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Q.
At what temperature, the root-mean-square velocity of $SO_{2}$ will be the same as that of $CH_{4}$ at $27^{\circ}C$ ?
States of Matter
Solution:
Root-mean-square velocity $=\sqrt{\frac{3RT}{M}}$
The value for $CH_{4}$ at $27^{\circ}C$ or $300\,K =\sqrt{\frac{3R\times300}{16}}$
Now for $SO_{2} $
Root-mean-square velocity $=\sqrt{\frac{3RT}{64}}$
or, $\sqrt{\frac{3R\times300}{16}}$
$=\sqrt{\frac{3R\times T}{64}}$
or $T=1200\,K$