States of Matter and Gas Laws

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam. Matter exists as solid, liquid or gas — distinguished by how strongly intermolecular forces hold particles together versus how much kinetic energy they possess. Solids keep a fixed shape (particles vibrate in a lattice); liquids flow and take the shape of their container; gases expand to fill any container (particles move in random straight lines with negligible attractions between them). Gas behaviour is governed by four laws and the ideal gas equation PV = nRT. Use absolute temperature in kelvin (T(K) = °C + 273), never Celsius, in every gas-law calculation. Molar volume at STP = 22.4 dm³ mol⁻¹. High-yield NABTEB facts: convert all temperatures to kelvin first, and remember that Boyle’s law needs constant T and n, Charles’s needs constant P and n, and Gay-Lussac’s needs constant V and n.

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

The Three States and What Distinguishes Them

In a solid, particles are tightly packed in an ordered lattice; they only vibrate about fixed positions, so the substance has definite shape and volume. In a liquid, particles are still close enough that volume is essentially fixed, but they slide past each other, allowing the liquid to conform to the shape of its container. In a gas, particles are far apart, have negligible intermolecular attraction, and move freely — producing indefinite shape and indefinite volume as well as high compressibility.

Kinetic Theory of Gases

Gas particles are assumed to (i) move in continuous random straight lines, (ii) collide elastically (no net energy loss), (iii) occupy negligible volume compared with the container, and (iv) exert no intermolecular forces. Combining these postulates yields PV = nRT, where R = 0.0821 dm³·atm·K⁻¹·mol⁻¹ (or 8.314 J·K⁻¹·mol⁻¹).

The Four Gas Laws

Boyle’s law: V ∝ 1/P (T and n constant) → P₁V₁ = P₂V₂
Charles’s law: V ∝ T (P and n constant) → V₁/T₁ = V₂/T₂
Gay-Lussac’s law: P ∝ T (V and n constant) → P₁/T₁ = P₂/T₂
Avogadro’s law: V ∝ n (T and P constant) → V₁/n₁ = V₂/n₂

Dalton’s Law and Mixtures

Dalton’s law of partial pressures: the total pressure of a non-reacting gas mixture equals the sum of each component’s partial pressure — P_T = P₁ + P₂ + P₃ + … A gas collected over water must have the aqueous vapour pressure subtracted to obtain the dry-gas pressure.

NABTEB Question Patterns

Multiple-choice items typically give two of (P, V, T, n) and ask you to calculate the third using the appropriate law, or they ask for molar mass via the rearranged ideal-gas form M = mRT/PV. Always convert °C → K before substituting.

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

When Ideal Behaviour Breaks Down

The ideal gas equation assumes point-like particles with no attractions. At high pressure, particle volume becomes a significant fraction of container volume; at low temperature, intermolecular attractions pull particles together and slow them. The van der Waals equation corrects both effects: (P + a(n/V)²)(V − nb) = nRT, where a corrects for attractions and b for particle volume. Gases most closely obey ideal behaviour at high temperature and low pressure.

Diffusion and Effusion

Diffusion is the gradual mixing of gases through random motion; effusion is a gas escaping through a tiny hole into vacuum. Graham’s law compares rates of effusion: rate₁/rate₂ = √(M₂/M₁) — lighter molecules effuse faster. NABTEB questions sometimes combine Graham’s law with molar-mass determination.

Worked Example

A 2.50 g sample of a volatile liquid is vaporised at 150 °C and 1.00 atm, occupying 1.04 dm³. Calculate the molar mass. First convert T: 150 + 273 = 423 K. Rearrange PV = nRT to n = PV/RT = (1.00)(1.04)/[(0.0821)(423)] = 0.0300 mol. Molar mass M = mass/n = 2.50/0.0300 ≈ 83.4 g mol⁻¹.

Common Mistakes

Leaving temperature in °C — every gas law collapses numerically.
Applying Boyle’s/Charles’s/Gay-Lussac’s when n is changing (use PV = nRT instead).
Forgetting to subtract water-vapour pressure in gas-collection problems.
Mixing up diffusion (mixing within a medium) with effusion (escape through a hole).

Practice Prompts

A 0.500 dm³ container holds N₂ at 1.20 atm and 298 K. To what temperature must it be heated at constant volume to raise the pressure to 2.40 atm?
Oxygen effuses through a pinhole in 84 s; an equal volume of an unknown gas takes 132 s under identical conditions. Find the molar mass of the unknown.

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States of Matter and Gas Laws