Changes of State and the Particle Model

Density is mass per unit volume:

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

• $\rho$ (Greek rho) in kg/m³ or g/cm³.
• $m$ in kg or g.
• $V$ in m³ or cm³.

Conversion: 1 g/cm³ = 1000 kg/m³.

Typical densities:

Material	Density (kg/m³)
Air	1.2
Petrol	800
Water	1000
Aluminium	2700
Iron	7900
Lead	11,300
Gold	19,300

Worked example. A copper block has mass 89 g and volume 10 cm³. Find density.

$\rho = 89 / 10 = 8.9\,\text{g/cm}^3 = 8900\,\text{kg/m}^3$

This matches the known density of copper.

Solids — particles touch in a regular pattern; very high density. Liquids — particles still touching but disordered; density slightly less than solid (water is unusual: liquid water is denser than ice — that's why ice floats). Gases — particles far apart in random motion; density 1000× less than liquid/solid.

Regular solid (cube/cylinder):

1. Measure mass with a balance.
2. Measure dimensions with a ruler or vernier calipers.
3. Compute V (= L × W × H for a cube, $\pi r^2 h$ for a cylinder).
4. ρ = m/V.

Irregular solid:

1. Measure mass with a balance.
2. Lower into a partly-filled measuring cylinder of water; note volume rise = volume of the object.
3. Alternative: 'eureka can' — fill to overflow, drop object in, catch and measure displaced water.
4. ρ = m/V.

Liquid:

1. Measure mass of empty measuring cylinder.
2. Pour in a known volume of liquid; measure new mass.
3. Mass of liquid = total − empty.
4. ρ = m/V.

Sources of error:

• Reading the meniscus at eye level (parallax error).
• Air bubbles trapped on irregular solid → falsely high V.
• Wet object placed on balance → falsely high mass.
• Water spillage from eureka can before object enters.

Solid ↔ Liquid:

• Melting (solid → liquid) at the melting point (e.g. water 0 °C).
• Freezing (liquid → solid) at the freezing point (same temperature for pure substances).

Liquid ↔ Gas:

• Boiling (liquid → gas throughout, at the boiling point — e.g. water 100 °C).
• Evaporation (liquid → gas at the surface, at any temperature).
• Condensation (gas → liquid).

Solid ↔ Gas (skipping liquid):

• Sublimation (solid → gas directly — e.g. dry ice, iodine).
• Deposition (gas → solid — e.g. frost forming on a window).

A physical change is one that does NOT alter the chemical identity of the substance. Water molecules (H₂O) stay as water molecules whether ice, liquid water or steam.

A chemical change would form new substances (e.g. burning wood → CO₂ + H₂O — different chemicals).

Consequences:

1. State changes are reversible — you can freeze melted water back into ice indefinitely.
2. Mass is conserved — if you melt 1 kg of ice, you get exactly 1 kg of liquid water (no particles are created or destroyed).
3. Energy is needed to OVERCOME the inter-particle forces — covered as 'latent heat' in 4.3.2.3.

Boiling vs evaporation:

• Evaporation: only at the surface; happens at any temperature; speeds up at higher T, lower humidity, larger surface area, more airflow.
• Boiling: bubbles form throughout the liquid; only at the boiling point.