At what temperature, the RMS speed of hydrogen molecules exceeds their most probable speed by 400 m/ — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

The difference is: u_rms - u_mp = 400 → √(3RT/M) - √(2RT/M) = 400 → (√3 - √2) × √(RT/M) = 400. For $H_2$ (M = 0.002 kg/mol): (1.732 - 1.414) × √(8.0 × T / 0.002) = 400 → 0.318 × √4000T = 400 → 20 × 0.318 × √T = 400 → 6.36 √T = 400 → √T ≈ 62.89 → T ≈ 400 K = 127°C.