What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

Solution

Physics sir · 3 steps

Both the temperature and the mass change here, so write v_rms as √(T/M) and update both at once.

1. RMS speed formula. For a gas, vᵣₘₛ = √(3RT/M), where M is the molar mass. So vᵣₘₛ depends only on the ratio T/M.
2. What changes. The temperature goes from T to 2T. When O₂ splits into atomic O, the molar mass goes from 32 to 16 g mol⁻¹, so M becomes M/2.

   v'/v = √((T'/M')/(T/M)) = √((2T × M)/(T × M/2)) = √4 = 2

3. So. The ratio T/M becomes four times larger, and the square root of 4 is 2. The rms speed of atomic oxygen is double the original value, which is option (b).

The idea to keep. Since vᵣₘₛ ∝ √(T/M), find how much the ratio T/M changes first, then take its square root. Dissociation halves M, so it acts like doubling T.

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