**Correct Option: B. It halves** ### 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 unchanged. **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 of the gas 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 the inverse relationship defined by Boyle's Law. If pressure doubles, volume cannot double; it must decrease. - **Option C: It quadruples.** - This option implies a much larger increase in volume, which again contradicts the inverse relationship. If pressure increases, volume cannot increase at all, let alone quadruple. - **Option D: It remains the same.** - This option suggests that volume does not change with an increase in pressure, which is incorrect. According to Boyle's Law, volume must change inversely with pressure. ### Common Pitfalls: - **Misunderstanding Inverse Relationships:** Students often confuse direct and inverse relationships. Remember, if one quantity increases, the other must decrease in an inverse relationship. - **Ignoring Temperature:** Boyle's Law only applies when temperature is constant. If temperature changes, the relationship described by Boyle's Law does not hold. - **Forgetting to Use the Correct Units:** Always ensure that pressure and volume are in compatible units when applying Boyle's Law. ### Revision Summary: - Boyle's Law states that pressure and volume of a gas are inversely related at constant temperature. - Doubling the pressure of a gas results in halving its volume. - The correct answer to the question is that the volume of the gas halves when the pressure is doubled. - Remember to always check the conditions (like temperature) when applying gas laws.