Question

Which of the following objects is chiral: $(\mathbf{a})$ a pencil, $(\mathbf{b})$ a computer keyboard, (c) a grand piano, (d) a molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2,(\mathbf{e})$ a piece of plane $\mathrm{A}4$ paper?

Short answer

Objects (a) a pencil, (b) a computer keyboard, (c) a grand piano, and (d) a molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$ are chiral, while object (e) a piece of plane A4 paper is not chiral.

Step-by-step solution

Object (a): A pencil

Consider a regular pencil with a sharpened end and an eraser at the other end. When we look at its mirror image, we can observe that it has a different orientation (tip-to-eraser) than the original. Thus, the pencil and its mirror image cannot be superimposed and are distinct. Therefore, a pencil is a chiral object.

Object (b): A computer keyboard

A computer keyboard is designed to have a specific layout of keys, typically QWERTY. The mirror image of the keyboard would have reversed key placements. Since the mirror image of a keyboard does not have the same arrangement of keys as the original, the two cannot be superimposed and are distinct. Therefore, a computer keyboard is a chiral object.

Object (c): A grand piano

A grand piano has a large, asymmetric shape, and its interior components, such as strings and hammers, are also arranged in a specific asymmetric pattern. If we compare the mirror image of a grand piano to the original, the two cannot be superimposed and are distinct. Therefore, a grand piano is a chiral object.

Object (d): A molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$

In a molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$, the iron atom is at the center, surrounded by two bipyridine (bipy) ligands and two chlorine atoms. The term 'cis' means that the two chlorine atoms are on the same side of the molecule. Since the cis-isomer of this complex has a specific and distinct 3D arrangement, the mirror image of the molecule cannot be superimposed onto the original. Therefore, the molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$ is chiral.

Object (e): A piece of plane A4 paper

A piece of plane A4 paper has a rectangular shape with two long sides and two short sides. The mirror image of the paper will still have the same rectangular shape with its sides having equal lengths. Thus, the original and its mirror image can be superimposed and are identical. Therefore, a piece of plane A4 paper is not a chiral object. In conclusion, objects (a) a pencil, (b) a computer keyboard, (c) a grand piano, and (d) a molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$ are chiral, while object (e) a piece of plane A4 paper is not chiral.

Key concepts

Mirror Image

A mirror image is what you see when you look at an object reflected in a mirror. It shows a reversed version of the object, much like how your right hand appears as a left hand when viewed in a mirror. This concept is vital when discussing chirality because if an object and its mirror image can coincide perfectly, they are considered achiral. For example, a simple object like a spoon typically can be superimposed with its mirror image.

• The idea of mirror images helps explain why some objects are chiral and others are not.
• An object is chiral if it cannot be perfectly superimposed on its mirror image, showing a non-identical relationship.

Understanding mirror images assists in visualizing why certain 3D structures, like the molecular model of $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$, cannot align with their mirror reflections.

Superimposition

Superimposition refers to the capability of placing one object over another, ensuring that all parts match exactly. In chirality, if an object's mirror image can be superimposed onto the object itself, the object is considered achiral. Take, for instance, a hand and its reflected image—no matter how you try, you cannot superimpose them perfectly.

• Superimposition illustrates the symmetry aspect of a molecule or object.
• Chiral objects fail to superimpose because they have unique 3D orientations that their mirror images do not match.

In the context of chirality, understanding superimposition helps identify if an object, such as a pencil or a grand piano, possesses a distinct asymmetry that makes it chiral.

Asymmetric Molecules

Asymmetric molecules lack symmetry, meaning they do not have identical parts that face each other or align. This is common in chiral molecules, where the asymmetry makes them non-superimposable on their mirror images. Molecular chirality often results from these asymmetric features, making molecules like $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$ chiral.

• An asymmetric molecule typically contains a central atom bonded to different atoms or groups, creating a unique spatial arrangement.
• This asymmetry is what leads to the chiral property of substances and many everyday objects.

Recognizing asymmetric structures allows better comprehension of why certain substances exhibit chirality and their mirror images are distinct.

Cis-Isomer

A cis-isomer refers to a specific type of isomer where two substituents are on the same side of a molecule. This arrangement is crucial in creating chirality in molecules, as seen in $cis-\mathrm{Fe}(\text{ bipy }{)}_2{\mathrm{Cl}}_2$. In such complexes, the distinctive spatial layout of atoms or groups is crucial.

• The cis configuration contributes to the lack of symmetry in chiral molecules.
• It influences the molecule's 3D shape and how it interacts with its mirror image.

The presence of a cis-isomer arrangement allows us to understand why some molecular models have properties making them chiral, contributing to their unique roles in biochemical processes and their applications.