A balloon holds 27.8 kg of helium. What is the volume of the balloon if the pressure is 0.97 atm and the temperature is 24 °C
PV = nRT
Remember T must be in kelvin.
n = grams/molar mass He = 27800g/molar mass He.
mfd
To find the volume of the balloon, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the given temperature of 24 °C to Kelvin by adding 273 to it:
T = 24 °C + 273 = 297 K
Now, we need to calculate the number of moles (n) of helium in the balloon. To do this, we'll use the mass of helium (27.8 kg) and the molar mass of helium (4.0026 g/mol):
n = mass/molar mass
n = 27.8 kg / 4.0026 g/mol
Converting kg to g:
n = 27.8 kg * 1000 g/kg
Substituting the values:
n = 27,800 g / 4.0026 g/mol
Calculating n:
n ≈ 6942.21 mol
Now, we can substitute the known values into the ideal gas law equation:
PV = nRT
(0.97 atm) * V = (6942.21 mol) * (0.0821 L·atm/mol·K) * (297 K)
Simplifying the equation gives:
0.97V = 169,792.56 L·atm
Finally, divide both sides of the equation by 0.97 to solve for V:
V ≈ 175,080.4 L
Therefore, the volume of the balloon is approximately 175,080.4 liters when the pressure is 0.97 atm and the temperature is 24 °C.