**Correct Option: B. The volume 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 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, the new pressure \( P_2 \) becomes: \[ P_2 = 2P_1 \] 3. **Applying Boyle's Law Again:** We can now apply Boyle's Law with the new pressure: \[ P_2 \times V_2 = k \] Substituting \( P_2 \): \[ 2P_1 \times V_2 = k \] 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 the New Volume \( V_2 \):** - Dividing 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 of the gas is halved. ### Why Other Options Are Incorrect: - **Option A: The volume doubles.** - This option suggests that increasing the pressure would increase the volume, which contradicts Boyle's Law. According to the law, an increase in pressure leads to a decrease in volume. - **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 volume and pressure are inversely related when temperature is constant. - **Option D: The volume increases by 25%.** - This option suggests a slight increase in volume, which again contradicts the inverse relationship defined by Boyle's Law. An increase in pressure should lead to a decrease in volume, 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). - **Ignoring Temperature:** Boyle's Law only applies when the temperature is held constant. Changes in temperature can affect gas behavior significantly. - **Misinterpretation of Doubling Pressure:** Some may mistakenly think that doubling pressure means doubling volume, which is a misunderstanding of the 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 B: The volume halves. - Remember to always consider the conditions (constant temperature) when applying gas laws.