**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 equation form: \[ P_1 V_1 = P_2 V_2 \] 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 \( V_2 \): 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. Therefore, the correct answer is **A. The volume is halved**. ### Why Other Options Are Incorrect: - **Option B: The volume is doubled** - This option suggests that increasing the pressure would lead to an increase in volume, which contradicts Boyle's Law. According to Boyle's Law, if pressure increases, volume must decrease, not increase. - **Option C: The volume remains the same** - This option implies that pressure changes do not affect volume, which is incorrect. Boyle's Law clearly states that pressure and volume are inversely related; thus, a change in pressure will result in a change in volume. - **Option D: The volume is tripled** - This option also contradicts Boyle's Law. Tripling the volume would imply a significant decrease in pressure, which is not the case when 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, the other decreases. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is constant. If temperature changes, other gas laws (like Charles's Law) may need to be considered. - **Assuming Ideal Gas Behavior:** Boyle's Law is derived under the assumption of 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 A: The volume is halved. - Remember to always consider the conditions (constant temperature) when applying gas laws.