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 T_{R} and P_{R} and use the Generalized
Compressibility Charts to determine Z & V_{R}^{ideal}. Then, we can use either Z or V_{R}^{ideal} 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/molK 



T_{c} 
513.38 
K 

MW 
32.042 
g NH_{3} / mol NH_{3} 


P_{c} 
8.216 
MPa 











Compressibility
EOS : 


















Given T_{R} and the ideal reduced molar volume, use the compressibility
charts to evaluate either P_{R} or the
compressibility, Z. T_{R}, P_{R} 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. 











T_{R} 
1.412 




P_{R} 
3.286 












Read the Generalized Compressibility
Chart for P_{R} = 0 to 7 : 


Z 
0.74 








V_{R}^{ideal} 
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 
m^{3}/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 
m^{3}/mol 








0.169 
L/mol 










Verify: 
There are no assumptions
to verify. 
















Answers : 
Z: 
V 
0.165 
L/mol 

V_{r}^{ideal}_{:} 
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%. 









