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: (a) 5/2 (b) 25/4 (c) 4/25 (d) 2/5

Answer: (a). Vapour density ∝ molar mass M, so (M₁)/(M₂) = 4/25. At the same T, (v₁)/(v₂) = √((M₂)/(M₁)) = √(25/4) = 5/2 So the answer is (a) 5/2.

The ratio of vapour densities of two gases at the same temperature is… | JEE Main 2025 (28 Jan, Shift 2)

Q16JEE Main 2025 · 28 JAN · SHIFT 2Easy

Molecular Speeds & Maxwell Distribution

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

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Answer: (a)

Vapour density $\propto$ molar mass $M$ , so $\frac{M_1}{M_2} = \frac{4}{25}$ .
At the same $T$ , $\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{25}{4}} = \frac{5}{2}$
So the answer is (a) $\frac{5}{2}$ .

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