States of Matter

States of Matter

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Matter is anything with mass and volume; MDCAT tests three classical states — solid, liquid, gas — distinguished by the balance between intermolecular forces and the kinetic energy of particles. Solids: fixed shape, fixed volume, incompressible, particles vibrate in fixed lattice positions. Liquids: fixed volume, variable shape, slightly compressible, particles slide past one another. Gases: neither fixed shape nor volume, highly compressible, particles move freely. The unifying equation is the ideal gas law: PV = nRT, where P is pressure (atm), V is volume (L), n is moles, T is temperature (K), and R = 0.0821 L·atm·K⁻¹·mol⁻¹. Always convert °C to Kelvin (K = °C + 273) before substituting. High-yield points: Boyle’s law (P₁V₁ = P₂V₂), Charles’s law (V₁/T₁ = V₂/T₂), Dalton’s law of partial pressures (P_T = ΣP_i), and Graham’s law (r₁/r₂ = √(M₂/M₁)).

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Particle Model and Properties

In solids, strong intermolecular forces lock particles into a rigid lattice; they only vibrate, giving a fixed shape and volume. Liquids have weaker binding energy relative to thermal motion, so particles translate past each other — volume is fixed but shape follows the container. Gases have kinetic energy overwhelming intermolecular attractions, so particles occupy the entire container. This explains why gases are compressible (large empty space between particles) while solids and liquids are nearly incompressible, and why diffusion is fastest in gases, slowest in solids.

Gas Laws

Boyle’s Law (constant T): P₁V₁ = P₂V₂. Charles’s Law (constant P): V₁/T₁ = V₂/T₂. Gay-Lussac’s Law (constant V): P₁/T₁ = P₂/T₂. Avogadro’s Law (constant T, P): V ∝ n. Combined: PV/T = constant, leading directly to PV = nRT. A 2.5 L flask at 300 K containing 0.40 mol of O₂ gives P = nRT/V = (0.40)(0.0821)(300)/2.5 ≈ 3.94 atm.

Partial Pressure and Graham’s Law

Dalton’s Law: total pressure = sum of partial pressures of each gas. Used when collecting gas over water, where observed pressure = gas pressure + water vapour pressure. Graham’s law states the rate of effusion/diffusion is inversely proportional to √M — light gases (H₂, He) escape faster than heavy ones (CO₂, SO₂).

Phase Changes

Melting, vaporisation, and sublimation absorb latent heat; freezing, condensation, and deposition release it. Vapour pressure rises with temperature; boiling point is reached when vapour pressure equals external pressure. Stronger intermolecular forces (H-bonding in water) raise the boiling point. Water is anomalous: ice is less dense than liquid water because hydrogen bonding forces an open hexagonal lattice — a recurring MCQ trap.

Exam Pattern for MDCAT

Expect 1–2 MCQs in Chemistry (≈3% weight). Formats: numerical gas-law calculations, identify-correct-statement, or assertion-reason on intermolecular forces and density order. Always check unit consistency and Kelvin conversion before computing.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Kinetic Molecular Theory (KMT) and Ideal Gases

KMT assumes: (1) gas particles are in constant random motion, (2) their own volume is negligible compared with container volume, (3) collisions are perfectly elastic, and (4) no intermolecular forces act between particles. From these, the average translational kinetic energy per molecule is KE_avg = (3/2)kT, where k = 1.38 × 10⁻²³ J/K is Boltzmann’s constant. This proves temperature is a direct measure of average molecular KE, not heat content.

Real Gases and Van der Waals Equation

Real gases deviate at high P and low T because molecular volume (constant b) and intermolecular attraction (constant a) become significant. The van der Waals correction is:

(P + a/V²)(V − b) = RT for one mole.

• a/V² corrects for attractive forces pulling molecules inward, reducing measured pressure.
• b corrects for the excluded volume occupied by molecules themselves.

Real gases behave ideally when T is high (KE ≫ attractions) and P is low (volume ≫ molecular volume).

Worked Example: Combined Gas Law

A gas at 1.50 atm occupies 4.00 L at 27 °C. Find its volume at STP (1.00 atm, 273 K).

Using combined form P₁V₁/T₁ = P₂V₂/T₂: T₁ = 300 K, T₂ = 273 K. V₂ = (P₁V₁T₂)/(T₁P₂) = (1.50 × 4.00 × 273)/(300 × 1.00) = 5.46 L.

Common Traps and Pitfalls

• Forgetting K conversion — substituting 27 instead of 300 produces wrong answers.
• Using R = 0.0821 with Pa or m³ — always convert P to atm and V to L, or use R = 8.314 J·K⁻¹·mol⁻¹ with Pa and m³.
• Confusing diffusion (through another medium) with effusion (through a small hole) — Graham’s law applies to both, but MCQ wording varies.
• Misapplying Dalton’s law: only valid when gases don’t react.

Connections to Adjacent Topics

States of matter links directly to Chemical Bonding (intermolecular forces determine phase), Thermodynamics (latent heat, enthalpy of vaporisation), and Solutions (vapour-pressure lowering by non-volatile solutes — Raoult’s law extension).

Practice Prompts

1. A 6.00 L cylinder at 2.00 atm and 400 K is heated isochorically to 600 K. What is the new pressure?
2. Two gases, CH₄ (M = 16) and SO₂ (M = 64), effuse through the same pinhole. Which is faster and by what factor?

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