Example Problem with Complete Solution

2E-2 : Ideal Gas or Not: Dioxide An Ideal Gas? 2 pts
Carbon Dioxide (CO2) gas is held in a tank at 225 kPa and 240 K. Can the carbon dioxide be treated as an ideal gas with less than 1% error?
Read : Apply the Ideal Gas EOS to determine the molar volume of the CO2 in the tank. If this value is greater than 20 L/mol, the IG EOS is accurate to within 1%.
Given: T 240 K P 225 kPa
Find: Can CO2 be accurate treated as an ideal gas?
Assumptions: 1- Assume the CO2 behaves as an ideal gas. Be sure to verify this assumption.
Equations / Data / Solve:
Ideal Gas EOS :
Eqn 1
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 2
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 pressure from kPa to Pascals. P 225,000 Pa
Plugging values into Eqn 2 yields: V 0.0088683 m3/mol
8.87 L/mol
Verify: CO2 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 8.87 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 : No. Under these conditions, CO2 cannot be accurately treated as an ideal gas.