Question

Which of the following objects is chiral: (a) a left shoe, (b) a slice of bread, \((c)\) a wood screw, (d) a molecular model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\) (e) a typical golf club?

Short answer

Out of the given objects, a left shoe and a wood screw are chiral, while a slice of bread, a molecular model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\), and a typical golf club are achiral.

Step-by-step solution

(a) Analyzing a Left Shoe

A left shoe and its mirror image (which corresponds to a right shoe) cannot be superimposed on each other. Therefore, a left shoe is chiral.

(b) Analyzing a Slice of Bread

A slice of bread, when considered as an object, can be placed flat on a mirror and their images can be superimposed. Therefore, a slice of bread is achiral.

(c) Analyzing a Wood Screw

A wood screw has a helical structure. Its mirror image will have the helix going in the opposite direction and the two structures cannot be superimposed. Therefore, a wood screw is chiral.

(d) Analyzing a Molecular Model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\)

The molecular formula \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\) indicates that the molecule has a central zinc ion that is coordinated to two chlorine atoms and an ethylenediamine molecule. The molecule has a tetrahedral arrangement in three dimensions. However, the molecular structure is symmetric, and the mirror image can be superimposed onto the original molecule. Therefore, the molecular model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\) is achiral.

(e) Analyzing a Typical Golf Club

A typical golf club has a symmetric shape that allows it to be superimposed on its mirror image. For example, a right-handed club can be flipped and superimposed onto a left-handed club. Therefore, a typical golf club is achiral. In conclusion, out of the given objects, a left shoe and a wood screw are chiral, while a slice of bread, a molecular model of \(\mathrm{Zn}(\mathrm{en}) \mathrm{Cl}_{2}\), and a typical golf club are achiral.

Key concepts

Superimposability

Superimposability is a crucial concept when discussing chirality, particularly in determining whether an object is chiral or achiral. When we say two objects are superimposable, we mean that one object can be placed over the other in such a way that all parts match up perfectly. In the context of the exercise, superimposability is the principle used to ascertain whether something is chiral.

• If an object and its mirror image can be superimposed, they are achiral.
• If an object cannot be superimposed on its mirror image, it is chiral.

For example, a left shoe is chiral because when you attempt to superimpose it on its mirror image (a right shoe), they do not match. Similarly, a wood screw has a distinct orientation that prevents it from matching with its mirror image. These examples highlight that lack of superimposability is a hallmark of chirality. On the other hand, objects like a slice of bread or a typical golf club can perfectly align with their mirror images, rendering them achiral.

Molecular Symmetry

Molecular symmetry involves the symmetrical arrangement of components in a molecule, which greatly impacts its superimposability and chirality. Symmetry can lead to superimposability because symmetrical objects often match their mirror images.
Molecules with central points or axes of symmetry tend to be achiral. In the given exercise, the molecular model of \(\mathrm{Zn}(\mathrm{en})\mathrm{Cl}_{2}\) exemplifies this concept. Its tetrahedral arrangement is symmetric enough that the whole molecule can be superimposed onto its mirror image, making it achiral.

• Centrosymmetric molecules: These have a center of symmetry and are often achiral.
• Axially symmetric molecules: These have rotational symmetry around an axis.

Understanding molecular symmetry aids in predicting the behavior and interactions of molecules in biological systems. Chirality, born from a lack of symmetry, is crucial in fields such as pharmaceuticals where molecular arrangement affects drug interaction.

Mirror Image

The concept of a mirror image is integral to understanding chirality and superimposability. A mirror image is essentially a reflected duplicate of an object. This reflection can create a non-superimposable partner, indicating chirality.
In the realm of everyday objects and molecules, the mirror image principle helps determine whether they are chiral:

• If the original object and its mirror image are indistinguishable when overlapped, they are achiral.
• Distinct mirror images that can't be aligned perfectly with the original reveal chirality.

Taking the wood screw from the exercise, its mirror image would twist in the opposite direction, which cannot align with the original screw—an example of a chiral object. In contrast, a golf club's mirror image can be aligned with its original due to the club's symmetry, making it achiral. This concept applies to molecules and more complex structures, demonstrating how vital the concept of mirror images is to understanding chirality in chemistry and beyond.