States of Matter (Gases, Liquids, Solids)

States of Matter (Gases, Liquids, Solids)

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Matter exists in four states — solid, liquid, gas, and plasma — distinguished by the balance between intermolecular forces (cohesion) and the kinetic energy of particles (thermal motion). The ideal gas law, PV = nRT, combines Boyle’s, Charles’s, and Avogadro’s laws and is tested almost every ECAT cycle, usually with a numerical twist. Always use absolute temperature in Kelvin (T = °C + 273.15) when plugging into PV = nRT or Charles’s law. Real gases deviate from ideality at high pressure and low temperature, corrected by the van der Waals equation: (P + an²/V²)(V − nb) = nRT, where a accounts for attractions and b for the finite molecular volume.

---

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Intermolecular Forces vs. Thermal Energy

The physical state of a substance is decided by which factor dominates. Solids have the strongest effective cohesive forces — particles vibrate in fixed lattice positions, giving a definite shape and volume. Liquids retain a definite volume but flow into the container’s shape; intermolecular forces are still significant, but kinetic energy lets particles slide past each other. Gases have negligible cohesive forces — particles move in rapid, random, straight-line trajectories, filling any container completely (no fixed shape or volume). Plasma, the fourth state, consists of ionised gas with free electrons and ions, formed at very high temperatures (e.g. stars, neon signs, lightning).

Gas Laws and the Kinetic Molecular Theory

The Kinetic Molecular Theory idealises a gas as point-like particles in constant elastic collisions, with no intermolecular attraction and a kinetic energy proportional to absolute temperature: KE_avg = (3/2)RT per mole. From this, the combined gas law emerges:

P₁V₁/T₁ = P₂V₂/T₂, with T in Kelvin.

For a fixed amount of gas this reduces to Boyle’s law (P ∝ 1/V at constant T), Charles’s law (V ∝ T at constant P), and Avogadro’s law (V ∝ n at constant T, P). The master form PV = nRT lets you solve for any unknown when three are known.

Real Gases and the van der Waals Equation

At high P or low T, the ideal model breaks down because molecules attract each other and occupy real volume. The van der Waals correction is:

(P + an²/V²)(V − nb) = nRT

Constant a reflects attractive forces (large for polar/ H-bonding molecules), constant b reflects excluded volume (larger for bigger molecules). ECAT MCQs frequently ask which gas deviates most from ideality — typically the most polarisable or most polar (e.g. CO₂, NH₃, H₂O).

Phase Transitions and Phase Diagrams

A phase diagram plots pressure against temperature, marking:

• Triple point: solid, liquid, and gas coexist in equilibrium (unique P, T).
• Critical point: end of the liquid–gas boundary; above this, the substance is a supercritical fluid.
• Boiling point: temperature at which vapour pressure equals atmospheric pressure (760 mmHg at standard pressure).
• Sublimation: solid → gas directly (e.g. dry ice, naphthalene). Deposition: gas → solid directly (e.g. frost formation).

Common ECAT Traps

1. Forgetting to convert °C → K before substituting into PV = nRT or Charles’s law.
2. Inverting Graham’s law — r₁/r₂ = √(M₂/M₁) means the lighter gas effuses faster.
3. Treating boiling point and vapour pressure as unrelated — they are linked by definition.

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Worked Example — Density Form of the Ideal Gas Law

A frequent ECAT-style numerical uses PM = dRT, where M is molar mass (kg/mol) and d is gas density (kg/m³). Given 2.0 g of an unknown gas occupying 1.25 L at 300 K and 1.0 atm, compute the molar mass:

• n = PV/RT = (1.0)(1.25)/(0.0821 × 300) ≈ 0.0507 mol
• M = mass/n = 2.0 / 0.0507 ≈ 39.4 g/mol → candidate gas is argon (Ar = 39.95 g/mol).

This style links gas law numerics with stoichiometry, and examiners love cross-topic synthesis.

Edge Cases and Mechanism Depth

• Compressibility factor Z = PV/nRT quantifies non-ideality: Z < 1 means attractions dominate (common at moderate P); Z > 1 means repulsions dominate (very high P).
• Hydrogen bonding explains water’s anomalously high boiling point, surface tension, and viscosity compared with H₂S and H₂Se.
• Vapour pressure depends only on the substance and temperature — not on the amount of liquid or the container size (a common ECAT misconception).
• Critical temperature: the maximum temperature at which a gas can be liquefied by pressure alone. Above it, no amount of compression produces a liquid phase.

Practice Prompts

1. A 5.0 L flask at 27 °C contains 0.20 mol N₂ and 0.30 mol O₂. Find total pressure and the partial pressure of O₂. (Hint: P_total = n_totalRT/V; mole fraction × P_total.)
2. Using Graham’s law, calculate how many times faster H₂ effuses than CO₂ at the same temperature. (√(44/2) = √22 ≈ 4.7×.)

---

Content adapted based on your selected roadmap duration. Switch tiers using the selector above.