Polarity and stability

Why is cis-1,2-cyclohexadiol less polar than trans-1,2-cyclohexadiol? I know it has something to do with stability and chair conformations, but I'm not sure how it relates to polarity. I know cis-1,2-cyclohexadiol has a more stable chair conformation than trans.




If I assume you refer to 1,2-cylohexanediols, the two isomers to consider were (*cis*), and (*trans*)


[![enter image description here](https://i.stack.imgur.com/2czj4.png)](https://i.stack.imgur.com/2czj4.png)


Assuming the cyclohexane ring as a plane, an (axial, equatorial) orientation of the two O-substitutents is puts them both on the same side of this reference plane; the relative orientation of the two substituents is (*cis*):


[![enter image description here](https://i.stack.imgur.com/tont9.png)](https://i.stack.imgur.com/tont9.png)


This contrasts to the case of the (*trans*)-configuration, where the two substituents may be either both in axial, or (likely preferred by thermodynamics) both in equatorial orientation:


[![enter image description here](https://i.stack.imgur.com/uIBDo.png)](https://i.stack.imgur.com/uIBDo.png)


From the later picture, taking into account *i*) the relative orientation of the two hydroxyl groups towards each other as well in respect to the cyclohexane moiety and *ii*) the (assumed) conformational preference for this form over the conformer with two axial oriented hydroxyl groups, I would assume the two individual vectorial contributions along $\ce{C -> O}$ are better lined up than in the instance of the (*cis*)-configuration to yield a larger (global) dipolar moment.


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