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(A) The average speed $(V_{avg})$ of a gas is given by the formula: $V_{avg} = \sqrt{\frac{8RT}{\pi M}}$.Since $R$,$T$,and $\pi$ are constant at a giv

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$2 \sqrt{2}$

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(A) The average speed $(V_{avg})$ of a gas is given by the formula: $V_{avg} = \sqrt{\frac{8RT}{\pi M}}$.Since $R$,$T$,and $\pi$ are constant at a given temperature,the average speed is inversely proportional to the square root of the molar mass $(M)$: $V_{avg} \propto \frac{1}{\sqrt{M}}$.For helium $(He)$ and oxygen $(O_2)$: $M_{He} = 4 \ g/mol$ and $M_{O_2} = 32 \ g/mol$.The ratio of their average speeds is: $\frac{V_{He}}{V_{O_2}} = \sqrt{\frac{M_{O_2}}{M_{He}}} = \sqrt{\frac{32}{4}} = \sqrt{8} = 2 \sqrt{2}$.Thus,the average speed of helium is higher than that of oxygen by a factor of $2 \sqrt{2}$.

At room temperature,the average speed of helium is higher than that of oxygen by a factor of

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