed to change the state of 1 kg of a substance without a temperature change.
E = mL
E = energy (J), m = mass (kg), L = specific latent heat (J/kg)
| Type | Process | Meaning |
|---|---|---|
| Specific latent heat of fusion (Lf) | Melting / Freezing | Energy to change 1 kg between solid and liquid |
| Specific latent heat of vaporisation (Lv) | Boiling / Condensation | Energy to change 1 kg between liquid and gas |
Worked Example 4: Latent heat of fusion
The specific latent heat of fusion of ice is 334 000 J/kg. Calculate the energy required to melt 2 kg of ice at 0°C.
E = m × Lf = 2 × 334 000 = 668 000 J (or 668 kJ)
Worked Example 5: Latent heat of vaporisation
The specific latent heat of vaporisation of water is 2 260 000 J/kg. How much energy is needed to boil 0.5 kg of water at 100°C into steam?
E = m × Lv = 0.5 × 2 260 000 = 1 130 000 J (or 1130 kJ)
Worked Example 6: Finding mass from latent heat
840 000 J of energy is supplied to melt a block of ice at 0°C. The specific latent heat of fusion of ice is 334 000 J/kg. Calculate the mass of ice melted.
m = E / Lf = 840 000 / 334 000 = 2.52 kg
❓ Practice Questions
Q1: Foundation Describe the arrangement and movement of particles in a gas.
Q2: Foundation A metal block has a mass of 2.7 kg and a volume of 0.001 m³. Calculate its density in kg/m³.
Q3: Foundation Explain why the temperature of a substance does not change while it is melting, even though energy is being supplied.
Q4: Higher 500 kJ of energy is supplied to change water at 100°C into steam. The specific latent heat of vaporisation of water is 2 260 000 J/kg. Calculate the mass of water that boils.
Q5: Higher An irregular object has a mass of 250 g. When placed in a measuring cylinder, the water level rises from 30 cm³ to 80 cm³. Calculate the density in g/cm³ and kg/m³.
Q6: Higher Sketch a heating curve for water from −20°C to 120°C. Label the melting point, boiling point, and the sections where changes of state occur.
✅ Answers
- Particles in a gas are arranged randomly, far apart, and move rapidly in all directions. They have the highest energy of the three states.
- ρ = m / V = 2.7 / 0.001 = 2700 kg/m³ (this is aluminium)
- The energy is being used to break intermolecular bonds (increase potential energy) rather than increase the kinetic energy of particles. Since temperature depends on average kinetic energy, the temperature stays constant.
- m = E / Lv = 500 000 / 2 260 000 = 0.221 kg (221 g)
- V = 80 − 30 = 50 cm³. ρ = 250 / 50 = 5.0 g/cm³. In kg/m³: 5.0 × 1000 = 5000 kg/m³
- The heating curve should show: a rising slope from −20°C to 0°C (ice warming), a flat section at 0°C (melting), a rising slope from 0°C to 100°C (water warming), a flat section at 100°C (boiling), and a rising slope above 100°C (steam warming). The melting point is 0°C and the boiling point is 100°C.
🎯 Exam Tips
- Remember the difference between specific latent heat of fusion (melting/freezing) and vaporisation (boiling/condensation) — check which one the question is asking for
- On heating curves, the flat sections are where changes of state happen — energy goes into breaking bonds, not raising temperature
- For density calculations, always check your units — convert g to kg and cm³ to m³ before using ρ = m/V in standard units
- In the density required practical, describe the method step by step and mention measuring mass before the displacement method to avoid measuring water mass too
- Sublimation goes directly from solid to gas — it is rare (e.g. dry ice / CO₂) but may appear in exam questions
- Internal energy = kinetic energy + potential energy of all particles — don't confuse with temperature, which depends only on average kinetic energy
🔬 Required Practical
Required Practical: Measuring Density of Regular and Irregular Objects
Aim: To measure the density of a regular solid, an irregular solid and a liquid.
