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Molecular Speeds - Vrms, Vavg, Vmps

At what tempe...

Question

At what temperature, the rms velocity of $S O_{2}$ be same as that of $O_{2}$ at $303 K$ ?

273 K

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606 K

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303 K

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403 K

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Solution

The correct option is B $606 K$
$U_{r m s} = \sqrt{\frac{3 R T}{M}}$

$\frac{U_{r m s} ({S O}_{2})}{U_{r m s} (O_{2})} = \sqrt{\frac{T ({S O}_{2})}{M ({S O}_{2})} \times \frac{M (O_{2})}{T (O_{2})}}$
ie, $1 = \sqrt{\frac{T ({S O}_{2})}{64} \times \frac{32}{303}}$
$T ({S O}_{2}) = 606 K$

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