Which of the following pairs will diffuse at the same rate through a porous plug ?

Options

A. `CO, NO_2`
B. `NO_2, CO_2`
C. `NH_3, PH_3`
D. `NO, C_2 H_6`

Explanation

To determine which pair of gases will diffuse at the same rate through a porous plug, we can use Graham's law of effusion and diffusion. According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, if two gases have the same molar mass, they will diffuse at the same rate.

### Step-by-Step Solution:

1. **Understand Graham's Law**:
- The rate of diffusion (R) of a gas is inversely proportional to the square root of its molar mass (M).
- Mathematically, this can be expressed as:
\[ R \propto \frac{1}{\sqrt{M}} \]
- If two gases have the same molar mass, their rates of diffusion will be equal.

2. **List the Given Gases**:
- The options provided are:
1. CO and NO2
2. NO2 and CO2
3. NH3 and PH3
4. NO and C2H6

3. **Calculate the Molar Mass of Each Gas**:
- **CO (Carbon Monoxide)**:
\[ 12 \, (C) + 16 \, (O) = 28 \, g/mol \]
- **NO2 (Nitrogen Dioxide)**:
\[ 14 \, (N) + 32 \, (O_2) = 46 \, g/mol \]
- **CO2 (Carbon Dioxide)**:
\[ 12 \, (C) + 32 \, (O_2) = 44 \, g/mol \]
- **NH3 (Ammonia)**:
\[ 14 \, (N) + 3 \times 1 \, (H) = 17 \, g/mol \]
- **PH3 (Phosphine)**:
\[ 31 \, (P) + 3 \times 1 \, (H) = 34 \, g/mol \]
- **NO (Nitric Oxide)**:
\[ 14 \, (N) + 16 \, (O) = 30 \, g/mol \]
- **C2H6 (Ethane)**:
\[ 2 \times 12 \, (C) + 6 \times 1 \, (H) = 30 \, g/mol \]

4. **Compare the Molar Masses**:
- Now we compare the molar masses of the gases in each option:
- **Option 1**: CO (28 g/mol) and NO2 (46 g/mol) - Different
- **Option 2**: NO2 (46 g/mol) and CO2 (44 g/mol) - Different
- **Option 3**: NH3 (17 g/mol) and PH3 (34 g/mol) - Different
- **Option 4**: NO (30 g/mol) and C2H6 (30 g/mol) - Same

5. **Conclusion**:
- The pair of gases that will diffuse at the same rate through a porous plug is **NO and C2H6** since they have the same molar mass of 30 g/mol.

### Final Answer:
The pair that will diffuse at the same rate through a porous plug is **NO and C2H6**.