The rms speed of a gas at room temperature of | vedclass

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(A) The formula for $rms$ speed is given by $v_{rms} = \sqrt{\frac{3RT}{M_w}}$,where $R = 8.31 \ J/(mol \cdot K)$,$T = 27 + 273 = 300 \ K$,and $v_{rms

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$CO_2$

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(A) The formula for $rms$ speed is given by $v_{rms} = \sqrt{\frac{3RT}{M_w}}$,where $R = 8.31 \ J/(mol \cdot K)$,$T = 27 + 273 = 300 \ K$,and $v_{rms} = 412 \ m/s$.Squaring both sides,we get $v_{rms}^2 = \frac{3RT}{M_w}$.Rearranging for molar mass $M_w$: $M_w = \frac{3RT}{v_{rms}^2}$.Substituting the values: $M_w = \frac{3 	imes 8.31 	imes 300}{412^2} \approx \frac{7479}{169744} \approx 0.044 \ kg/mol = 44 \ g/mol$.The molar mass of $CO_2$ is $12 + (2 	imes 16) = 44 \ g/mol$. Therefore,the gas is $CO_2$.

The $rms$ speed of a gas at room temperature of $27^{\circ}C$ is found to be $412 \ m/s$. The gas is:

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