States of Matter

Concept overview

States of matter is the chapter where you first learn to reason about macroscopic properties (pressure, volume, temperature) from microscopic behaviour (molecular motion). The classical gas laws — Boyle's, Charles's, Gay-Lussac's, Avogadro's — condense into the ideal gas equation PV = nRT, which will appear inside dozens of problems across Thermodynamics, Chemical Kinetics and Solutions.

Kinetic theory of gases derives PV = nRT from first principles, treating gas molecules as point particles in perfectly elastic random motion. The root-mean-square, average and most-probable speeds emerge from the Maxwell-Boltzmann distribution and are all proportional to √(T/M) — a fact that JEE loves to test in comparison-style questions.

Real gases deviate from ideal behaviour at high pressure and low temperature. The van der Waals equation (P + a/V²)(V − b) = RT corrects for intermolecular attraction (a) and finite molecular volume (b). The compressibility factor Z = PV/RT is 1 for an ideal gas, greater than 1 when repulsive forces dominate, and less than 1 when attractive forces dominate.

The chapter also covers liquefaction (critical temperature, critical pressure), surface tension, and viscosity — smaller topics that contribute a predictable single question each year on JEE Main.

Key formulas & concepts

• Ideal gas equation: PV = nRT
• Combined gas law: P₁V₁/T₁ = P₂V₂/T₂
• Molar volume at STP: 22.4 L per mole
• Dalton's law (mixtures): P_total = ΣP_i
• RMS speed: v_rms = √(3RT/M)
• Average speed: v_avg = √(8RT/πM)
• Most probable speed: v_mp = √(2RT/M)
• van der Waals: (P + an²/V²)(V − nb) = nRT

Common mistakes to avoid

• Using P in kPa but R = 0.0821 L·atm/mol·K — always match units to the R value.
• Confusing rms, average and most probable speeds — v_rms > v_avg > v_mp always.
• Forgetting that Charles's law needs absolute temperature (K), not Celsius.
• Ignoring vapour pressure of water when a gas is collected over water — subtract it from total P to get the dry-gas partial pressure.

JEE Main relevance

JEE Main drops 1 direct gas-laws or kinetic-theory numerical every paper. In addition, PV=nRT appears inside stoichiometry problems (gas evolved), inside solutions problems (vapour pressure), and inside chemical equilibrium problems (K_p ↔ K_c interconversion). Missing this chapter has cascading consequences downstream.

JEE Advanced relevance

Advanced problems combine kinetic theory with real-gas behaviour — asking, for example, when a real gas behaves most ideally (moderate T, low P) or comparing van der Waals a-values across gases and inferring intermolecular attraction. Compressibility factor problems are also common in Advanced.

Previous-year questions (PYQ)

The JEETutorAI PYQ bank has ~470 tagged problems for this chapter. Filter by 'ideal gas + kinetic theory' as your first pass — real gas questions are best attempted only after ideal gas is fluent.