| 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? |
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| 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%. |
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| Given: |
T |
240 |
K |
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P |
225 |
kPa |
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| Find: |
Can CO2 be accurate treated as
an ideal gas? |
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| Assumptions: |
1- Assume the CO2 behaves as an ideal gas. Be sure to verify this assumption. |
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| Equations
/ Data / Solve: |
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Ideal
Gas EOS : |
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Eqn 1 |
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Let's solve for the
molar volume because we know we will need this value to test whether the Ideal Gas EOS is applicable. |
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Eqn 2 |
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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. |
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R |
8.314 |
J/mol-K |
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Next we need to
convert the pressure from kPa
to Pascals. |
P |
225,000 |
Pa |
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Plugging values into Eqn 2 yields: |
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V |
0.0088683 |
m3/mol |
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8.87 |
L/mol |
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| 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. |
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Above, we found the
molar volume of propane under the conditions in this problem is 8.87 L/mol. |
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Therefore, we conclude
that it may not be accurate to use the Ideal Gas EOS to solve this problem. |
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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. |
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| Answers : |
No. Under these conditions, CO2 cannot be accurately treated as an ideal
gas. |
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