Final answer:
Using the combined gas law, we can determine the final volume of a balloon when it ascends to an altitude with different temperature and pressure by setting up the equation V2 = (P1V1T2)/(P2T1) and plugging in the given values after converting the pressures to the same units.
Step-by-step explanation:
The question involves the application of the Ideal Gas Law and the combined gas law to determine the final volume of a gas-filled balloon when it rises to a different altitude with changes in temperature and pressure. The Ideal Gas Law is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
For this problem, since the number of moles of gas and the gas constant are constant, we use the combined gas law, which arises from the Ideal Gas Law: (P1V1)/T1 = (P2V2)/T2, where the subscript 1 refers to initial conditions and subscript 2 refers to final conditions. Given the initial conditions of 1.00 atm, 20.0°C (293.15 K), and 200.0 L volume, and the final conditions of 0.9 torr (which is 0.001183 atm), and -3.5°C (269.65 K), we must find the final volume V2.
To convert the pressures to the same units, we know that 1 atm = 760 torr. By plugging in our known values and solving for V2, we have: V2 = (P1V1T2)/(P2T1) = (1.00 atm * 200.0 L * 269.65 K) / (0.001183 atm * 293.15 K). After calculating, we find the final volume of the balloon. The calculation will show the volume the balloon would have to expand to in order to maintain the same number of gas moles at the higher altitude despite lower pressure and temperature.