The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at 47 is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively) (a) 47 (b) 132 (c) 320 (d) 405

Answer: (b). (vH)/(vO) = √((TH)/(TO)·(MO)/(MH)) with TO = 320 K, (MO)/(MH) = 16 4.5² = 20.25 = (16 TH)/(320) ⇒ TH = 405 K So the answer is (b) 132.

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5… | MHT CET 2024 (2 May, Shift 2)

Q32MHT CET 2024 · 2 MAY · SHIFT 2Medium

Molecular Speeds & Maxwell Distribution

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ\text{C}$ is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

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Answer: (b)

$\frac{v_H}{v_O} = \sqrt{\frac{T_H}{T_O}\cdot\frac{M_O}{M_H}}$ with $T_O = 320\text{ K}$ , $\frac{M_O}{M_H} = 16$
$4.5^2 = 20.25 = \frac{16\,T_H}{320} \Rightarrow T_H = 405\text{ K}$
So the answer is (b) $132^\circ\text{C}$ .

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