**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: \[ P \propto \frac{1}{V} \] or, more commonly, in equation form: \[ P_1 V_1 = P_2 V_2 \] where: - \( P_1 \) and \( V_1 \) are the initial pressure and volume, - \( P_2 \) and \( V_2 \) are the final pressure and volume. **Scenario Analysis:** In this question, we are told that the pressure of the gas is doubled while the temperature remains 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 \( V_2 \): 1. **Set up the equation using Boyle's Law:** \[ P_1 V_1 = P_2 V_2 \] 2. **Substitute \( P_2 \) with \( 2P_1 \):** \[ P_1 V_1 = (2P_1) V_2 \] 3. **Divide both sides by \( P_1 \) (assuming \( P_1 \neq 0 \)):** \[ V_1 = 2 V_2 \] 4. **Rearranging gives us:** \[ V_2 = \frac{V_1}{2} \] This shows that when the pressure is doubled, the volume is halved. Thus, 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 Boyle's Law, pressure and volume have an inverse relationship; if one increases, the other must decrease. - **Option C: The volume remains the same.** - This option implies that volume does not change with pressure, which is incorrect. Boyle's Law clearly states that volume must change in response to pressure changes when temperature is constant. - **Option D: The volume quadruples.** - This option suggests a much larger increase in volume, which is also contrary to Boyle's Law. A quadrupling of volume would imply a significant decrease in pressure, not an increase. ### 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). Remember, Boyle's Law is an inverse relationship. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is constant. If temperature changes, other gas laws (like Charles's Law) must be considered. - **Assuming Real Gases Behave Like Ideal Gases:** While Boyle's Law is derived from ideal gas behavior, real gases may deviate from this behavior 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. - Doubling the pressure of a gas results in halving its volume. - The correct answer to the question is B: The volume is halved. - Remember to distinguish between direct and inverse relationships in gas laws.