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

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(B) The $rms$ velocity of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ velocity of hydrogen $(H_2)$ is equal to th

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$20$

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(B) The $rms$ velocity of a gas molecule is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ velocity of hydrogen $(H_2)$ is equal to that of oxygen $(O_2)$:$\sqrt{\frac{3RT_{H_2}}{M_{H_2}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$Squaring both sides and canceling common terms $(3R)$:$\frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$Here,$M_{H_2} = 2 \ g/mol$,$M_{O_2} = 32 \ g/mol$,and $T_{O_2} = 47 + 273 = 320 \ K$.Substituting the values:$\frac{T_{H_2}}{2} = \frac{320}{32}$$\frac{T_{H_2}}{2} = 10$$T_{H_2} = 20 \ K$.

At what temperature (in $K$) is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^o \ C$?

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