Under the conditions given, consider containers 1, 2, and 4 only. The average speed of the gas parti — States of Matter Chemistry Question

STEPS:

1. Identify the constant variable: The problem states that all four containers are maintained at a constant temperature of $273\text{ K}$.
2. Understand the relationship between temperature and kinetic energy: According to the Kinetic Molecular Theory, the average kinetic energy ($KE_{\text{avg}}$) of gas particles depends solely on the absolute temperature ($T$). Because all containers are at the same temperature of $273\text{ K}$, the average kinetic energy of the gas particles in containers 1, 2, and 4 is identical.
3. Analyze the relationship between speed, mass, and kinetic energy: The formula for kinetic energy is:
$$KE_{\text{avg}} = \frac{1}{2}mv^2$$
where $m$ is the mass of a gas particle and $v$ is its speed. This can also be represented as root-mean-square speed:
$$v_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$
where $M$ is the molar mass. At a constant temperature, average speed is inversely proportional to the square root of the molar mass of the gas particles ($v \propto \sqrt{\frac{1}{M}}$). Therefore, the lighter the gas particles, the faster they must move on average to have the same average kinetic energy.
4. Determine the molar mass of each gas: Find the molar masses for the gases in containers 1, 2, and 4:
* Container 1: Helium ($\text{He}$) has a molar mass of approximately $4.00\text{ g/mol}$.
* Container 2: Neon ($\text{Ne}$) has a molar mass of approximately $20.18\text{ g/mol}$.
* Container 4: Sulfur dioxide ($\text{SO}_2$) has a molar mass of approximately $64.1\text{ g/mol}$.
5. Compare speeds and select the correct option: Since helium ($\text{He}$) has the lowest molar mass ($4.00\text{ g/mol}$), its particles must have the greatest average speed to maintain the same average kinetic energy as the heavier neon and sulfur dioxide molecules. This confirms that the average speed is greatest in container 1, making Option A the correct answer.

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WHY_OTHERS_WRONG:

• B is incorrect: Neon ($\text{Ne}$) has a molar mass of $20.18\text{ g/mol}$. Because its particles are heavier than those of helium ($4.00\text{ g/mol}$), they move at a slower average speed than helium at the same temperature.
• C is incorrect: Sulfur dioxide ($\text{SO}_2$) has the highest molar mass ($64.1\text{ g/mol}$) among the three gases. Because its molecules are the heaviest, they move at the slowest average speed among the three gases at $273\text{ K}$.
• D is incorrect: The average speed of the gas particles is not the same because the gases have different molar masses. Only their average kinetic energy is the same, which requires the lighter particles ($\text{He}$) to travel at a higher average velocity than the heavier particles ($\text{Ne}$ and $\text{SO}_2$).