A closed vessel contains equal number of nitrogen and oxygen molecules at pressure of `P mm`. If nitrogen is removed from the system, then the pressure will be:

Options

A. P
B. 2P
C. `(P)/(2)`
D. `P^(2)`

Answer

To solve the problem, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- We have a closed vessel containing equal numbers of nitrogen (N₂) and oxygen (O₂) molecules.
- The total pressure in the vessel is given as P mm.

2. **Applying Dalton's Law of Partial Pressures**:
- According to Dalton's Law, the total pressure (P) in a mixture of gases is the sum of the partial pressures of each gas.
- Therefore, we can express the total pressure as:
\[ P = P_{N_2} + P_{O_2} \]

3. **Determining the Partial Pressures**:
- Since there are equal numbers of nitrogen and oxygen molecules, the partial pressures will also be equal.
- Let \( P_{N_2} = P_{O_2} \).
- Thus, we can write:
\[ P_{N_2} = P_{O_2} = \frac{P}{2} \]

4. **Removing Nitrogen from the System**:
- If nitrogen is removed from the system, only oxygen remains in the vessel.
- The pressure of the remaining gas (oxygen) will now be equal to its partial pressure, which we calculated as:
\[ P_{O_2} = \frac{P}{2} \]

5. **Final Pressure Calculation**:
- Since only oxygen is present after the removal of nitrogen, the final pressure in the vessel will be:
\[ P_{final} = P_{O_2} = \frac{P}{2} \]

### Conclusion:
The final pressure in the vessel after removing nitrogen will be \( \frac{P}{2} \).