Which of the pairs of gases diffuse at a slower rate than `CO_(2)`?

Options

A. `H_(2)` and He
B. `SO_(2)` and `SO_(3)`
C. `N_(2)` and CO
D. `N_(2)O` and `C_(3)H_(8)`

Answer

To determine which pairs of gases diffuse at a slower rate than carbon dioxide (CO₂), we can use Graham's law of diffusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, gases with a higher molar mass will diffuse more slowly than those with a lower molar mass.

### Step-by-Step Solution:

1. **Identify the Molar Mass of CO₂**:
- The molar mass of carbon dioxide (CO₂) can be calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- CO₂ = 12 + (2 × 16) = 12 + 32 = 44 g/mol

2. **Determine the Molar Mass of Other Gases**:
- For each pair of gases, calculate their molar masses and compare them to 44 g/mol.

3. **Evaluate Each Pair**:
- **Pair 1: Hydrogen (H₂) and Helium (He)**:
- H₂ = 1 × 2 = 2 g/mol
- He = 4 g/mol
- Both are less than 44 g/mol, so they diffuse faster than CO₂.

- **Pair 2: Sulfur Dioxide (SO₂) and Sulfur Trioxide (SO₃)**:
- SO₂ = 32 (S) + 2 × 16 (O) = 32 + 32 = 64 g/mol
- SO₃ = 32 (S) + 3 × 16 (O) = 32 + 48 = 80 g/mol
- Both are greater than 44 g/mol, so they diffuse slower than CO₂.

- **Pair 3: Nitrogen (N₂) and Carbon Monoxide (CO)**:
- N₂ = 14 × 2 = 28 g/mol
- CO = 12 (C) + 16 (O) = 28 g/mol
- Both are less than 44 g/mol, so they diffuse faster than CO₂.

- **Pair 4: Nitrous Oxide (N₂O) and Propane (C₃H₈)**:
- N₂O = 14 × 2 + 16 = 28 + 16 = 44 g/mol
- C₃H₈ = 3 × 12 + 8 = 36 + 8 = 44 g/mol
- Both have a molar mass equal to 44 g/mol, so they diffuse at the same rate as CO₂.

4. **Conclusion**:
- The only pair of gases that diffuse at a slower rate than carbon dioxide is **Sulfur Dioxide (SO₂) and Sulfur Trioxide (SO₃)**.

### Final Answer:
The pair of gases that diffuse at a slower rate than CO₂ is **Sulfur Dioxide (SO₂) and Sulfur Trioxide (SO₃)**.