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(B) The formula for $RMS$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given: $T = 27 + 273 = 300 \, K$,$M = 32 \, g/mol = 32 	imes 10^{-3} \, kg/mol$,$

Vedclass · Accepted Answer

$RMS$ speed of $8 \, g$ oxygen gas in a container at $27 \, ^\circ C$ is approximately $968 \, m/s$.

Vedclass · Answer

(B) The formula for $RMS$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given: $T = 27 + 273 = 300 \, K$,$M = 32 \, g/mol = 32 	imes 10^{-3} \, kg/mol$,$R = 8.314 \, J/(mol \cdot K)$.$v_{rms} = \sqrt{\frac{3 	imes 8.314 	imes 300}{32 	imes 10^{-3}}} = \sqrt{\frac{7482.6}{0.032}} \approx \sqrt{233831} \approx 483.55 \, m/s \approx 484 \, m/s$.Thus,statement $A$ is correct.Since statement $A$ is correct,statement $B$ $(968 \, m/s)$ is incorrect.For any gas,$v_{rms} = \sqrt{\frac{3RT}{M}}$,$v_{avg} = \sqrt{\frac{8RT}{\pi M}}$,and $v_{mp} = \sqrt{\frac{2RT}{M}}$.Comparing the coefficients: $\sqrt{3} \approx 1.732$,$\sqrt{8/\pi} \approx 1.596$,$\sqrt{2} \approx 1.414$.Since $1.732 > 1.596$,$v_{rms} > v_{avg}$ is correct.Real gases approach ideal behavior at low pressure and high temperature,so statement $D$ is correct.Therefore,the incorrect statement is $B$.

Select the $incorrect$ statement$(s)$.

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