In an underground gas reserve, a bubble of methane gas (CH₄) has a volume of 45.0 mL at 1.60 atm pressure. What volume, in milliliters, will the gas bubble occupy when it reaches the surface where the atmospheric pressure is 744 mmHg, if there is no change in temperature?

• A. 36.0 mL
• B. 54.0 mL
• C. 60.0 mL
• D. 45.0 mL

Answer: (B)

Verified step by step guidance

1. Identify the given values: initial volume \( V_1 = 45.0 \text{ mL} \), initial pressure \( P_1 = 1.60 \text{ atm} \), and final pressure \( P_2 = 744 \text{ mmHg} \).
2. Convert the final pressure from mmHg to atm for consistency in units. Use the conversion factor: \( 1 \text{ atm} = 760 \text{ mmHg} \). Calculate \( P_2 \) in atm.
3. Apply Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure and volume are inversely proportional: \( P_1 \times V_1 = P_2 \times V_2 \).
4. Rearrange the equation to solve for the final volume \( V_2 \): \( V_2 = \frac{P_1 \times V_1}{P_2} \).
5. Substitute the known values into the equation and solve for \( V_2 \) to find the volume of the gas bubble at the surface.