Final answer:
Using Boyle's law, the new volume of the balloon at 50.0 kPa would be 120.0 liters, as volume and pressure are inversely proportional for a gas at constant temperature.
Step-by-step explanation:
The student's question pertains to the behavior of gases under changing pressure conditions, which is described by Boyle's law. Boyle's law states that for a given mass of gas at a constant temperature, the volume of the gas is inversely proportional to the pressure it is under. In the case of the balloon released at a pressure of 80.0 kPa with a volume of 75.0 L, when the pressure decreases to 50.0 kPa at a higher altitude, we can calculate the new volume (V2) using the formula P1V1 = P2V2 where P1 is 80.0 kPa, V1 is 75.0 L, and P2 is 50.0 kPa.
Following these steps:
- Write the initial equation: P1V1 = P2V2.
- Substitute the known values: 80.0 kPa × 75.0 L = 50.0 kPa × V2.
- Solve for V2: V2 = (80.0 kPa × 75.0 L) / 50.0 kPa.
- Calculate the new volume: V2 = 120.0 L.
Therefore, the new volume of the balloon when it reaches an altitude with a pressure of 50.0 kPa will be 120.0 liters.