Method: 1. For a regular object (e.g. cuboid): measure length, width and height using a ruler or vernier calliper, then calculate volume using V = l × w × h. 2. Measure the mass using a digital balance. 3. For an irregular object: measure mass first, then use the displacement method — fill a Eureka can until water drips from the spout, lower the object in, and collect the displaced water in a measuring cylinder. The volume of water displaced equals the volume of the object. 4. Calculate density using ρ = m / V for each object.
Variables: IV: the object being measured (material/shape), DV: density (calculated from mass and volume), Control: temperature of water, same balance and measuring equipment used throughout.
🔢 Maths Skills
Mathematical Skills
You need to rearrange ρ = m / V to find mass (m = ρV) or volume (V = m/ρ). You must also convert between units: 1 g/cm³ = 1000 kg/m³, and convert cm³ to m³ by dividing by 1 000 000. For latent heat, use E = mL and rearrange to find any unknown.
Maths Example
A substance has density 2.5 g/cm³. Convert to kg/m³: 2.5 × 1000 = 2500 kg/m³. If 0.4 kg of this substance is needed, find the volume: V = m/ρ = 0.4 / 2500 = 1.6 × 10⁻⁴ m³. Energy to melt it at 0°C (Lf = 334 000 J/kg): E = mL = 0.4 × 334 000 = 133 600 J.
⚠️ Common Misconceptions
Watch Out!
1. Wrong: Temperature changes during a change of state. Correct: Temperature stays constant during melting/boiling — energy goes into breaking bonds, not increasing kinetic energy.
2. Wrong: Boiling and evaporation are the same process. Correct: Boiling happens at a specific temperature throughout the liquid; evaporation happens at any temperature from the surface only.
3. Wrong: Internal energy is the same as temperature. Correct: Internal energy = total kinetic + potential energy of ALL particles. Temperature depends only on average kinetic energy.
✍️ 6-Mark Question
Extended Answer
6 marks: Explain, in terms of particles, what happens to a solid as it is heated from below its melting point to above its boiling point. Include references to internal energy and the changes that occur.
Initially, the solid is heated and particles vibrate faster about their fixed positions — kinetic energy increases and temperature rises. At the melting point, energy breaks intermolecular bonds so particles can move past each other — this is the change from solid to liquid. Temperature stays constant because energy increases potential energy, not kinetic energy. Once fully melted, the liquid is heated and particles move faster — kinetic energy and temperature increase again. At the boiling point, energy breaks the remaining bonds completely so particles can move freely in all directions — the liquid changes to a gas. Temperature stays constant again as energy goes into increasing potential energy. After boiling, the gas particles move even faster and temperature continues to rise.
Mark scheme: 1 mark for each of — particles vibrate faster in solid; KE increases and temperature rises; flat section at melting point — bonds breaking; PE increases not KE; particles move freely as liquid; flat section at boiling point — remaining bonds break; gas particles move rapidly. (6 marks total)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student measures the density of two metal blocks. Block A (regular cube): mass = 21.6 g, sides = 2.0 cm. Block B (irregular): mass = 68.4 g, water displacement = 25.3 cm³. The student looks up the density of aluminium as 2.70 g/cm³ and gold as 19.3 g/cm³.
(a) Calculate the density of Block A and identify the metal.
(b) Calculate the density of Block B and identify the metal.
(c) The student's displacement volume for Block B was 25.3 cm³ but the true value is 25.0 cm³. Explain how this error could have occurred and its effect on the calculated density.
Answers: (a) V = 2.0³ = 8.0 cm³, ρ = 21.6/8.0 = 2.70 g/cm³ → aluminium. (b) ρ = 68.4/25.3 = 2.70 g/cm³ → also aluminium (both blocks are the same metal). (c) Some water may have splashed out or the student read the measuring cylinder at an angle (parallax error), giving a larger volume. This would give a smaller calculated density, making the metal appear less dense than it really is.
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