If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km / s, the root mean square velocity of oxygen at the same condition in km / s is :

Solution

Physics sir · 3 steps

Same temperature, so vᵣₘₛ depends only on molar mass: oxygen is 16 times heavier, 4 times slower.

1. What sets the speed. For an ideal gas, vᵣₘₛ = √(3RT/M). At the same temperature, 3RT is the same for both gases, so vᵣₘₛ ∝ 1/√M.

   v_(O₂)/v_(H₂) = √(M_(H₂)/M_(O₂)) = √(2/32) = 1/4

2. Put in numbers. v_(O₂) = 1/4 × 2 km s⁻¹ = 0.5 km s⁻¹.
3. So. The rms speed of oxygen is 0.5 km s⁻¹, option (d).

The idea to keep. At a fixed temperature, every gas has the same average kinetic energy, so vᵣₘₛ ∝ 1/√M. Take the square root of the mass ratio, not the ratio itself.

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