The correct option is **B**. ### Explanation of the Correct Answer (B) **Statement B: "At constant temperature, the volume of a gas increases as the pressure increases."** This statement is incorrect because it contradicts Boyle's Law, which states that at constant temperature, the volume of a gas is inversely proportional to its pressure. This means that if the pressure of a gas increases, its volume must decrease, provided the temperature remains constant. **Mathematically, Boyle's Law is expressed as:** \[ P_1 V_1 = P_2 V_2 \] Where: - \( P_1 \) and \( V_1 \) are the initial pressure and volume, - \( P_2 \) and \( V_2 \) are the final pressure and volume. If we rearrange this equation, we can see that: \[ V \propto \frac{1}{P} \] This indicates that as pressure (P) increases, volume (V) decreases, confirming that statement B is incorrect. ### Explanation of the Other Options **Option A: "The average kinetic energy of a gas is directly proportional to its temperature."** This statement is correct. The average kinetic energy of gas molecules is directly related to the temperature of the gas in Kelvin. The formula for the average kinetic energy (\( KE \)) of a gas is given by: \[ KE = \frac{3}{2} k T \] Where: - \( k \) is the Boltzmann constant, - \( T \) is the absolute temperature in Kelvin. As the temperature increases, the average kinetic energy of the gas molecules also increases, which is consistent with the principles of kinetic molecular theory. **Option C: "The pressure of a gas is inversely proportional to the density."** This statement is also correct. The relationship between pressure (P), density (ρ), and temperature (T) can be described by the ideal gas law: \[ PV = nRT \] Where: - \( n \) is the number of moles, - \( R \) is the ideal gas constant. Rearranging this equation gives: \[ P = \frac{nRT}{V} \] Since density (ρ) is defined as mass per unit volume (ρ = m/V), we can see that as density increases (for a fixed mass), the volume decreases, leading to an increase in pressure. Thus, pressure is inversely proportional to density when temperature is held constant. **Option D: "The temperature of a gas is directly proportional to its volume."** This statement is correct under the conditions of Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. The relationship can be expressed as: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \] Where: - \( V \) is the volume, - \( T \) is the absolute temperature in Kelvin. This means that if the temperature of a gas increases, its volume will also increase, provided the pressure remains constant. ### Summary of Key Points - **Boyle's Law** states that at constant temperature, volume and pressure are inversely related (B is incorrect). - **Kinetic Molecular Theory** indicates that the average kinetic energy of gas molecules is directly proportional to temperature (A is correct). - **Ideal Gas Law** shows that pressure is inversely related to density (C is correct). - **Charles's Law** states that volume is directly proportional to temperature at constant pressure (D is correct). ### Revision Summary - Boyle's Law: Volume decreases as pressure increases at constant temperature. - Average kinetic energy of gas is proportional to temperature. - Pressure is inversely related to density. - Charles's Law: Volume increases with temperature at constant pressure.