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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$(s)$.

Similar Questions

Assertion $(A):$ The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and volume.
Reason $(R):$ The molecules of gas collide with each other and the velocities of the molecules change due to the collision.

Which of the following statements about the kinetic theory of gases is wrong?

$A$ very tall vertical cylinder is filled with a gas of molar mass $M$ under isothermal conditions at temperature $T$. The density and pressure of the gas at the base of the container are $\rho_0$ and $p_0$,respectively. Choose the correct statement$(s)$.

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Select the correct statement.

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