To solve this problem, we can use the combined gas law formula, which relates the pressure, volume, and temperature of a gas.
1. Write down the combined gas law formula:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure = 730 mm Hg
V1 = initial volume = 752 mL
T1 = initial temperature = 41.0 °C + 273.15 (convert to Kelvin) = 314.15 K
P2 = final pressure = 760 mm Hg
V2 = final volume (what we want to find)
T2 = final temperature = 31.0 °C + 273.15 = 304.15 K
2. Plug the values into the formula:
(730 * 752) / 314.15 = (760 * V2) / 304.15
3. Solve for V2:
(730 * 752 * 304.15) / (314.15 * 760) = V2
V2 ≈ 727 mL
Therefore, the carbon dioxide will occupy a volume of approximately 727 mL when the temperature drops to 31.0 °C and the pressure changes to 760 mm Hg.
