Question

A gas occupies a volume of 5.0 L at 300 K and 1.0 atm pressure. What will be the volume of the gas if the pressure is increased to 2.0 atm while the temperature is kept constant?

• A. \( 2.5 \, \text{L} \)
• B. \( 10.0 \, \text{L} \)
• C. \( 5.0 \, \text{L} \)
• D. \( 1.0 \, \text{L} \)

Hint:

Boyle's law applies when the temperature of the gas remains constant. If the pressure increases, the volume decreases, and vice versa. The relationship between pressure and volume is inversely proportional.

Answer 1

The Correct Option is A

We can use Boyle's law to solve this problem, which states that for a constant temperature, the volume of a gas is inversely proportional to its pressure. The formula for Boyle’s law is: \[ P_1 V_1 = P_2 V_2 \] Where: - \( P_1 = 1.0 \, \text{atm} \) is the initial pressure, - \( V_1 = 5.0 \, \text{L} \) is the initial volume, - \( P_2 = 2.0 \, \text{atm} \) is the final pressure, - \( V_2 \) is the final volume, which we need to find. Rearranging the formula to solve for \( V_2 \): \[ V_2 = \frac{P_1 V_1}{P_2} \] Substitute the known values: \[ V_2 = \frac{1.0 \times 5.0}{2.0} = 2.5 \, \text{L} \] Thus, the volume of the gas at 2.0 atm pressure is \( 2.5 \, \text{L} \).