A sample of gas occupies 10 L at 1 atm and 25°C. If the temperature remains constant at 25°C, what volume will the gas occupy at 500 atm?

• A. 0.2 L
• B. 0.02 L
• C. 50 L
• D. 5 L

Answer: (B)

Verified step by step guidance

1. Identify the gas law that relates pressure and volume at constant temperature, which is Boyle's Law. Boyle's Law states that \(P_1 V_1 = P_2 V_2\) when temperature is constant.
2. Write down the known values: initial pressure \(P_1 = 1\) atm, initial volume \(V_1 = 10\) L, final pressure \(P_2 = 500\) atm, and the final volume \(V_2\) is what we need to find.
3. Rearrange Boyle's Law to solve for the final volume \(V_2\): \(V_2 = \frac{P_1 V_1}{P_2}\).
4. Substitute the known values into the equation: \(V_2 = \frac{1 \text{ atm} \times 10 \text{ L}}{500 \text{ atm}}\).
5. Calculate the value of \(V_2\) to find the volume the gas will occupy at 500 atm while keeping the temperature constant.