JEE Main 2021 · 26 August · morning · Single correct · +4 / −1
The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are V H , V O and V C respectively then :
- (a) V H > V O > V C
- (b) V C > V O > V H
- (c) V H = V O > V C
- (d) V H = V O = V C
Answer and solution
Answer (a) V H > V O > V C
Solution
Physics sir · 2 steps
Same temperature means same kinetic energy per molecule, so the lightest gas has to move fastest.
- RMS speed formula. The rms speed depends on temperature and molar mass. At a fixed temperature, only the molar mass M changes from gas to gas.
vᵣₘₛ = √(3RT/M) ⇒ vᵣₘₛ ∝ 1/√M
Gas Molar mass (g mol⁻¹) vᵣₘₛ compared with O₂ H₂ 2 √(32/2) = 4 times, fastest O₂ 32 1 times CO₂ 44 √(32/44) ≈ 0.85 times, slowest - So. Lighter molecules move faster, so V_H > V_O > V_C, which is option (a).
The idea to keep. At the same temperature every gas has the same average kinetic energy per molecule, not the same speed. Speed goes as 1/√M, so the lighter gas always wins.
Answer from the NTA final answer key. Solution by PrepWiser.