To solve the problem, we will follow these steps:
### Step 1: Understand the relationship between mass, volume, and molar mass
According to Avogadro's law, at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules. Therefore, we can relate the mass of gas X to the mass of CO₂ using their respective volumes.
### Step 2: Calculate the mass of CO₂ that occupies 0.44 L
Given that 0.1 g of CO₂ occupies 0.32 L, we can find out how much mass of CO₂ would occupy 0.44 L.
Using the proportion:
\[
\text{Mass of CO₂ for 0.44 L} = \left(\frac{0.1 \, \text{g}}{0.32 \, \text{L}}\right) \times 0.44 \, \text{L}
\]
Calculating this gives:
\[
\text{Mass of CO₂ for 0.44 L} = \frac{0.1 \times 0.44}{0.32} = 0.1375 \, \text{g}
\]
### Step 3: Relate the mass of gas X to the mass of CO₂
Since gas X occupies the same volume (0.44 L) under the same conditions, we can set up the equation:
\[
\text{Moles of gas X} = \text{Moles of CO₂}
\]
The number of moles can be calculated using the formula:
\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}
\]
### Step 4: Set up the equation for gas X
Let the molar mass of gas X be \( M \). The number of moles of gas X can be expressed as:
\[
\frac{0.2 \, \text{g}}{M}
\]
And for CO₂:
\[
\frac{0.1 \, \text{g}}{44 \, \text{g/mol}} \text{ (since molar mass of CO₂ is 44 g/mol)}
\]
### Step 5: Equate the moles of gas X and CO₂
Setting the two expressions for moles equal gives:
\[
\frac{0.2}{M} = \frac{0.1}{44}
\]
### Step 6: Solve for M
Cross-multiplying gives:
\[
0.2 \times 44 = 0.1 \times M
\]
\[
8.8 = 0.1M
\]
\[
M = \frac{8.8}{0.1} = 88 \, \text{g/mol}
\]
### Step 7: Identify gas X
Now we need to identify a gas with a molar mass of 88 g/mol. The common gas that fits this molar mass is sulfur dioxide (SO₂), which has a molar mass of 64 g/mol. However, based on the calculations, it appears that the molar mass of gas X is 88 g/mol.
### Conclusion
Gas X can be identified as a gas with a molar mass of 88 g/mol, which is likely to be a heavier gas such as ozone (O₃) or another compound.
