A sample of gas occupies 1000 mL at a pressure of 15 atm. If the gas is compressed to a volume of 500 mL at constant temperature, what is the new pressure of the gas?

• A. 7.5 atm
• B. 30 atm
• C. 1.5 atm
• D. 15 atm

Answer: (B)

Verified step by step guidance

1. Identify the type of gas law applicable. Since the temperature is constant and the pressure and volume are changing, this is a problem involving Boyle's Law.
2. Recall Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, this is expressed as \(P_1 \times V_1 = P_2 \times V_2\).
3. Write down the known values: initial pressure \(P_1 = 15\) atm, initial volume \(V_1 = 1000\) mL, and final volume \(V_2 = 500\) mL. The final pressure \(P_2\) is what we need to find.
4. Rearrange Boyle's Law to solve for the final pressure: \(P_2 = \frac{P_1 \times V_1}{V_2}\).
5. Substitute the known values into the equation: \(P_2 = \frac{15 \, \text{atm} \times 1000 \, \text{mL}}{500 \, \text{mL}}\). This will give the new pressure after compression.