**Correct Option: B. The volume 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. **Doubling the Pressure:** If the pressure is doubled, we have: \[ P_2 = 2P_1 \] 3. **Finding the New Volume:** We need to find the new volume \( V_2 \) when the pressure is doubled. Using Boyle's Law again: \[ P_2 \times V_2 = k \] Substituting \( P_2 \) into the equation gives: \[ (2P_1) \times V_2 = k \] 4. **Setting the Equations Equal:** Since \( k \) is constant, we can set the two equations equal to each other: \[ P_1 \times V_1 = (2P_1) \times V_2 \] 5. **Solving for \( V_2 \):** Dividing both sides by \( P_1 \) (assuming \( P_1 \neq 0 \)): \[ V_1 = 2 \times V_2 \] Rearranging gives: \[ V_2 = \frac{V_1}{2} \] This shows that when the pressure is doubled, the volume is halved, confirming that the correct answer is **B. The volume is halved.** ### Why Other Options Are Incorrect: - **Option A: The volume doubles.** - This option suggests that if pressure increases, volume also increases, which contradicts Boyle's Law. According to the law, pressure and volume have an inverse relationship. - **Option C: The volume remains the same.** - This option implies that changes in pressure do not affect volume, which is incorrect. Boyle's Law clearly states that volume changes in response to pressure changes when temperature is constant. - **Option D: The volume quadruples.** - This option also contradicts Boyle's Law. If the pressure increases, the volume cannot increase; it must decrease. A quadrupling of volume would imply a significant decrease in pressure, which is not the case here. ### Common Pitfalls: - **Confusing Direct and Inverse Relationships:** Students often confuse direct relationships (where both variables increase or decrease together) with inverse relationships (where one variable increases while the other decreases). - **Ignoring Temperature:** Boyle's Law only applies when temperature is constant. If temperature changes, the relationship between pressure and volume is not simply described by 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 formula \( P_1 \times V_1 = P_2 \times V_2 \) is key to solving problems related to Boyle's Law. - Always remember that temperature must remain constant for Boyle's Law to apply.