At what temperature will the rms speed of N_2 | vedclass

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(A) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $CO_2$ at $STP$,$T = 273 \, K$ and $M = 44 \, g/mol$.For $N_2$,$M = 28 \, g/mo

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$-99.27 \, ^\circ C$

Vedclass · Answer

(A) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.For $CO_2$ at $STP$,$T = 273 \, K$ and $M = 44 \, g/mol$.For $N_2$,$M = 28 \, g/mol$.Equating the $rms$ speeds:$\sqrt{\frac{3R 	imes 273}{44}} = \sqrt{\frac{3RT}{28}}$Squaring both sides:$\frac{273}{44} = \frac{T}{28}$$T = \frac{273 	imes 28}{44} = 173.73 \, K$Converting to Celsius:$T(^\circ C) = 173.73 - 273 = -99.27 \, ^\circ C$.

At what temperature will the $rms$ speed of $N_2$ gas at $1 \, atm$ pressure be equal to the $rms$ speed of $CO_2$ at $STP$?

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