Question

A sample of an ideal gas occupies 10 liters at a pressure of 2 atm and a temperature of 300 K. What is the volume of the gas at 1 atm pressure and 300 K temperature?

• A. 5 L
• B. 10 L
• C. 20 L
• D. 40 L

Hint:

Remember: Boyle’s law states that for a fixed amount of gas at constant temperature, the volume is inversely proportional to the pressure. Decreasing pressure increases the volume.

Answer 1

The Correct Option is B

Step 1: Use Boyle's Law to calculate the new volume Boyle’s law states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional: \[ P_1 V_1 = P_2 V_2 \] where: - \( P_1 \) and \( V_1 \) are the initial pressure and volume, - \( P_2 \) and \( V_2 \) are the final pressure and volume. Step 2: Substitute the given values Given: - Initial pressure \( P_1 = 2 \, \text{atm} \), - Initial volume \( V_1 = 10 \, \text{L} \), - Final pressure \( P_2 = 1 \, \text{atm} \), - Final volume \( V_2 \) is what we need to calculate. Substitute the values into Boyle’s law: \[ 2 \times 10 = 1 \times V_2 \] \[ V_2 = 20 \, \text{L} \] Answer: Therefore, the volume of the gas at 1 atm pressure and 300 K temperature is \( 20 \, \text{L} \). So, the correct answer is option (3).