Final answer:
Using the Combined Gas Law and converting temperatures to Kelvin, the final pressure experienced by the balloon at Mount Crumpit is calculated to be 0.584 atm. The correct option is a).
Step-by-step explanation:
The question asks for the final pressure experienced by a balloon as it clears Mount Crumpit, given its initial and final volumes and temperatures. The relationship between pressure, volume, and temperature for a gas is described by the Combined Gas Law, which combines Charles's Law, Boyle's Law, and Gay-Lussac's Law.
The formula for the Combined Gas Law is (P1 * V1) / T1 = (P2 * V2) / T2, where P is pressure, V is volume, and T is temperature in Kelvin.
To solve for the final pressure (P2), we first convert all temperatures to Kelvin: T1 = 21 °C + 273.15 = 294.15 K and T2 = 5.24 °C + 273.15 = 278.39 K. Then, we rearrange the formula to solve for P2: P2 = (P1 * V1 * T2) / (V2 * T1).
Substituting the given values into the equation, we get:
P2 = (0.981 atm * 100.21 L * 278.39 K) / (144.53 L * 294.15 K) = 0.584 atm
Therefore, the pressure experienced by the balloon as it clears Mount Crumpit is 0.584 atm. Option a) is the correct one.