**Correct Option: C. It doubles.** ### 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: \[ PV = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. **Step-by-Step Analysis:** 1. **Initial Conditions:** Let's assume we have an initial volume \( V_1 \) and an initial pressure \( P_1 \). According to Boyle's Law, we can write: \[ P_1 V_1 = k \] 2. **Halving the Volume:** If the volume is halved, the new volume \( V_2 \) becomes: \[ V_2 = \frac{V_1}{2} \] 3. **Applying Boyle's Law Again:** We can now apply Boyle's Law to find the new pressure \( P_2 \): \[ P_2 V_2 = k \] Substituting \( V_2 \): \[ P_2 \left(\frac{V_1}{2}\right) = k \] 4. **Relating the New Pressure to the Old Pressure:** Since we know \( k = P_1 V_1 \), we can substitute this into the equation: \[ P_2 \left(\frac{V_1}{2}\right) = P_1 V_1 \] 5. **Solving for \( P_2 \):** To isolate \( P_2 \), we can rearrange the equation: \[ P_2 = \frac{P_1 V_1}{\frac{V_1}{2}} \] Simplifying this gives: \[ P_2 = 2P_1 \] This shows that when the volume is halved, the pressure doubles. ### Why Other Options Are Incorrect: - **Option A: It decreases by half.** - This option suggests that the pressure would reduce to half its original value. However, according to Boyle's Law, halving the volume results in doubling the pressure, not reducing it. - **Option B: It remains constant.** - This option implies that pressure does not change with a change in volume. This contradicts Boyle's Law, which clearly states that pressure and volume are inversely related when temperature is constant. - **Option D: It quadruples.** - This option suggests that the pressure would increase fourfold. This is incorrect because the relationship is linear in terms of the inverse; halving the volume results in a doubling of pressure, not quadrupling. ### Common Pitfalls: - **Misunderstanding Inverse Relationships:** Students often confuse direct and inverse relationships. Remember, if one quantity increases, the other must decrease in an inverse relationship. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is held constant. Changes in temperature can affect pressure and volume in different ways (as described by the Ideal Gas Law). ### Revision Summary: - Boyle's Law states that pressure and volume are inversely related at constant temperature: \( PV = k \). - Halving the volume of a gas while keeping temperature constant results in doubling the pressure. - The correct answer to the question is that the pressure doubles (Option C). - Remember to always consider the conditions (constant temperature) when applying gas laws.