The table below contains information about samples of four different gases at 273 K. The samples are — States of Matter Chemistry Question

STEPS:

1. Identify constant variables across containers: The problem states that four identical rigid containers (which means they have the same volume, $V$) are maintained at a constant temperature of $273\text{ K}$.
2. Apply the Ideal Gas Law relationship: The ideal gas law is expressed as $PV = nRT$. When volume ($V$) and temperature ($T$) are held constant, pressure ($P$) is directly proportional to the number of moles of gas ($n$):
$$P \propto n$$
This means that containers with equal pressures must contain the same number of moles of gas.
3. Use Container 4 as a stoichiometric reference: Container 4 contains sulfur dioxide ($\text{SO}_2$) at a pressure of $1.96\text{ atm}$ with a sample mass of $64.1\text{ g}$.
* The molar mass of $\text{SO}_2$ is calculated as:
$$M_{\text{SO}_2} \approx 32.1\text{ g/mol (S)} + 2 \times 16.0\text{ g/mol (O)} = 64.1\text{ g/mol}$$
* Solve for the moles of gas in Container 4:
$$n = \frac{\text{mass}}{\text{molar mass}} = \frac{64.1\text{ g}}{64.1\text{ g/mol}} = \mathbf{1.0\text{ mol}}$$
4. Relate Container 3 to the reference: The pressure in Container 3 is $2.00\text{ atm}$, which is extremely close to the pressure of Container 4 ($1.96\text{ atm}$). Since the pressures are virtually identical, the two containers must hold approximately the same number of moles of gas:
$$n_{\text{Container 3}} \approx \mathbf{1.0\text{ mol}}$$
5. Determine the molar mass of the unknown gas in Container 3: The problem lists the mass of the sample in Container 3 as $16.0\text{ g}$. Using the number of moles estimated in Step 4:
$$\text{Molar Mass} = \frac{\text{mass}}{\text{moles}} \approx \frac{16.0\text{ g}}{1.0\text{ mol}} = \mathbf{16.0\text{ g/mol}}$$
6. Identify the gas matching this molar mass: Compare the calculated molar mass of $16.0\text{ g/mol}$ to the options:
* Methane ($\text{CH}_4$) has a molar mass of $12.0\text{ g/mol (C)} + 4 \times 1.0\text{ g/mol (H)} = \mathbf{16.0\text{ g/mol}}$.
This confirms that the gas in Container 3 could be $\text{CH}_4$, making Option A the correct answer.

*

WHY_OTHERS_WRONG:

• B is incorrect: Oxygen gas ($\text{O}_2$) has a molar mass of $32.0\text{ g/mol}$. If Container 3 held $\text{O}_2$, $1.0\text{ mol}$ of the gas would weigh $32.0\text{ g}$, which is double the reported mass of $16.0\text{ g}$.
• C is incorrect: Argon ($\text{Ar}$) has a molar mass of approximately $40.0\text{ g/mol}$. If Container 3 held $\text{Ar}$, $1.0\text{ mol}$ of the gas would weigh $40.0\text{ g}$, which is much higher than the reported mass of $16.0\text{ g}$.
• D is incorrect: Carbon dioxide ($\text{CO}_2$) has a molar mass of $44.0\text{ g/mol}$. If Container 3 held $\text{CO}_2$, $1.0\text{ mol}$ of the gas would weigh $44.0\text{ g}$, which does not align with the analytical data of $16.0\text{ g}$.