Which one of the following set of gases will same rate under similar conditions? `

Options

A. `NO,CO,O_2`
B. `NO_2,CO_2, SO_2`
C. `CH_4,O_2, NO`
D. `N_2O, CO_2, C_2H_4`

Explanation

To determine which set of gases will have the same rate of diffusion under similar conditions, we can use Graham's law of diffusion. According to this law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, for two gases to have the same rate of diffusion, they must have the same molar mass.

### Step-by-Step Solution:

1. **Understand Graham's Law of Diffusion**:
- The law states that the rate of diffusion (r) is inversely proportional to the square root of the molar mass (M) of the gas.
- Mathematically, it can be expressed as:
\[ r \propto \frac{1}{\sqrt{M}} \]
- This implies that for two gases to diffuse at the same rate, their molar masses must be equal.

2. **Calculate Molar Masses of Given Gases**:
- For each gas in the options provided, we need to calculate the molar mass.

3. **Example Calculations**:
- **NO (Nitric Oxide)**:
- Nitrogen (N) = 14 g/mol, Oxygen (O) = 16 g/mol
- Molar mass of NO = 14 + 16 = 30 g/mol
- **CO (Carbon Monoxide)**:
- Carbon (C) = 12 g/mol, Oxygen (O) = 16 g/mol
- Molar mass of CO = 12 + 16 = 28 g/mol
- **O2 (Oxygen)**:
- Molar mass of O2 = 16 * 2 = 32 g/mol
- **NO2 (Nitrogen Dioxide)**:
- Molar mass of NO2 = 14 + (16 * 2) = 14 + 32 = 46 g/mol
- **CO2 (Carbon Dioxide)**:
- Molar mass of CO2 = 12 + (16 * 2) = 12 + 32 = 44 g/mol
- **SO2 (Sulfur Dioxide)**:
- Molar mass of SO2 = 32 + (16 * 2) = 32 + 32 = 64 g/mol
- **CH4 (Methane)**:
- Molar mass of CH4 = 12 + (1 * 4) = 12 + 4 = 16 g/mol
- **N2O (Nitrous Oxide)**:
- Molar mass of N2O = (14 * 2) + 16 = 28 + 16 = 44 g/mol
- **C2H4 (Ethylene)**:
- Molar mass of C2H4 = (12 * 2) + (1 * 4) = 24 + 4 = 28 g/mol
- **C3H8 (Propane)**:
- Molar mass of C3H8 = (12 * 3) + (1 * 8) = 36 + 8 = 44 g/mol

4. **Compare Molar Masses**:
- After calculating the molar masses, we compare them to find a set of gases with the same molar mass.
- If none of the sets have the same molar mass, then none of the options will have the same rate of diffusion.

5. **Conclusion**:
- Based on the calculations, if no two gases from the options provided have the same molar mass, then the answer is that none of the sets will have the same rate of diffusion.