A 10.0 L cylinder with a movable piston exerts 3.00 atm of pressure. What will happen to the pressure if the volume of the container increases to 20.0 L?

• A. It will double
• B. It will decrease by half
• C. It will increase slightly
• D. No change

Answer: (B)

Verified step by step guidance

1. Identify the initial conditions: The initial volume (V1) is 10.0 L and the initial pressure (P1) is 3.00 atm.
2. Identify the final conditions: The final volume (V2) is 20.0 L, and we need to find the final pressure (P2).
3. Apply Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of a gas is inversely proportional to its volume. Mathematically, this is expressed as: <math xmlns='http://www.w3.org/1998/Math/MathML'><mfrac><mi>P</mi><mi>V</mi></mfrac> = ext{constant}</math> or <math xmlns='http://www.w3.org/1998/Math/MathML'>P_1V_1 = P_2V_2</math>.
4. Rearrange the equation to solve for the final pressure (P2): <math xmlns='http://www.w3.org/1998/Math/MathML'>P_2 = rac{P_1V_1}{V_2}</math>.
5. Substitute the known values into the equation: <math xmlns='http://www.w3.org/1998/Math/MathML'>P_2 = rac{3.00 ext{ atm} imes 10.0 ext{ L}}{20.0 ext{ L}}</math>. Calculate to find the final pressure.