Question

Absence of which of the following symmetry is a must condition for chiral compound? (A) \(C_{n}(n\)-fold axis of Symmetry) (B) \(\mathrm{C}_{\mathrm{i}}\) (Centre of Inversion) (C) \(\mathrm{S}_{\mathrm{n}}(n\)-fold alternating axis of Symmetry) (D) \(\sigma\) (Plane of Symmetry)

Short answer

The absence of \(\sigma\) (Plane of Symmetry) is a must condition for a chiral compound to exist.

Step-by-step solution

Symmetry Elements in Compounds

Symmetry elements in compounds are geometrical transformations that, when applied to an object, result in an indistinguishable arrangement. The most common symmetry elements are 1. \(C_n\) (n-fold axis of symmetry) 2. \(C_{i}\) (Centre of inversion) 3. \(S_n\) (n-fold alternating axis of symmetry) 4. \(\sigma\) (Plane of symmetry)

Chiral Compounds

Chiral compounds are molecules that are structurally asymmetrical and cannot be superimposed onto their mirror image. They are optically active, meaning they have the ability to rotate the plane of polarized light. Now, let's discuss each type of symmetry and its relation to chirality.

\(C_n\) (n-fold axis of symmetry)

The \(C_n\) symmetry element in a compound represents a single axis of rotation around which the whole molecule can be rotated by an angle of 360°/n and still maintain the same arrangement. The presence or absence of \(C_n\) symmetry does not inherently determine whether a compound is chiral or achiral.

\(C_{i}\) (Centre of inversion)

The \(C_{i}\) center of inversion is a single point within the compound through which all atoms are inverted by moving through the center to the opposite side. A molecule with center of inversion symmetry is achiral; if no center of inversion exists, the molecule might be chiral or achiral depending on the other symmetry elements present.

\(S_n\) (n-fold alternating axis of symmetry)

The \(S_n\) symmetry element in a compound represents an axis of rotation combined with a reflection in a plane perpendicular to that axis. If a molecule possesses an alternating axis of symmetry with an odd value of n (such as \(S_1, S_3, S_5\) ...) it is achiral. If a molecule lacks \(S_n\) with an odd value of n, it might be chiral or achiral depending on the presence of other symmetry elements.

\(\sigma\) (Plane of symmetry)

The \(\sigma\) symmetry element in a compound represents a plane of reflection, in which the molecule can be reflected to produce an identical arrangement. If a molecule possesses at least one plane of symmetry, it is achiral. A molecule with no planes of symmetry might be chiral or achiral depending on other symmetry elements. After analyzing all types of symmetry elements and their relationship with chirality, we can conclude:

Answer

The answer to the exercise is (D) \(\sigma\) (Plane of Symmetry). The absence of this type of symmetry is a must condition for a chiral compound to exist.

Key concepts

Symmetry Elements in Compounds

Symmetry elements in compounds are integral to understanding molecular geometry and stability. They reveal how certain movements or transformations can be applied to a molecule without changing its overall appearance. There are four primary symmetry elements:

• Rotate on an Axis (\(C_n\)) - An n-fold axis of symmetry around which the compound can be rotated a fraction of a full circle (specifically 360°/n) and appear the same. A molecule can have several of these axes, and the value of 'n' indicates the number of times the molecule maps onto itself in a full 360° rotation.
• Centre of Inversion (\(C_{i}\)) - A point within the molecule such that every atom at a given distance and direction from that point has an equivalent atom at the same distance but opposite direction. An inversion centre is like flipping the molecule inside out through the center point.
• Alternating Axis of Symmetry (\(S_n\)) - A combination of a rotation about an axis followed by reflection through a plane perpendicular to that axis. This transformation is more complex and less commonly observed than simple rotational symmetry.
• Plane of Symmetry (\(\sigma\)) - A virtual plane slicing through the molecule such that one half is the mirror image of the other. This is often the most discussed symmetry element when considering chirality because of its direct implication on optical activity.

Symmetry considerations provide an avenue for predicting physical and chemical properties of compounds, including their interactions with light, which is a cornerstone in the study of chirality.

Optical Activity

Optical activity is a fascinating property of some chiral compounds that allows them to rotate the plane of polarized light. This ability stems from a lack of internal symmetry, meaning the molecule is not superimposable on its mirror image, akin to left and right hands. When polarized light passes through a solution containing an optically active compound, its plane of polarization is rotated either to the right (dextrorotatory) or to the left (levorotary). This physical property is quantifiable and is measured using instruments called polarimeters.
Optical activity is not just an intriguing optical phenomenon; it has practical implications in fields such as pharmaceuticals and organic chemistry. Compounds with differing optical rotations, despite having the same molecular formula, can have vastly different biological effects. Hence, understanding and identifying optical activity is crucial in the development and assessment of many chemicals and drugs.

Plane of Symmetry and Chirality

The plane of symmetry, represented by \(\sigma\), is perhaps the most intuitive symmetry element to understand. If you can draw a plane through a molecule and see that the atoms on one side of the plane are mirrored on the other, the molecule has a plane of symmetry. Chiral compounds, in stark contrast, do not possess such symmetry. Absence of a plane of symmetry is indeed a defining characteristic of chirality, as it ensures that the structure and its mirror image are non-superimposable - they are as distinct as a left hand is from a right hand. This absence inherently means the molecule cannot be divided into two identical halves, thus allowing it to interact with polarized light in a manner that shifts its plane - a hallmark of optical activity.
For students wrestling with visualizing these concepts, models or molecular visualization software can be invaluable. Seeing a molecule in three dimensions makes it easier to identify whether any planes of symmetry are present, thereby revealing potential chirality. This understanding is fundamental in organic chemistry where chirality plays a pivotal role, from the synthesis of new medicinal compounds to elucidating biological pathways at the molecular level.