Kinetic_Theory_of_Gases_Chapter_Notes.pptx

Kinetic theory of gas

1. Kinetic Theory of Gases Chapter Notes — Key concepts, formulas & solved examples

2. Learning Objectives Understand assumptions of kinetic theory Derive ideal gas equation from molecular model Relate temperature to average kinetic energy Solve basic problems and apply formulas

3. Basic Assumptions Gas consists of a large number of identical molecules in random motion Molecules are point particles with negligible volume Collisions are perfectly elastic (no energy loss) No intermolecular forces except during collisions

4. Pressure from Molecular Collisions Pressure = force per unit area from molecular impacts Derivation leads to: P = (1/3) * (Nm/V) * v_rms^2 Where v_rms is root-mean-square speed

5. Ideal Gas Equation PV = NkT (microscopic form, N = number molecules) PV = nRT (macroscopic form, n = moles) Relate k (Boltzmann) and R: R = N_A * k

6. Temperature & Kinetic Energy Average translational kinetic energy per molecule: (3/2) kT Per mole: (3/2) RT So temperature measures average kinetic energy of molecules

7. Speed Measures v_rms = sqrt(3kT/m) or sqrt(3RT/M) (M = molar mass in kg/mol) Mean speed and most probable speed differ (Maxwell distribution)

8. Sample Problem (Solved) Problem: Find v_rms of N2 at 300 K. M(N2)=28 g/mol Solution steps: convert M to kg/mol, use v_rms = sqrt(3RT/M) Answer (worked): v_rms ≈ 517 m/s (approx.)

9. Important Formulas (Quick Reference) PV = nRT P = (1/3) (Nm/V) v_rms^2 v_rms = sqrt(3RT/M) E_avg (per molecule) = (3/2) kT

10. Summary & Revision Tips Remember assumptions — they justify the formulas Practice conversions (grams ↔ kg, moles ↔ molecules) Memorize core formulas and practice 3–5 problems