Answer:
We can solve this problem using the combined gas law, which relates the initial and final volumes and temperatures of a gas:
(P1 x V1) / T1 = (P2 x V2) / T2
where P is the pressure, V is the volume, and T is the temperature.
Let's convert the initial volume to liters and the initial temperature to Kelvin:
V1 = 436.1 mL = 0.4361 L
T1 = 298 K
Next, let's convert the final temperature to Kelvin:
T2 = (20°C + 273.15) K = 293.15 K
Finally, let's plug in the given pressures and solve for V2:
P1 = P2
V2 = (P1 x V1 x T2) / (T1 x P2)
V2 = (4.45 atm x 0.4361 L x 293.15 K) / (298 K x 0.289 atm)
V2 ≈ 0.699 L
V2 ≈ 699 mL
Therefore, the volume of the gas inside the balloon is approximately 699 mL when the temperature decreases by 20°C.
Step-by-step explanation: