A 1.0 mol sample of He(g) at 25°C is mixed with a 1.0 mol sample of Xe(g) at 50°C. Which of the foll — Thermodynamics Chemistry Question

STEPS:

1. Relate temperature to the initial average kinetic energy of the gases:
According to kinetic molecular theory, the average kinetic energy of a gas sample is directly proportional to its absolute temperature ($KE_{\text{avg}} \propto T$). Because the $1.0\text{ mol}$ sample of $\text{Xe}(g)$ is initially at a higher temperature ($50^\circ\text{C}$) than the $1.0\text{ mol}$ sample of $\text{He}(g)$ ($25^\circ\text{C}$), the xenon atoms initially possess a greater average kinetic energy than the helium atoms.

2. Understand the thermal equilibration process:
When the two gas samples are mixed, their particles collide with one another. Through these elastic collisions, kinetic energy is net-transferred from the hotter, higher-energy gas particles ($\text{Xe}$) to the colder, lower-energy gas particles ($\text{He}$). This transfer continues until the mixture approaches thermal equilibrium, where both gases reach a shared final temperature (between $25^\circ\text{C}$ and $50^\circ\text{C}$) and therefore have the same final average kinetic energy.

3. Determine the change in average kinetic energy for the xenon ($\text{Xe}$) atoms:
Because the xenon atoms started at the higher temperature and lost kinetic energy to the helium atoms during mixing, the average kinetic energy of the $\text{Xe}$ atoms must decrease.

4. Determine the change in average speed for the xenon ($\text{Xe}$) atoms:
The relationship between molecular kinetic energy, mass ($m$), and speed ($v$) is defined by the formula:
$$KE = \frac{1}{2}mv^2$$
Because the mass ($m$) of a xenon atom is constant, if the average kinetic energy ($KE$) of the xenon atoms decreases, their average molecular speed ($v$) must also decrease.

5. Identify the correct choice:
Since both the average kinetic energy and the average molecular speed of the xenon atoms decrease, the correct prediction is represented by Option D.

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WHY_OTH_ERS_WRONG:

• Option A is incorrect: It claims that both the average kinetic energy and average speed of $\text{Xe}$ atoms will increase. This is impossible because $\text{Xe}$ starts at a higher temperature and must transfer energy to the cooler $\text{He}$ atoms, leading to a decrease in its own kinetic energy and speed.
• Option B is incorrect: It incorrectly predicts that the average kinetic energy of the $\text{Xe}$ atoms will increase. As the hotter gas in the mixture, $\text{Xe}$ loses energy to $\text{He}$ to reach thermal equilibrium, causing its average kinetic energy to decrease, not increase.
• Option C is incorrect: It claims that the average speed of the $\text{Xe}$ atoms will increase while their average kinetic energy decreases. Because kinetic energy is directly proportional to the square of the speed ($KE = \frac{1}{2}mv^2$), a decrease in the average kinetic energy of particles with constant mass mathematically requires a corresponding decrease in their average speed.