The ratio of vapour densities of two gases at the same temperature is 4/25 , then the ratio of r.m.s. velocities will be :

Solution

Physics sir · 3 steps

Vapour density is just half the molar mass, so swap it in and use vᵣₘₛ ∝ 1/√M.

1. Vapour density to mass. Vapour density is half the molar mass, VD = M/2. So the ratio of vapour densities equals the ratio of molar masses: M₁/M₂ = 4/25.

   vᵣₘₛ = √(3RT/M) ⇒ v₁/v₂ = √(M₂/M₁)

2. Same temperature. With T the same for both gases, 3RT cancels in the ratio. The lighter gas moves faster, so the mass ratio flips and then goes under a square root.
3. So. v₁/v₂ = √(25/4) = 5/2, which is option (a).

The idea to keep. At a fixed temperature, vᵣₘₛ ∝ 1/√M, and vapour density is proportional to M. Invert the ratio first, then take the square root.

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