Practice question

**Ideal gas equation** combines Boyle, Charles, Avogadro laws, P V = N k_B T, N number of molecules, k_B Boltzmann constant, for 1 mole N_A=6.022×10²³, R = N_A k_B, enabling calculation of volume from P,T,n. v_rms = √((3k_B T)/(m)), m = 28 × 10⁻³⁶.02 × 10²³ = 4.65 × 10⁻²⁶ kg.600² = 3 × 1.38 × 10⁻²/³ × T4.65 × 10⁻²⁶, T = 3.6 × 10⁵ × 4.65 × 10⁻²⁶/⁴.14 × 10⁻²/³ ≈ 404 K. Substituting values gives 404 K, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T