### Correct Option: A. 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: \[ P \propto \frac{1}{V} \] or, more commonly, in the form of the equation: \[ P_1 V_1 = P_2 V_2 \] where: - \( P_1 \) and \( V_1 \) are the initial pressure and volume of the gas, - \( P_2 \) and \( V_2 \) are the final pressure and volume of the gas. **Scenario Analysis:** In the scenario given, we are told that the pressure of the gas is doubled while keeping the temperature constant. Let's denote the initial pressure as \( P_1 \) and the initial volume as \( V_1 \). If the pressure is doubled, we have: \[ P_2 = 2P_1 \] Now, we can use Boyle's Law to find the new volume \( V_2 \): \[ P_1 V_1 = P_2 V_2 \] Substituting \( P_2 \) into the equation gives: \[ P_1 V_1 = (2P_1) V_2 \] To isolate \( V_2 \), we can divide both sides by \( 2P_1 \): \[ V_2 = \frac{P_1 V_1}{2P_1} \] This simplifies to: \[ V_2 = \frac{V_1}{2} \] This means that the new volume \( V_2 \) is half of the original volume \( V_1 \). Therefore, if the pressure is doubled, the volume is halved. ### Why Other Options Are Incorrect: - **Option B: The volume remains constant.** - This option is incorrect because it contradicts Boyle's Law. If the pressure increases while the temperature remains constant, the volume must change to maintain the relationship defined by Boyle's Law. - **Option C: The volume is doubled.** - This option is also incorrect. Doubling the pressure does not lead to an increase in volume; rather, it leads to a decrease in volume, as established by the inverse relationship in Boyle's Law. - **Option D: The volume quadruples.** - This option is incorrect for the same reason as option C. An increase in pressure results in a decrease in volume, not an increase. The volume cannot quadruple when the pressure is doubled. ### Common Pitfalls: - **Misunderstanding Inverse Relationships:** Students often confuse direct and inverse relationships. Remember that in Boyle's Law, as one quantity increases (pressure), the other (volume) must decrease. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is held constant. If temperature changes, the relationship described by Boyle's Law does not hold. ### 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 formula \( P_1 V_1 = P_2 V_2 \) is key to solving problems involving Boyle's Law. - Always remember that changes in pressure and volume must maintain the inverse relationship defined by Boyle's Law.