4.3.1 Changes of State and the Particle Model

4.3.1.1 Density of Materials

The density of materials is a fundamental property that describes how much "stuff" (mass) is packed into a certain amount of space (volume). In physics, density is determined by the mass of the atoms and how closely together those atoms are arranged.

1. The Definition of Density

Density is defined as the mass per unit volume of a substance. It is a characteristic property of a material, meaning it does not change regardless of the size of the sample (as long as the substance remains the same).

2. The Formula and Units

To calculate density, we use the following equation:

$\rho =\frac{m}{V}$

Where:

1. $\rho$(rho) is the density, measured in kilograms per cubic metre ($kg/m^3$) or grams per cubic centimetre ($g/c{m}^3$).
2. m is the mass, measured in kilograms (kg) or grams (g).
3. V is the volume, measured in cubic metres ($m^3$) or cubic centimetres ($c{m}^3$).

Exam Tip: A common pitfall is forgetting to convert units. If mass is in kg and volume is in $c{m}^3$, you must convert one to match the other. $1,000kg/m^3=1g/c{m}^3$.

3. Density and the Particle Model

The states of matter—solid, liquid, and gas—differ primarily in their density because of how their particles are arranged:

1. Solids: Particles are packed very closely together in a regular arrangement. Solids usually have the highest density.
2. Liquids: Particles are close together but can move past each other. Their density is usually slightly lower than solids (with the notable exception of water/ice).
3. Gases: Particles are far apart and move randomly. Gases have very low densities because there is a large amount of empty space between particles.

Visual Representation:

1. Solid: A grid of spheres touching each other.
2. Liquid: Spheres touching but in a disorganized pile.
3. Gas: A few spheres spread far apart with arrows indicating movement.

4. Required Practical: Measuring Density

You must know how to determine the density of different objects experimentally.

A. Regular Solids (e.g., a metal cube)

1. Measure the mass using a digital balance.
2. Measure the dimensions (length, width, height) using a ruler or digital calipers.
3. Calculate volume: $V=l\times w\times h$.
4. Apply the density formula.

B. Irregular Solids (e.g., a stone)

For objects where you cannot calculate volume with a ruler, use the Displacement Method (Eureka Can):

1. Measure the mass of the object using a balance.
2. Fill a Eureka can (displacement can) with water until it is level with the spout.
3. Place a measuring cylinder under the spout.
4. Gently lower the object into the water.
5. The volume of the water displaced into the measuring cylinder is exactly equal to the volume of the object.
6. Apply the density formula.

C. Liquids

1. Place an empty measuring cylinder on a balance and zero (tare) it.
2. Pour a specific volume of the liquid (e.g., 50ml) into the cylinder.
3. Record the mass shown on the balance.
4. Apply the density formula ($1ml=1c{m}^3$).

5. Edge Cases and Anomalies

1. The Water/Ice Anomaly: Most substances are denser as solids than as liquids. However, ice is less dense than liquid water because the particles in ice form a crystalline structure that holds them further apart. This is why ice floats.
2. Compressibility: The density of a gas can change easily. If you compress a gas into a smaller volume, its density increases because the same mass is now in a smaller space.

6. Mathematical Example

Question:

A decorative statue has a mass of 405g. To find its volume, it is lowered into a Eureka can. It displaces $150c{m}^3$ of water. Calculate the density of the statue in $kg/m^3$.

Step 1: Identify known values

$m=405g$

$V=150c{m}^3$

Step 2: Calculate density in $g/cm^3$

$\rho =\frac{405}{150}=2.7g/c{m}^3$

Step 3: Convert to $kg/m^3$

To convert $g/c{m}^3$ to $kg/m^3$, multiply by 1,000.

$\rho =2.7\times 1,000=2,700kg/m^3$

Answer: The density of the statue is $2,700kg/m^3$. (Note: This is the density of Aluminium!)

4.3.1.2 Changes of State

In physics, matter doesn't just stay in one form. By adding or removing energy, we can cause a substance to change its state. Under the AQA specification, you must understand the terminology of these transitions and why they are fundamentally different from chemical reactions.

1. The Physical Nature of State Changes

A change of state is a physical change, not a chemical one.

1. Reversibility: If you reverse the energy change (e.g., cool down steam), the substance recovers its original properties.
2. Conservation of Mass: The number of particles remains the same; they are simply rearranged. Therefore, the mass of the substance does not change during a state change.

2. The Six Transitions

You must be able to name and describe the following transitions:

Note on Evaporation vs. Boiling: Boiling happens throughout the liquid at a specific temperature (the boiling point). Evaporation happens only at the surface and can occur at temperatures below the boiling point.

3. Energy and the Particle Model

To understand why states change, we look at the Internal Energy of the particles.

1. Heating: When you heat a substance, you transfer energy to its particles. This increases their kinetic energy (they move/vibrate faster) or their potential energy (the bonds/forces between them are broken).
2. Breaking Bonds: During melting or boiling, the energy being put in is used to break the attractive forces holding the particles together, rather than increasing the temperature. This is why the temperature remains constant during a state change.

4. Heating and Cooling Graphs

A heating graph shows how the temperature of a substance changes as energy is added.

Visual Guide for a Heating Graph:

1. Sloped Line (Solid): Temperature rises as particles vibrate faster.
2. Flat Line (Melting): Temperature stays constant while the solid turns to liquid (Potential energy increases).
3. Sloped Line (Liquid): Temperature rises as particles move faster.
4. Flat Line (Boiling): Temperature stays constant while the liquid turns to gas.
5. Sloped Line (Gas): Temperature rises further.

5. Mathematical Context: Conservation of Mass

While "Changes of State" is largely conceptual, it is often linked to density calculations. Because mass is conserved, we can use the following logic:

The Principle:

$m_{solid}=m_{liquid}=m_{gas}$

Example Scenario:

If $1kg$ of ice melts, it produces exactly 1kg of water. However, because the density of water is higher than ice, the volume will decrease.

$V=\frac{m}{\rho }$

If $\rho$ (density) increases while m (mass) stays the same, V (volume) must decrease.

6. Edge Cases & Common Misconceptions

1. "Disappearing" Mass: Students often think mass is lost when a liquid boils because the steam escapes. In a closed system, the mass recorded on a balance would remain identical.
2. Sublimation: This is rare but important. Dry Ice (solid $C{O}_2$) and Iodine are classic examples of substances that skip the liquid phase entirely at standard pressure.
3. Temperature Plateaus: Remember: During a change of state, the temperature does NOT change. If you see a flat line on a temperature-time graph, a state change is occurring.