At what temperature (in K) is the rms velocit | vedclass

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(C) The formula for $rms$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $v_{rms}$ of $SO_2$ to be equal to $v_{rms}$ of $O_2$,we have $\sqrt{\frac{

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$600$

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(C) The formula for $rms$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $v_{rms}$ of $SO_2$ to be equal to $v_{rms}$ of $O_2$,we have $\sqrt{\frac{3RT_{SO_2}}{M_{SO_2}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$.Squaring both sides and canceling common terms,we get $\frac{T_{SO_2}}{M_{SO_2}} = \frac{T_{O_2}}{M_{O_2}}$.Given $T_{O_2} = 27 + 273 = 300 \ K$,$M_{O_2} = 32 \ g/mol$,and $M_{SO_2} = 64 \ g/mol$.Substituting the values: $\frac{T_{SO_2}}{64} = \frac{300}{32}$.$T_{SO_2} = \frac{300 	imes 64}{32} = 300 	imes 2 = 600 \ K$.

At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?

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