Carbon Dioxide (CO_{2}) 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 CO_{2} 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 CO_{2} be accurate treated as
an ideal gas? 















Assumptions: 
1 Assume the CO_{2} 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/molK. 







R 
8.314 
J/molK 











Next we need to
convert the pressure from kPa
to Pascals. 
P 
225,000 
Pa 











Plugging values into Eqn 2 yields: 


V 
0.0088683 
m^{3}/mol 








8.87 
L/mol 










Verify: 
CO_{2} 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, CO_{2} cannot be accurately treated as an ideal
gas. 































