At what temperature will the RMS velocity of | vedclass

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Question

(B) The formula for $RMS$ velocity is $U_{rms} = \sqrt{\frac{3RT}{M}}$.For the velocities to be equal: $\sqrt{\frac{3RT_{SO_2}}{M_{SO_2}}} = \sqrt{\fr

Vedclass · Accepted Answer

$606$

Vedclass · Answer

(B) The formula for $RMS$ velocity is $U_{rms} = \sqrt{\frac{3RT}{M}}$.For the velocities to be equal: $\sqrt{\frac{3RT_{SO_2}}{M_{SO_2}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$.This simplifies to $\frac{T_{SO_2}}{M_{SO_2}} = \frac{T_{O_2}}{M_{O_2}}$.Given $M_{SO_2} = 64 \ g/mol$,$M_{O_2} = 32 \ g/mol$,and $T_{O_2} = 303 \ K$.Substituting the values: $\frac{T_{SO_2}}{64} = \frac{303}{32}$.$T_{SO_2} = \frac{303 	imes 64}{32} = 303 	imes 2 = 606 \ K$.

At what temperature will the $RMS$ velocity of $SO_2$ be the same as that of $O_2$ at $303 \ K$?

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