At what temperature is the rms speed of hydro | vedclass

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(B) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speed of hydrogen $(H_2)$ equals the $rms$ speed of oxygen $(

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$20$

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(B) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given that the $rms$ speed of hydrogen $(H_2)$ equals the $rms$ speed of oxygen $(O_2)$:$\sqrt{\frac{3RT_{H_2}}{M_{H_2}}} = \sqrt{\frac{3RT_{O_2}}{M_{O_2}}}$Squaring both sides and cancelling 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 is the $rms$ speed of hydrogen molecules equal to the $rms$ speed of oxygen molecules at $47^{\circ}C$ (in $K$)?

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