Gas Laws and Kinetic Theory

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Kinetic Theory — Key Facts Assumptions: gas consists of many point molecules, random motion, no forces between molecules except collisions, collisions are elastic rms speed: v_rms = √(3RT/M) = √(3P/ρ); at 300K, v_rms(N₂) ≈ 517 m/s Ideal gas: PV = nRT; kinetic interpretation: P = (1/3)ρv_rms² ⚡ Exam tip: Average KE of gas molecules depends ONLY on temperature: KE_avg = (3/2)kT

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Kinetic Theory — NEET/JEE Study Guide Degrees of freedom: monatomic (3), diatomic (5 at room temp, 7 at high T), non-linear triatomic (6) Equipartition: each degree of freedom contributes (1/2)kT to energy; total KE = (f/2)nRT Mean free path: λ = 1/(√2 π d² n*) where n* = number density; inversely proportional to pressure Brownian motion: evidence for kinetic theory; pollen grain random motion due to molecular collisions

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Kinetic Theory — Comprehensive Notes Maxwell speed distribution: fraction with speed between v and v+dv; most probable, mean, rms speeds differ Van der Waals gas: corrections to ideal — attractive forces (a) and finite molecular volume (b); a = 1.39 L² atm/mol², b = 0.039 L/mol for N₂ Transport phenomena: viscosity (η = (1/3)ρv_rms λ), thermal conductivity (K = (1/3)ρv_rms λ c_v), diffusion (D = (1/3)v_rms λ) Graham’s law of effusion: rate ∝ 1/√M; lighter gas effuses faster; used in uranium enrichment

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