Kinetic Molecular Theory Question 1

A $\pu{0.5 mol}$ sample of $\ce{He(g)}$ and a $\pu{0.5 mol}$ sample of $\ce{Ne(g)}$ are placed separately in two $\pu{5.0 L}$ rigid containers at $\pu{20} ^\circ \text{C}$ . Each container has a pinhole opening. Which of these gases, $\ce{He(g)}$ or $\ce{Ne(g)}$ , will escape faster through the pinhole and why?

\ce{He(g)}

will escape faster because the

\ce{He(g)}

atoms are moving at a higher average speed than the

\ce{Ne(g)}

atoms.

\ce{Ne(g)}

will escape faster because its initial pressure in the container is higher.

\ce{Ne(g)}

will escape faster because the

\ce{Ne(g)}

atoms have a higher average kinetic energy than the

\ce{He(g)}

atoms.

Both gases will escape at the same rate because the atoms of both gases have the same average kinetic energy.

Approach

At $\pu{20} ^\circ \text{C}$ , the two gases have the same kinetic energy. Using the following equation:

KE=\frac{1}{2}mv^2

v= \sqrt{\frac{2KE}{m}}

Note that a larger mass results in a lower velocity. The molecular mass of Neon gas is significantly larger than that of Helium gas. Therefore, Helium gas has a greater average velocity and will escape faster.