Considering positional disorder, would you expect a crystal of octahedral cisMX2Y4 to have the same, higher, or lower residual entropy than the corresponding trans isomer? Explain your conclusion
The solutions manual says that for the cis compound there will be 12 different orientations while for the trans compound there will be 3 different orientations. How did they get 12 and 3?
higher entropy cis or trans
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Re: higher entropy cis or trans
The geometry it is talking about is the octahedral arrangement, where there are 6 directions for ligands: up, down, left, right, front, and back
With a little visualization it should be clear that there are only 3 pairs of positions that are 180 degrees apart but there are 12 pairs of positions that are 90 degrees apart
With a little visualization it should be clear that there are only 3 pairs of positions that are 180 degrees apart but there are 12 pairs of positions that are 90 degrees apart

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Re: higher entropy cis or trans
I am still confused though, is the trans isomer only looking at the molecules 180 degrees apart?

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Re: higher entropy cis or trans
The molecule featured possesses an octahedral geometry. Consider X1, X2, X3, and X4 to span horizontally across the molecule, with odd numbers being positioned opposite from each other and even numbers being positioned opposite from each other. Now, consider Y1 and Y2 to be the points on the opposite top and bottom ends of the molecule. This arrangement should reflect that present in the book.
Now, in a trans molecule the occupied positions must lie opposite from each other, so (Y1, Y2), (X1, X3), and (X2, X4) fit this requirement. If occupied, only these three positions would lie opposite from each other. Because they are opposite from each other, these positions also lie 180 degrees apart. (It is required that there be 180 degrees of separation in a trans molecule in order to maintain nonpolarity and proper symmetry.)
In a cis molecule, positions must not lie opposite from each other. Therefore, (X1, X2), (X2, X3), (X3, X4), (X4, X1), (Y1, X1), (Y1, X2), (Y1, X3), (Y1, X4), (Y2, X1), (Y2, X2), (Y2, X3), and (Y2, X4) fit this requirement. If occupied, these twelve positions satisfy a cis arrangement in that they are not opposite from each other. In fact, they all lie 90 degrees apart from each other.
I realize this is abstract, but please try to visualize it and I think it will make more sense.
Now, in a trans molecule the occupied positions must lie opposite from each other, so (Y1, Y2), (X1, X3), and (X2, X4) fit this requirement. If occupied, only these three positions would lie opposite from each other. Because they are opposite from each other, these positions also lie 180 degrees apart. (It is required that there be 180 degrees of separation in a trans molecule in order to maintain nonpolarity and proper symmetry.)
In a cis molecule, positions must not lie opposite from each other. Therefore, (X1, X2), (X2, X3), (X3, X4), (X4, X1), (Y1, X1), (Y1, X2), (Y1, X3), (Y1, X4), (Y2, X1), (Y2, X2), (Y2, X3), and (Y2, X4) fit this requirement. If occupied, these twelve positions satisfy a cis arrangement in that they are not opposite from each other. In fact, they all lie 90 degrees apart from each other.
I realize this is abstract, but please try to visualize it and I think it will make more sense.

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Re: higher entropy cis or trans
I drew them out so that it's easier to visualize the 12 cis and the 3 trans in case anyone is also struggling like me; the above comment definitely helped me understand this problem a lot better, thank you so much!
I circled the X so that it's easier to see how each molecule differs in position! :>

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Re: higher entropy cis or trans
Annie Chantasirivisal_4G wrote:IMG_0853 2.jpg
I drew them out so that it's easier to visualize the 12 cis and the 3 trans in case anyone is also struggling like me; the above comment definitely helped me understand this problem a lot better, thank you so much!
I circled the X so that it's easier to see how each molecule differs in position! :>
Is this something that was covered in class or we should know for the midterm?

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Re: higher entropy cis or trans
KaleenaJezycki_1I wrote:Annie Chantasirivisal_4G wrote:IMG_0853 2.jpg
I drew them out so that it's easier to visualize the 12 cis and the 3 trans in case anyone is also struggling like me; the above comment definitely helped me understand this problem a lot better, thank you so much!
I circled the X so that it's easier to see how each molecule differs in position! :>
Is this something that was covered in class or we should know for the midterm?
Sorry for the late reply, but as you can tell it was not on the midterm. This is just a review of 14A with cis and trans placement, but I think we'll get into more detail of it during 14C and D with Ochem :>
Edit:
Sorry, for clarification: drawing them out isn't necessary but I did it so that I could obtain the maximum possible number of positions the molecule could be in (14A stuff). But technically, that position part is what we need to know for 14B since it's part of entropy (the W in S=KblnW) and since we didn't get a chance to use that formula in the midterm I suspect it might be in the final.
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