Question

A gas-filled balloon with a volume of 2.00 L at 1.20 atm and 20°C is allowed to rise to the stratosphere (about 30 km above the surface of the Earth), where the temperature and pressure are −23°C and 3.00 × 10−3 atm, respectively. Calculate the final volume of the balloon.

Answer 1

To solve this problem, we can use the combined gas law, which relates the pressure (P), volume (V), and temperature (T) of a gas:

P1V1/T1 = P2V2/T2

where the subscripts 1 and 2 refer to the initial and final states of the gas, respectively.

We can start by converting the initial and final temperatures to Kelvin, which is necessary when using the gas laws:

T1 = 20°C + 273.15 = 293.15 K
T2 = −23°C + 273.15 = 250.15 K

Next, we can plug in the given values and solve for the final volume:

P1V1/T1 = P2V2/T2

(1.20 atm)(2.00 L)/(293.15 K) = (3.00 × 10−3 atm)V2/(250.15 K)

Multiplying both sides by (250.15 K)/(3.00 × 10−3 atm), we get:

V2 = (1.20 atm)(2.00 L)(250.15 K)/(293.15 K)(3.00 × 10−3 atm)

V2 = 310 L

Therefore, the final volume of the balloon is 310 L when it rises to the stratosphere where the temperature and pressure are −23°C and 3.00 × 10−3 atm, respectively.