A 0.5 mol sample of He(g) and a 0.5 mol sample of Ne(g) are placed separately in two 10.0 L rigid co — States of Matter Chemistry Question

STEPS:

1. Identify the physical phenomenon: The movement of gas molecules escaping from a container through a tiny opening (pinhole) into a region of lower pressure is known as effusion.
2. Understand what determines the rate of effusion: The rate at which a gas effuses is directly determined by the average speed (specifically, the root-mean-square speed) of its individual gas particles. Faster-moving particles are statistically more likely to collide with the small pinhole opening and escape the container.
3. Analyze the relationship between temperature and average kinetic energy: According to the Kinetic Molecular Theory, the average kinetic energy of gas particles is directly proportional to the absolute temperature (in Kelvin). Because both containers are held at the exact same temperature ($25^\circ\text{C}$), the helium atoms and the neon atoms must have the exact same average kinetic energy.
4. Relate average kinetic energy to mass and molecular speed: Average kinetic energy is mathematically defined by the mass ($m$) and speed ($v$) of the particles:
$$KE = \frac{1}{2}mv^2$$
Since the average kinetic energies are equal, we can set their terms equal to each other:
$$\frac{1}{2}m_{\text{He}}v_{\text{He}}^2 = \frac{1}{2}m_{\text{Ne}}v_{\text{Ne}}^2$$
This demonstrates that average speed is inversely proportional to the square root of the particle's mass. Therefore, lighter particles must move at a higher average speed to maintain the same average kinetic energy as heavier particles.
5. Compare the molar masses of the two gases:
* Helium ($\text{He}$): Has a molar mass of approximately $4.00\text{ g/mol}$.
* Neon ($\text{Ne}$): Has a molar mass of approximately $20.18\text{ g/mol}$.
6. Determine which gas escapes faster: Because helium has a significantly lower molar mass than neon, helium atoms move with a higher average speed than neon atoms at $25^\circ\text{C}$. This means helium atoms will hit the pinhole much more frequently, allowing $\text{He}(g)$ to escape faster through the pinhole, which matches Option A.

*

WHY_OTHERS_WRONG:

• Option B is incorrect: According to the Ideal Gas Law, pressure is calculated as $P = \frac{nRT}{V}$. Because both gas samples contain the exact same number of moles ($0.5\text{ mol}$), are in the exact same volume ($10.0\text{ L}$), and are at the exact same temperature ($25^\circ\text{C}$), their initial pressures are completely identical. Neon's pressure is not higher.
• Option C is incorrect: Because temperature is a direct measure of average kinetic energy and both systems are at the same temperature, the helium and neon atoms have the same average kinetic energy.
• Option D is incorrect: While this option correctly notes that both gases have the same average kinetic energy, it makes a conceptual error by claiming they will escape at the same rate. Since neon atoms are heavier, they move slower than helium atoms and therefore will not escape at the same rate.