Assertion: On compressing a gas to half the volume, the number of molecules is halved.
Reason: The number of moles present decreases with decrease in volume keeping the pressure and temperature constant.

Options

A. If both (`A`) and (`R`) are correct and (`R`) is the correct explanation of (`A`).
B. If both (`A`) and (`R`) are correct, but (`R`) is not the correct explanation of (`A`).
C. If (`A`) is correct, but (`R`) is incorrect.
D. If (`A`) is incorrect, but (`R`) is correct.

Explanation

To solve the question, let's break it down into the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states: "On compressing a gas to half the volume, the number of molecules is halved."

- When a gas is compressed to half its volume in a closed container, the number of gas molecules does not change. The gas molecules are simply occupying a smaller space. Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
The reason states: "The number of moles present decreases with decrease in volume keeping the pressure and temperature constant."

- According to the ideal gas law (PV = nRT), if the pressure (P) and temperature (T) are kept constant, then the volume (V) is directly proportional to the number of moles (n). This means that if the volume decreases, the number of moles must also decrease to maintain the equation. However, in a closed system, the number of moles does not decrease just because the volume decreases; the gas is simply compressed. Therefore, the reason is also **false**.

### Conclusion
- The assertion is **false** because compressing a gas does not change the number of molecules.
- The reason is **false** because the number of moles does not decrease when the volume decreases in a closed system.

### Final Answer
Both the assertion and the reason are false.

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