Van der Waals EOS using reduced molar volume

  • Thread starter jbowers9
  • Start date
  • #1
89
1

Homework Statement


I'm taking an online PChem course where the instructor throws out
Z = 3Vr/(3Vr – 1) – 9/(8 VrTr); where Vr is the reduced molar volume.

2. Homework Equations

{P + a/Vm^2}{Vm – b} = RT; where Vm is the molar volume
Tc = 8a/27Rb ; Vc = 3b ; Pc = a/27b^2

3. The Attempt at a Solution

Start with
(Pr + 3/Vr^2)( Vr – 1/3) = (8/3)Tr
Then
Pr = {8 Tr/(3Vr – 1) - 3/ Vr^2}
and
Z = PrVr/RTr = {8 Tr/(3Vr – 1) - 3/ Vr^2} Vr/RTr
gives
Z = {8 Vr/R(3Vr – 1) - 3/R VrTr}
I can’t figure out where to go next without chasing my tail with a’s and b’s to get the R to go away and give me the correct coefficients in the rhs of the eq. Help!
 

Answers and Replies

  • #2
mjc123
Science Advisor
Homework Helper
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574
I think you're misinterpreting Z (or the instructor is).
Let's call Zr = PrVr/Tr
Then Zr = 8Vr/(3Vr-1) - 3/VrTr
Z = PV/RT = PcVc/RTc*PrVr/Tr = ZcZr
Now Zc = 3/8, as you can get by the definitions of Pc, Vc and Tc
Hence you get the answer for Z.
 
  • #3
89
1
2028e2e05b7130d2567a31a3ab48b391.png

Using a = Tc 27Rb/8 & b = Vc/3 and dividing through by Vc,Tc & R it gives the desired result. Thanks. Phew! Now it's so simple. (Homer Simpson doi)
 

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