The volume of a gas is V cm³ at P mmHg. What is its new volume if the pressure is reduced to half at constant temperature?

Correct Answer: 2V cm³

Explanation:

• This is an application of Boyle’s Law, which states that for a fixed mass of gas at constant temperature: \[ P_1 V_1 = P_2 V_2 \]
• Here: - Initial pressure = \( P \) - Initial volume = \( V \) - Final pressure = \( \tfrac{P}{2} \) - Final volume = \( V_2 \) (unknown)
• Substitute into the equation: \[ P \times V = \frac{P}{2} \times V_2 \]
• Simplify: \[ V_2 = \frac{P \times V}{P/2} = 2V \]

Therefore, when the pressure is reduced to half, the volume doubles, giving 2V cm³.