A closed vessel contains equal number of oxygen and hydrogen molecules at a total pressure of 740 mm. If oxygen is removed from the system, the pressure: 1)becomes half of 740 mm 2)becomes `1/3` rd of 740 mm 3)becomes double of 740 mm 4)remains unchanged.

Options

A. becomes half of 740 mm
B. becomes `1/3` rd of 740 mm
C. becomes double of 740 mm
D. remains unchanged.

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Initial Conditions
We have a closed vessel containing equal numbers of oxygen (O₂) and hydrogen (H₂) molecules. The total pressure in the vessel is given as 740 mm.

### 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:
\[ P_{total} = P_{H_2} + P_{O_2} \]

### Step 3: Determine the Partial Pressures
Since there are equal numbers of hydrogen and oxygen molecules, we can denote the partial pressures of hydrogen and oxygen as:
- \( P_{H_2} = P \)
- \( P_{O_2} = P \)

Thus, the total pressure can be expressed as:
\[ P_{total} = P + P = 2P \]

### Step 4: Relate Total Pressure to Partial Pressures
From the total pressure of 740 mm, we can set up the equation:
\[ 2P = 740 \text{ mm} \]
From this, we can find the partial pressure of each gas:
\[ P = \frac{740}{2} = 370 \text{ mm} \]

### Step 5: Analyze the Effect of Removing Oxygen
If we remove all the oxygen from the system, the only gas remaining will be hydrogen. The pressure in the vessel will now only be the partial pressure of hydrogen:
\[ P_{new} = P_{H_2} = 370 \text{ mm} \]

### Step 6: Conclusion
Since the total pressure after removing oxygen is 370 mm, which is half of the original total pressure (740 mm), we conclude that the pressure becomes half of 740 mm.

### Final Answer
The pressure becomes half of 740 mm.