**Correct Option: A. As the volume of a gas increases, its pressure decreases.** ### 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, \[ PV = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. **Step-by-Step Explanation:** 1. **Inversely Proportional Relationship:** - The key aspect of Boyle's Law is that pressure and volume are inversely related. This means that if one quantity increases, the other must decrease to keep the product \( PV \) constant. - For example, if you have a gas in a sealed container and you increase the volume of the container (by pulling a piston, for instance), the gas molecules have more space to move around. As a result, they collide with the walls of the container less frequently, which leads to a decrease in pressure. 2. **Practical Example:** - Imagine a syringe filled with air. If you pull the plunger back, you increase the volume inside the syringe. According to Boyle's Law, as the volume increases, the pressure inside the syringe decreases. Conversely, if you push the plunger in, the volume decreases, and the pressure increases. 3. **Mathematical Representation:** - If you start with an initial state where \( P_1 \) is the initial pressure and \( V_1 \) is the initial volume, and then change to a new state with \( P_2 \) and \( V_2 \), Boyle's Law can be expressed as: \[ P_1 V_1 = P_2 V_2 \] - This equation shows that if \( V_2 > V_1 \) (volume increases), then \( P_2 < P_1 \) (pressure decreases), confirming option A. ### Why Other Options Are Incorrect: - **Option B: As the volume of a gas increases, its pressure increases.** - This statement contradicts Boyle's Law. If the volume increases, the pressure must decrease, not increase. This is a fundamental misunderstanding of the inverse relationship. - **Option C: The pressure of a gas is directly proportional to its volume.** - This is incorrect because it suggests a direct relationship, which is the opposite of what Boyle's Law states. Pressure and volume are inversely proportional, not directly proportional. - **Option D: The pressure of a gas is independent of its volume.** - This statement is also incorrect. According to Boyle's Law, pressure and volume are dependent on each other. If the volume changes, the pressure must change as well, provided the temperature remains constant. ### Common Pitfalls: - **Confusing Direct and Inverse Relationships:** Students often confuse direct and inverse relationships. Remember that in Boyle's Law, an increase in volume leads to a decrease in pressure. - **Ignoring Temperature:** Boyle's Law only applies when the temperature is held constant. If the temperature changes, the relationship between pressure and volume will also change. - **Assuming Real Gases Behave Like Ideal Gases:** 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 proportional at constant temperature. - Increasing the volume of a gas decreases its pressure, and vice versa. - The relationship can be mathematically expressed as \( PV = k \). - Remember that this law applies only to ideal gases and under constant temperature conditions.