if the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen molecules at 0°C.

Solution

Physics sir · 3 steps

Same temperature, so only the molar mass matters: the lighter gas is faster by the square root of the ratio.

1. RMS speed formula. For a gas, vᵣₘₛ = √(3RT/M), where M is the molar mass. Both gases are at 0°C, so T is the same and cancels in the ratio.

   v_(H₂)/v_(O₂) = √(M_(O₂)/M_(H₂)) = √(32/2) = √16 = 4

2. Put in numbers. v_(H₂) = 4 × 160 m s⁻¹ = 640 m s⁻¹.
3. So. Hydrogen molecules move 4 times faster than oxygen molecules at the same temperature, so the answer is (a) 640 m/s.

The idea to keep. At the same temperature, vᵣₘₛ ∝ 1/√M. The lighter gas is always the faster one, so check that your answer goes up when the molar mass goes down.

Answer from the NTA final answer key. Solution by PrepWiser.