Final answer:
After releasing 3.1 moles of gas from the balloon, increasing the temperature to 72°C, and decreasing the pressure to 725 torr, the balloon will take up a volume of approximately 19.91 liters.
Step-by-step explanation:
To solve this problem, the combined gas law which relates pressure, volume, and temperature is used. The combined gas law is expressed as (P1 x V1) / T1 = (P2 x V2) / T2, where P is the pressure, V is the volume, T is the temperature in Kelvin, and subscripts 1 and 2 refer to the initial and final states of the gas. Since 3.1 moles of gas are released from the balloon, the number of moles of gas left in the balloon is 15.2 - 3.1 = 12.1 moles.
First, convert the temperatures to Kelvin: T1 = 54°C + 273.15 = 327.15 K and T2 = 72°C + 273.15 = 345.15 K. Then, convert the pressures to the same units: P1 = 745 torr x (1 atm / 760 torr) = 0.9803 atm and P2 = 725 torr x (1 atm / 760 torr) = 0.9539 atm.
Applying the combined gas law and solving for V2 gives us:
V2 = (P1 x V1 x T2) / (P2 x T1) = (0.9803 atm x 18.9 L x 345.15 K) / (0.9539 atm x 327.15 K) = 19.91 L
Therefore, after releasing 3.1 moles of gas, increasing the temperature to 72°C and decreasing the pressure to 725 torr, the gas will take up a volume of approximately 19.91 liters.