**Correct Option: B. It is halved.** ### Detailed Explanation: **Understanding Boyle's Law:** Boyle's Law states that for a given mass of an ideal gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). This relationship can be mathematically expressed as: \[ P \times V = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. This means that if the pressure increases, the volume must decrease, and vice versa, as long as the temperature remains constant. **Step-by-Step Analysis:** 1. **Initial Conditions:** Let's assume we have a gas with an initial pressure \( P_1 \) and an initial volume \( V_1 \). According to Boyle's Law, we can write: \[ P_1 \times V_1 = k \] 2. **Changing the Pressure:** Now, if the pressure is doubled, we have: \[ P_2 = 2P_1 \] 3. **Applying Boyle's Law Again:** Since the temperature is constant, we can apply Boyle's Law again with the new pressure and the new volume \( V_2 \): \[ P_2 \times V_2 = k \] Substituting \( P_2 \): \[ 2P_1 \times V_2 = k \] 4. **Setting the Equations Equal:** Since both expressions equal \( k \), we can set them equal to each other: \[ P_1 \times V_1 = 2P_1 \times V_2 \] 5. **Solving for \( V_2 \):** We can divide both sides by \( P_1 \) (assuming \( P_1 \neq 0 \)): \[ V_1 = 2V_2 \] Rearranging gives: \[ V_2 = \frac{V_1}{2} \] This shows that when the pressure is doubled, the volume is halved. ### Why Other Options Are Incorrect: - **Option A: It doubles.** - This option suggests that if pressure increases, volume also increases, which contradicts Boyle's Law. According to Boyle's Law, pressure and volume have an inverse relationship. - **Option C: It remains the same.** - This option implies that changes in pressure do not affect volume, which is incorrect. Boyle's Law clearly states that volume must change in response to changes in pressure when temperature is constant. - **Option D: It increases by four times.** - This option suggests a direct proportionality that does not exist in Boyle's Law. If pressure doubles, volume cannot increase; it must decrease. The idea of increasing by four times is a misunderstanding of the inverse relationship. ### Common Pitfalls: - **Misunderstanding Inverse Relationships:** Students often confuse direct and inverse relationships. Remember, if one variable increases, the other must decrease in an inverse relationship. - **Ignoring Temperature:** Boyle's Law only applies when temperature is constant. Changes in temperature can affect gas behavior differently. - **Assuming Ideal Gas Behavior:** Boyle's Law is derived under the assumption of ideal gas behavior, which may not hold true for real gases under high pressure or low temperature. ### Revision Summary: - Boyle's Law states that pressure and volume of a gas are inversely related at constant temperature. - If pressure is doubled, volume is halved. - The relationship is expressed mathematically as \( P_1 \times V_1 = P_2 \times V_2 \). - Remember to consider the conditions (constant temperature) when applying Boyle's Law.