If the rms speed of oxygen molecules at $0^{\circ} \mathrm{C}$ is $160 \mathrm{~m} / \mathrm{s}$, find the rms speed of hydrogen molecules at $0^{\circ} \mathrm{C}$.

(B) $640 \mathrm{~m} / \mathrm{s}$

(A) $332 \mathrm{~m} / \mathrm{s}$

(C) $40 \mathrm{~m} / \mathrm{s}$

(D) $80 \mathrm{~m} / \mathrm{s}$

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Heat & Thermodynamics

If the rms speed of oxygen molecules at

0^{\circ} C

160 m / s

, find the rms speed of hydrogen molecules at

0^{\circ} C

(A) $332 m / s$
(B) $640 m / s$ ✓ Correct
(C) $40 m / s$
(D) $80 m / s$

Answer: (B)

Solution

At a fixed temperature the rms speed varies inversely with the square root of molar mass,

v_{r m s} \propto 1/ M

, so

\frac{v _{H_{2}}}{v _{O_{2}}} = \frac{M _{O_{2}}}{M _{H_{2}}} = \frac{32}{2} = 4.

Hence

v_{H_{2}} = 4 \times 160 = 640

m/s.

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Single correct option

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