Q.18 Considering cyclobutane to be planar, the number of planes of symmetry in the
following compound is _____________ (in integer).
The given molecule (a planar 1,3‑dimethylcyclobutane with one Me as wedge and the other as dash) has two planes of symmetry.
Understanding the structure
The structure shown is 1,3‑dimethylcyclobutane, drawn as a planar four‑membered ring with methyl groups on C‑1 and C‑3, one on a solid wedge and the other on a dashed wedge, meaning they are in a trans relationship with respect to the ring plane. In a planar representation of a substituted cycloalkane, wedges and dashes represent groups coming out of or going behind the plane, but the carbon skeleton itself is kept flat so symmetry elements are easier to visualize.
For 1,3‑dimethylcyclobutane, stereochemical analysis shows that such disubstituted cyclobutanes are meso because they possess internal symmetry elements, even though they may contain stereocenters. A meso compound is achiral due to the presence of a plane (or center) of symmetry that makes the molecule superimposable on its mirror image.
Identifying the planes of symmetry
When cyclobutane is considered perfectly planar, 1,3‑disubstitution allows two distinct mirror planes.
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Vertical plane (through C‑1 and C‑3):
This plane passes through the two substituted carbons (C‑1 and C‑3), cuts the ring into two equal halves, and bisects each of the two opposite C–C bonds; it also divides each methyl group into two mirror halves (you are allowed to “cut atoms in half” when defining a symmetry plane). Reflection across this plane interchanges the two unsubstituted carbons and maps each half‑methyl and half‑hydrogen at C‑1 and C‑3 onto the other half, giving an indistinguishable structure. -
Horizontal plane (through the ring plane):
Because the cyclobutane ring is assumed planar, a plane coincident with the ring itself acts as another mirror plane; it reflects the wedge methyl above the ring into the dash methyl below the ring while simultaneously reflecting the corresponding hydrogens, giving back the same overall arrangement. This “ring plane” mirror is a standard symmetry element in planar disubstituted small rings such as cis‑1,3‑dimethylcyclobutane and certain substituted cyclopropanes.
Thus, the total number of planes of symmetry is 2.
Why the wedge and dash do not destroy symmetry
Wedge and dash notation only indicates that one substituent is oriented above the plane and the other below; it does not fix them at “left” or “right” in 2D space. When a symmetry plane passes through a stereocenter, it can divide each substituent (for example, the methyl and hydrogen) into equal mirror halves so that the overall 3D arrangement still matches after reflection, which is why both cis‑ and trans‑1,3‑dimethylcyclobutanes can have internal symmetry and be meso in planar models.
Because of this internal symmetry, the molecule is achiral and exhibits two symmetry planes, matching the required integer answer 2.
