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
Chart 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%. |
|
|
|
|
|
|
|
|
|
|