Equal molecules of `N_2` and `O_2` are kept in a closed container at pressure P. If `N_2` is removed from the system, then the pressure of the container will be

Options

A. P
B. P//2
C. `P/4`
D. 2P

Answer

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the Initial Conditions
We have equal molecules of nitrogen gas (N₂) and oxygen gas (O₂) in a closed container at a pressure P. Since the number of molecules of both gases is equal, they contribute equally to the total pressure.

**Hint:** Remember that the total pressure in a gas mixture is the sum of the partial pressures of the individual gases.

### Step 2: Apply Dalton's Law of Partial Pressures
According to Dalton's Law of Partial Pressures, the total pressure (P_total) in a mixture of gases is equal to the sum of the partial pressures of each gas. In our case, since we have equal moles of N₂ and O₂, we can express the total pressure as:
\[ P_{total} = P_{N2} + P_{O2} \]

Given that the contributions to the pressure are equal:
\[ P_{N2} = P_{O2} = \frac{P}{2} \]

**Hint:** Think about how the partial pressures relate to the total pressure when the gases are present in equal amounts.

### Step 3: Remove N₂ from the System
When we remove N₂ from the system, only O₂ remains in the container. Therefore, the total pressure in the container will now be equal to the partial pressure of O₂ alone.

Since we previously established that the partial pressure of O₂ was \(\frac{P}{2}\), after removing N₂, the total pressure in the container becomes:
\[ P_{total} = P_{O2} = \frac{P}{2} \]

**Hint:** Consider what happens to the pressure when one of the gases is removed from the mixture.

### Step 4: Conclusion
Thus, the pressure of the container after removing N₂ will be \(\frac{P}{2}\).

**Final Answer:** The pressure of the container will be \(\frac{P}{2}\).