## Determining Residual Entropy in Crystal Form

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Cindy Chen_2I
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### Determining Residual Entropy in Crystal Form

How would you approach this problem?

If SO2F2 adopts a disordered arrangement in its crystal form, what would its residual molar entropy be?

AliceBarrington4c
Posts: 18
Joined: Fri Sep 25, 2015 3:00 am

### Re: Determining Residual Entropy in Crystal Form

There are 6 different ways S02F2 could be oriented, so the degeneracy is 6.
S=Kb(boltzman constant)lnW
because there is 1 mole, W^avogadros number

this gives us
S=(1.38x10^-23)ln6^(6.02x10^23)=14.9 J/K

Cindy Chen_2I
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### Re: Determining Residual Entropy in Crystal Form

Thank you!!

Kim Vu 2G
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### Re: Determining Residual Entropy in Crystal Form

I understand the calculations here, but just a general question to find the degeneracy. Do you just have to manually draw all the lewis structures for the molecule to find the degeneracy or is there another way?

Chem_Mod
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### Re: Determining Residual Entropy in Crystal Form

You can draw the Lewis structures out, or you can use a permutation to find the number of all possible structures. In an octohedral molecule MX2Y4, you have two sets of unique atoms, 2 X and 4 Y and there's six places they can be positioned in an octohedral molecule. The formula for a permutation is $\frac{m!}{(m-n)!n!}$ where m is your total number of objects you are trying to arrange (in this case 6 atoms) and n is the number atoms of one kind. So we can assign n=2 to represent the number of X atoms. Then the term (m-n) is 4 to represent the number of Y atoms. m! refers to the factorial which is the equivalent of writing (m)(m-1)(m-2)...*1. So in this case 6! is 6*5*4*3*2*1. We divide that by 4! and 2! to get 15 total unique conformations which you can try out yourself.

Christian Wooten 3A
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Joined: Fri Sep 25, 2015 3:00 am

### Re: Determining Residual Entropy in Crystal Form

I understand everything after we get the number 6, but I am very confused as to where the number 6 is coming from and how SO2F2 turned to MX2Y4

Daniel Lutz 2J
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Joined: Fri Sep 25, 2015 3:00 am

### Re: Determining Residual Entropy in Crystal Form

Christian Wooten 3A wrote:I understand everything after we get the number 6, but I am very confused as to where the number 6 is coming from and how SO2F2 turned to MX2Y4

It's 6 different possible configurations for SO2F2:
o o F F o F
/ / / / / /
o-S-F F-S-F o-S-o F-S-o F-S-o o-S-F
/ / / / / /
F o F o F o

Thus W (degeneracy)= 6

Daniel

Daniel Lutz 2J
Posts: 9
Joined: Fri Sep 25, 2015 3:00 am

### Re: Determining Residual Entropy in Crystal Form

Shoot it messed up the formatting of the 6 molecule configurations. But if you draw it out, you can see it.

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