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Among the following, identify the gas which has the greatest average speed of its molecules?
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The correct answer is:
$1.0 \mathrm{~mol}$ of $\mathrm{He}$ at $200 \mathrm{~K}$
The average molecular speed is inversely proportional to the square root of molar mass.
$v=\sqrt{\frac{8 R T}{\pi M}}$ i.e. $v \propto \frac{1}{\sqrt{M}}$
Among $\mathrm{O}_2, \mathrm{CO}_2$, He and $\mathrm{NH}_3$, He has very low molar mass. Therefore, it has greatest average velocity.
Order of molar mass $(\mathrm{g} / \mathrm{mol})$ is
$$
\begin{array}{ccc}
\mathrm{CO}_2> & \mathrm{O}_2 < \mathrm{NH}_3>\mathrm{He} \\
44.01 & 32.0 & 17.03
\end{array}
$$
Order of average velocity is $\mathrm{He}>\mathrm{NH}_3>\mathrm{O}_2>\mathrm{CO}_2$. Hence, helium has the greatest average speed of its molecules.
$v=\sqrt{\frac{8 R T}{\pi M}}$ i.e. $v \propto \frac{1}{\sqrt{M}}$
Among $\mathrm{O}_2, \mathrm{CO}_2$, He and $\mathrm{NH}_3$, He has very low molar mass. Therefore, it has greatest average velocity.
Order of molar mass $(\mathrm{g} / \mathrm{mol})$ is
$$
\begin{array}{ccc}
\mathrm{CO}_2> & \mathrm{O}_2 < \mathrm{NH}_3>\mathrm{He} \\
44.01 & 32.0 & 17.03
\end{array}
$$
Order of average velocity is $\mathrm{He}>\mathrm{NH}_3>\mathrm{O}_2>\mathrm{CO}_2$. Hence, helium has the greatest average speed of its molecules.
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