### Correct Option: A. It 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: \[ PV = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. **What Happens When Pressure is Doubled:** According to Boyle's Law, if the pressure of the gas is doubled (let's denote the initial pressure as \( P_1 \) and the new pressure as \( P_2 = 2P_1 \)), we can analyze the effect on the volume. 1. **Initial State:** - Let the initial volume be \( V_1 \). - The initial pressure is \( P_1 \). - According to Boyle's Law: \[ P_1 V_1 = k \] 2. **Final State:** - The new pressure is \( P_2 = 2P_1 \). - Let the new volume be \( V_2 \). - According to Boyle's Law for the new state: \[ P_2 V_2 = k \] - Substituting \( P_2 \): \[ 2P_1 V_2 = k \] 3. **Setting the Equations Equal:** Since both expressions equal \( k \), we can set them equal to each other: \[ P_1 V_1 = 2P_1 V_2 \] 4. **Solving for \( V_2 \):** 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 is halved. ### Why Other Options are Incorrect: - **Option B: It is doubled.** - This option suggests that increasing the pressure would increase the volume, which contradicts Boyle's Law. According to the law, pressure and volume have an inverse relationship; if pressure increases, volume must decrease. - **Option C: It remains the same.** - This option implies that pressure changes do not affect volume, which is incorrect. Boyle's Law clearly states that volume changes in response to pressure changes when temperature is held constant. - **Option D: It is quadrupled.** - 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 quantities increase or decrease together) with inverse relationships (where one quantity increases while the other decreases). - **Ignoring Temperature:** Boyle's Law only applies when temperature is constant. If temperature changes, the relationship between pressure and volume is not simply described by Boyle's Law. ### 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 relationship can be expressed as \( PV = k \). - Always remember that changes in pressure affect volume inversely when temperature is constant.