## 4G.5

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

Fatemah Yacoub 1F
Posts: 114
Joined: Thu Jul 11, 2019 12:16 am

### 4G.5

Can someone explain how the cis has 12 possible orientations while the trans only has 3? I don't understand how they got these numbers.

Alice Chang 2H
Posts: 101
Joined: Fri Aug 30, 2019 12:18 am

### Re: 4G.5

It's best if you look at it visually, and try to imagine it rotate as a 3-d model.

For cis-, there are 12 orientations. It helped me a lot to focus on the red dots (forgot what element they represented), and try to rotate them to different positions (1 on top and 1 on side, 1 on bottom and 1 on side... etc). It's kind of difficult to explain in words, but try to draw out all the possible positions the red dots can take in relation to the other!

For trans-, there are 3 orientations, and a bit easier to explain. Since the red dots have to be across from each other at all times, there are only 3 ways the red dots can fit: along the x-, y-, and z-planes. Thus, there are only 3 orientations that the trans- model can take.

Hope this helps somehow!

805303639
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Joined: Thu Jul 11, 2019 12:16 am
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### Re: 4G.5

There are 15 ways to group two items from a set of 6 (6 choose 2). This is the total number of configurations of a pair of distinct atoms around an octahedral molecule, so #cis configurations + #trans configurations = 15. There are 3 trans configurations because there are 3 ways to group two atoms (3 choose 2) along the three planes. 15 total configurations - 3 trans configurations = 12 cis configurations.

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