Problem 79 - Chemistry The Central Science In Si Units

Question

Which of the following objects is chiral: (a) a pencil, (b) a computer keyboard, \((\mathbf{c})\) a grand piano, (d) a molecular model of cis-Fe(bipy) \(_{2} \mathrm{Cl}_{2},\) (e) a piece of plane A4 paper?

Step-by-Step Solution

Answer

The chiral objects are the grand piano and the molecular model of cis-Fe(bipy)\(_2 \mathrm{Cl}_2\).

Step 1: Define Chirality

Chirality is a property of a geometric shape or object where it has no plane of symmetry, meaning it cannot be superimposed on its mirror image. To determine if an object is chiral, we check for this property.

Step 2: Analyze Each Object

We will analyze each object separately: (a) A pencil typically has rotational symmetry and a plane of symmetry (barring unique designs) and is not chiral. (b) A computer keyboard is designed symmetrically to accommodate function keys and is not chiral. (c) A grand piano is not symmetric; its shape resembles a right-hand or left-hand design, and it is chiral. (d) A molecular model of cis-Fe(bipy)_2Cl_2 is chiral because the cis configuration lacks symmetry allowing superimposition of its mirror images. (e) A piece of A4 paper is symmetric and can be superimposed on its mirror image, so it is not chiral.

Step 3: Identify the Chiral Object

From our analysis, the objects that exhibit chirality are the grand piano and the molecular model of cis-Fe(bipy)_2Cl_2. These do not possess a plane of symmetry and cannot be superimposed on their mirror images.

Key Concepts

Symmetry

Symmetry plays a crucial role in determining the chirality of an object. Simply put, symmetry is when one part of an object is a mirror image of another part. This concept can be readily observed in everyday items. For example:

• A pencil, unless crafted uniquely, usually possesses rotational symmetry. It can be rotated around its central axis without changing its appearance.
• A computer keyboard is designed to be symmetric around a central vertical line to allow functional key placement, making it non-chiral.
• On the contrary, a grand piano lacks this symmetry, exhibiting an asymmetric right or left-hand design that contributes to its chirality.

Objects that lack symmetry, meaning they don't have mirror images that can be superimposed on the original object, often display chirality. In contrast, items that do have symmetry are generally not chiral because their engendered mirror images can coincide with the original object.

Molecular Structure

The molecular structure is a critical factor in understanding the chirality of molecules. In chemistry, chirality results from the specific configuration of atoms in a molecule which creates a non-superimposable mirror image.

• Molecules like cis-Fe(bipy)_2Cl_2 are prime examples where chirality is introduced by their geometric arrangement. This specific cis configuration, where similar groups are on the same side, disrupts any potential symmetry, making the molecule chiral.
• By contrast, symmetrical arrangements in molecules tend to create achiral molecules, where the mirror image can align with the original structure.

Understanding the molecular structure helps clarify why certain molecules are chiral. It boils down to whether the atoms within allow for superimposable symmetry or not. Inherently, a lack of plane symmetry within the molecular geometry fosters chirality.

Geometric Properties

Geometric properties are essential in discerning whether an object is chiral. Geometry guides the spatial arrangement of structures, influencing how they interact with their mirror images. Several points help in this determination:

• For example, a piece of A4 paper is geometric by design. Its edges and angles adhere to precise symmetrical properties, rendering it achiral as it can be perfectly aligned with its mirror image.
• On the other hand, a grand piano uses asymmetrical geometry, resulting in a unique design that does not support such superimposition, making it chiral.

Thus, the geometric properties, such as asymmetry and spatial arrangement, determine whether superimposition on a mirror image is possible. Any disruption in symmetry within these properties typically indicates chirality, where an object or molecule lacks a superimposable mirror image.