Final answer:
Using the combined gas law to find the volume at which the weather balloon bursts, we obtain a value of 1125.3 L. This calculation considers a pressure drop to 26.0 torr and a temperature decrease to -50.0 °C.
Step-by-step explanation:
To determine the volume at which the balloon bursts, we can use the combined gas law, which is given by P1V1/T1 = P2V2/T2 where P stands for pressure, V for volume, and T for temperature in Kelvins.
Firstly, convert the initial and final temperatures to Kelvin by adding 273.15 to the Celsius values:
T1 = 20.0 °C + 273.15 = 293.15 K and T2 = -50.0 °C + 273.15 = 223.15 K.
Convert the final pressure from torr to atm, since there are 760 torr in 1 atm: P2 = 26.0 torr × (1 atm / 760 torr) = 0.03421 atm.
Inserting the given values into the combined gas law we get: (1.00 atm) × (41.5 L) / (293.15 K) = (0.03421 atm) × V2 / (223.15 K).
Solve for V2, the volume at which the balloon bursts:
V2 = (1.00 × 41.5 × 223.15) / (0.03421 × 293.15)
= 1125.3 L.
The balloon bursts at a volume of 1125.3 L when the pressure decreases to 26.0 torr at -50.0 °C.