Example Problem with Complete Solution

2E-3 : Compressibility Factor: Methanol 2 pts
Use the Generalized Compressibility Factor EOS to determine the molar volume of methanol at 725 K and 27 MPa.
Read : We can use T & P to calculate TR and PR and use the Generalized Compressibility Charts to determine Z & VRideal. Then, we can use either Z or VRideal to determine the molar volume. The values we get for the molar volume should agree within about 5%.
Given: T 725 K Find: V ??? L/mol
P 27 MPa
Assumptions: None.
Equations / Data / Solve:
Begin by collecting all of the constants needed for all Generalized Compressibility Equation of State.
R 8.314 J/mol-K Tc 513.38 K
MW 32.042 g NH3 / mol NH3 Pc 8.216 MPa
Compressibility EOS :
Given TR and the ideal reduced molar volume, use the compressibility charts to evaluate either PR or the compressibility, Z. TR, PR and Z are defined as follows.
Eqn 1
Eqn 2
Eqn 3
Because we know both T and P, we can immediately plug values into Eqns 1 & 2.
TR 1.412 PR 3.286
Read the Generalized Compressibility
for PR = 0 to 7 :
Z 0.74
VRideal 0.325
We can solve Eqn 3 for the molar volume and use the value of Z we just found to evaluate V.
Eqn 4
Plugging values into Eqn 4 yields: V 0.0001652 m3/mol
0.165 L/mol
Alternatively, we could us the ideal reduced molar volume that we found on the Generalized Compressibility Chart to determine the molar volume.
Eqn 5
Now, we can solve Eqn 5 and plug in values to determine V.
Eqn 6
V 0.0001688 m3/mol
0.169 L/mol
Verify: There are no assumptions to verify.
Answers : Z: V 0.165 L/mol Vrideal: V 0.169 L/mol
These values differ by less than 3%. If you read the chart correctly, they should agree to within about 5%.