Amount of Helium in a Blimp The Goodyear blimp Spirit of Akron is 62.6 m long and contains 7023 m^3 of helium. When the temperature of the helium is 280K , its absolute pressure is 110kPa .
Find the mass of the helium in the blimp.
m=_____kg
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Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass. You know n and molar mass, solve for grams.
I would convert cubic meters to L.
To find the mass of helium in the blimp, we can use the ideal gas law equation:
PV = nRT
Where:
P = absolute pressure of helium (in Pascals)
V = volume of helium (in cubic meters)
n = number of moles of helium
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature of helium (in Kelvin)
First, we need to convert the given pressure and volume units into Pascals and cubic meters, respectively. Since 1 kPa = 1000 Pa, we have:
P = 110kPa = 110,000 Pa
V = 7023m^3
Next, let's rearrange the ideal gas law equation to solve for n (number of moles):
n = PV / RT
Now, we can substitute the given values into the equation:
n = (110,000 Pa) * (7023m^3) / (8.314 J/(mol·K) * 280K)
Simplifying the equation gives:
n ≈ 34,010.53 mol
Finally, we can calculate the mass of helium using the molar mass of helium, which is approximately 4 g/mol:
Mass = n * molar mass
≈ 34,010.53 mol * 4 g/mol
≈ 136,042.12 g
≈ 136.04 kg
Therefore, the mass of helium in the blimp is approximately 136.04 kg.