Example Problem with Complete Solution

2E-1 : Mass of Propane in a Rigid Tank 2 pts
Determine the mass of propane in a 10 L tank if a temperature gauge on the tank reads -20oC and a pressure gauge on the tank reads 10 kPa. Assume propane behaves as an ideal gas, but verify this assumption.
Read : Apply the Ideal Gas EOS to determine the molar volume of the propane in the tank. If this value is greater than 20 L/mol, the IG EOS is accurate to within 1%.
Use the molar volume, the molecular weight and the volume of the tank to determine the mass of
propane in the tank.
Given: V 10 L Pgauge 10 kPa
T -20 oC
Find: MC3 ??? g
Assumptions: 1- Assume the propane behaves as an ideal gas. Be sure to verify this assumption.
Equations / Data / Solve:
We could use the following equation to determine the mass of propane in the tank if we knew the specific volume.
Eqn 1
Equations of state are written in terms of the molar volume. So we need the following equation to get from molar volume to the specific volume that we need to make use of Eqn 1.
Eqn 2
Now, we need to us the Ideal Gas EOS to determine the molar volume.
Ideal Gas EOS :
Eqn 3
Let's solve for the molar volume because we know we will need this value to test whether the Ideal Gas EOS is applicable.
Eqn 4
We need to be careful with our units in Eqn 2. Let's begin by looking up the Universal Gas Constant in my favorite units, J/mol-K.
R 8.314 J/mol-K
Next we need to convert the temperature to Kelvins and the gauge pressure to absolute pressure in Pascals.
T 253.15 K
Assume: Patm 101.325 kPa
Pabs 111.325 kPa
111,325 Pa
Plugging values into Eqn 2 yields: V 0.018906 m3/mol
18.91 L/mol
We can now look up the molecular weight of propane: MW 44.1 g/mol
Now, we can plug values into Eqn 2 and then Eqn 1 to complete this solution.
( Watch the units here! )   V 0.42870 m3/kg
MC3 0.02333 kg
23.33 g
Verify: Propane is not a diatomic molecule. Therefore, it cannot be accurately treated as an ideal gas unless its molar volume is greater than 20 L/mol.
Above, we found the molar volume of propane under the conditions in this problem is 18.91 L/mol.
Therefore we conclude that it may not be accurate to use the Ideal Gas EOS to solve this problem.
You should probably try a more sophisticated EOS such as the Generalized Compresibility EOS in this lesson or one of the equations of state in the next lesson.
Answers : MC3 23.33 g
(But this result is not reliable because the Ideal Gas assumption is not valid. A more accurate analysis yields MC3 = 24.1 g.)