Bill and Bob have been testing a new aluminised PET (Polyethylene Terephthalate) film and they now use the material to make helium filled balloons. Bill’s balloon is less inflated than Bob’s, and the latter jokes about it. However, Bill insists he has to be careful because if he were to take the balloon on hills and mountains, the atmospheric pressure would decrease and the balloon would expand and burst. Bill then makes a bet that he can walk, drive or climb somewhere high enough for his balloon to burst...
The balloons are partially filled with helium and they unfold as helium expands into them. The balloons burst once they reach a volume of 22.0 dm3; the pressure and temperature of the helium inside the balloons are always equal to the surrounding atmospheric pressure and temperature. Bill and Bob added respectively 8600 cm3 and 18000 cm3 of helium in their balloons, by the sea side where the altitude is 0 meters, the temperature is 25.0oC and the atmospheric pressure is 760mm Hg.
The conditions on Mount Everest during climbing season are typically: P = 0.330atm and
T = -20.0oC.
(a) Calculate the volume that would be occupied by the helium in Bill’s balloon on Mount Everest (3 sig. fig.). Can Bill ever hope to win his bet? [3 marks]
(b) The dependence of the atmospheric pressure with altitude can be approximated by the following formula:
Patm = -7.57x10-2 h + 1
where h is the altitude in km, Patm is the atmospheric pressure in atm.
Calculate the altitude at which Bob’s balloon would burst, assuming that the temperature remains constant and equal to 250C (3 sig. fig).
.l
To calculate the volume that would be occupied by the helium in Bill's balloon on Mount Everest, we need to apply the ideal gas law, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature
Using the given information, we can rearrange the equation to solve for V:
V = (nRT) / P
Let's start by calculating the volume of helium in Bill's balloon on Mount Everest:
Step 1: Convert the given values to the appropriate units
- Convert 8600 cm3 to L: 8600 cm3 = 8.6 L
- Convert -20.0 oC to Kelvin: T = -20.0 + 273.15 = 253.15 K
- Replace the values into the equation:
V = [(nRT) / P]
V = [(1 mol) * (0.0821 L·atm/(mol·K)) * (253.15 K) / (0.33 atm)]
Step 2: Calculate the volume V
V = [(1 * 0.0821 * 253.15) / 0.33] L
V ≈ 63.188 L ≈ 63.2 L
Based on this calculation, the volume that would be occupied by the helium in Bill's balloon on Mount Everest is approximately 63.2 L.
Now, let's determine if Bill can win his bet:
Bill's balloon bursts once it reaches a volume of 22.0 dm3, which is equivalent to 22.0 L. Since the volume of the helium in Bill's balloon on Mount Everest is 63.2 L, which is greater than 22.0 L, it means that Bill's balloon would burst before reaching Mount Everest. Therefore, Bill cannot win his bet.