Question

Number of mesoforms possible for the compound \(\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{C}_{6} \mathrm{H}_{5}\) is

Short answer

The compound has 1 mesoform.

Step-by-step solution

Understanding Mesoform

A meso compound is a molecule with multiple stereocenters that is superimposable on its mirror image due to an internal plane of symmetry. It is achiral despite having chiral centers.

Identifying Chiral Centers in the Compound

In the compound \(\mathrm{C}_{6}\mathrm{H}_{5}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{C}_{6}\mathrm{H}_{5}\), each \(\mathrm{CHCl}\) group represents a chiral center because of the presence of four different substituents: \(\mathrm{Ph}\) (phenyl group), \(\mathrm{Cl}\), \(\mathrm{H}\), and the rest of the carbon chain.

Analyzing Symmetry in the Molecule

The compound is symmetric about the center of the carbon chain. The symmetry arises from the identical substituents on the two ends (\(\mathrm{C}_{6}\mathrm{H}_{5}-\mathrm{CHCl}\)) and the repetitions of \(\mathrm{CHCl}\) in the chain.

Count Mesoforms

Since the compound has an internal plane of symmetry, the configuration can mirror itself in terms of opposite stereochemistry at the chiral centers. By systematically analyzing configurations, it can be determined there is exactly one configuration that results in achiral (meso) form with opposite configurations on either side of the center making it superimposable on its mirror image.

Key concepts

Stereocenters

Stereocenters are crucial in understanding the geometry and potential reactivity of molecules. A stereocenter, often referred to as a stereogenic center, is an atom where the swapping of any two groups leads to a stereoisomer. Typically, these are carbon atoms bound to four different substituents. This diversity in attachments creates unique three-dimensional arrangements leading to different spatial configurations.
Stereocenters are the central players in the formation of chiral molecules and the concept of optical activity. When analyzing molecules, identifying these centers helps determine the number of possible isomers a compound can possess.
In the given compound \[ \text{C}_6\text{H}_5-\text{CHCl}-\text{CHCl}-\text{CHCl}-\text{CHCl}-\text{C}_6\text{H}_5 \] each \(\text{CHCl}\) segment has a stereocenter. Each of these segments involves a carbon atom bonded to four different entities: a phenyl group (Ph), a chlorine atom (Cl), a hydrogen atom (H), and the rest of the surrounding carbon chain. This configuration makes each \(\text{CHCl}\) spot capable of existing in distinct stereoisomer arrangements.

Chiral Centers

Chiral centers are a specific type of stereocenter that leads directly to chirality in a molecule. They form when a carbon atom is connected to four distinct substituents, and this non-superimposable nature gives rise to optical isomers known as enantiomers.
In essence, chiral centers are what makes a molecule 'handed', similar to how your left and right hands are mirror images, yet not superimposable.
In our compound, each \(\text{CHCl}\) unit acts as a chiral center. Although a chiral center typically indicates that the molecule has a mirror image which is not superimposable (making it optically active), the presence of an internal plane of symmetry can nullify overall chirality, resulting in a meso compound. Chiral centers without symmetry lead to enantiomeric pairs, while those with symmetry, as is the case here, can yield unique achiral isomers.

Internal Plane of Symmetry

An internal plane of symmetry divides a molecule into two mirror image halves. This concept is pivotal for identifying meso compounds, which despite having chiral centers, are achiral and optically inactive due to such symmetry.
In a meso compound, the configuration around the chiral centers are such that an internal mirroring plane makes the whole molecule appear as one half reflecting the other.
In the provided compound configuration: \[ \text{C}_6\text{H}_5-\text{CHCl}-\text{CHCl}-\text{CHCl}-\text{CHCl}-\text{C}_6\text{H}_5 \] this molecule exhibits symmetry around its central carbon chain. This symmetry especially arises from the repeating \(\text{CHCl}\) groups being identical in arrangement on either side of the molecular plane, ensuring the same spatial reflection from the center.

• The plane runs through the molecule such that each half mirrors the other.
• This balanced geometry makes the compound non-enantiomeric and ensures it remains a single meso form, as it effectively cancels out the individual chiralities of its centers.

Thus, while it has multiple stereocenters, the internal symmetry dominates to give only one achiral meso form.