In a gaseous mixture which of `NO_2, CO_2` and `N_2O` gases have same rate of diffusion

Options

A. `NO_2, CO_2`
B. `CO_2, N_2O`
C. `NO_2, N_2O`
D. All

Answer

To determine which gases among NO₂, CO₂, and N₂O have the same rate of diffusion, we can use Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, gases with the same molar mass will have the same rate of diffusion.

### Step-by-Step Solution:

1. **Calculate the Molar Mass of NO₂**:
- The molar mass of nitrogen (N) = 14 g/mol
- The molar mass of oxygen (O) = 16 g/mol
- Molar mass of NO₂ = 14 + (2 × 16) = 14 + 32 = 46 g/mol

2. **Calculate the Molar Mass of CO₂**:
- The molar mass of carbon (C) = 12 g/mol
- The molar mass of oxygen (O) = 16 g/mol
- Molar mass of CO₂ = 12 + (2 × 16) = 12 + 32 = 44 g/mol

3. **Calculate the Molar Mass of N₂O**:
- The molar mass of nitrogen (N) = 14 g/mol
- The molar mass of oxygen (O) = 16 g/mol
- Molar mass of N₂O = (2 × 14) + 16 = 28 + 16 = 44 g/mol

4. **Compare the Molar Masses**:
- Molar mass of NO₂ = 46 g/mol
- Molar mass of CO₂ = 44 g/mol
- Molar mass of N₂O = 44 g/mol

5. **Identify Gases with the Same Molar Mass**:
- CO₂ and N₂O both have a molar mass of 44 g/mol.

6. **Conclusion**:
- Since CO₂ and N₂O have the same molar mass, they will have the same rate of diffusion. NO₂, with a different molar mass, will have a different rate of diffusion.

### Final Answer:
CO₂ and N₂O have the same rate of diffusion.