# Chirality of spirocyclic compound

I am facing trouble with the following problem.

Is (R)-1,7-dioxaspiro[5.5]undecane chiral? My idea is that the compound possess a plane of symmetry and thus should be achiral. However if we take its mirror image then the bond pointing below of the plane will become above the plane and thus it will not form a nonsuperimposable mirror image indicating that it is chiral. Certainly one of the approach is incorrect. I couldn't understand which one.

• This is a great example of axial chirality. – Zhe Dec 24 '16 at 20:43
• – user7951 Dec 25 '16 at 20:38

The only place where a plane of symmetry may make sense would be vertically through the centre, through the spiro carbon. However, as the image by Tetrahydrocannabinol shows, these rings are not in the same plane (implied by the wedge and dash notation). Therefore, using that plane as a plane of symmetry would map each of the two rings into the void.

The only element of symmetry I can see in the compound is a $C_2$ axis (rotation by $180^\circ$). This axis would also bisect the spiro carbon, but it would map the oxygens onto each other. Having only a $C_2$ axis allows a compound to be chiral (point group $C_2$) and thus your compound is chiral.

• Thank you for making it cleat that the compound does not possess any symmetry..However if we just take its mirror image about a plane which is perpendicular to the plane containing the compound,the two bonds with are pointing below and above the plane ( implied by the wedge and dash) will get interchanged but then also we would be able to perfectly superimpose over the original one..How do you look into this?.This would in fact make it achiral. – Pink Dec 25 '16 at 1:08
• @aniline You would be mapping an oxygen onto a carbon. That would not be the same thing. – Jan Dec 25 '16 at 1:12
• Oh yes so if in the first ring instead of oxygen there would have been carbon then the compound would be achiral. – Pink Dec 25 '16 at 1:14
• @aniline Absolutely correct! =) – Jan Dec 25 '16 at 1:16

The compound is chiral as there is no element of symmetry. The two rings are more or less perpendicular to each other. Something like this: Since it is disymmetric it is chiral.