## higher entropy cis or trans

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

Franca Park 3J
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### higher entropy cis or trans

Considering positional disorder, would you expect a crystal of octahedral cis-MX2Y4 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?

Chem_Mod
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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

Marsenne Cabral 1A
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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?

Michael Torres 4I
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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 non-polarity 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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