Problem 160 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

The compound has 1 meso form.

Step 1: Understand the Compound Structure

The compound given is \( \mathrm{C}_{6}\mathrm{H}_{5}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{C}_{6}\mathrm{H}_{5} \). This chain of carbon atoms with chlorine substituents means that we need to consider the stereochemistry that each chlorine introduces.

Step 2: Analyze Symmetry

This compound has two phenyl groups (\( \mathrm{C}_{6}\mathrm{H}_{5} \)) at each end, and four chiral carbons in the central chain. The potential for meso forms arises from the compound's ability to be superimposed on its mirror image when an internal plane of symmetry is present in certain configurations.

Step 3: Determine Chirality and Enantiomers

Each \( \mathrm{CHCl} \) unit is stereocentric, meaning it can have two configurations: \( R \) or \( S \). We must assess each stereocenter's configuration and its mirror, then look for the pair that offers internal symmetry.

Step 4: Identify Meso Forms

A meso compound occurs when the molecule has stereocenters but also has an internal plane of symmetry making it achiral. Closing this symmetry requires specific pairs of configurations. Here, this occurs when the configurations of stereocenters are such that you can divide the molecule into two symmetrical parts from left to right.

Step 5: Count the Mesoforms

Examine the configurations: \( (RSRS) \) or \( (SRSR) \) among others. Because these can be superimposed over their mirror image due to symmetry, they qualify as meso forms. There can be only one unique such symmetric reflection that ensures a non-chiral, optically inactive state.

Key Concepts

Stereochemistry

Stereochemistry is a fascinating branch of chemistry that deals with the spatial arrangement of atoms in molecules. It particularly focuses on how this arrangement affects the physical and chemical properties of a substance. In our compound, \[ \mathrm{C}_{6}\mathrm{H}_{5}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{C}_{6}\mathrm{H}_{5} \] stereochemistry comes into play because each chlorine atom attached to a carbon atom can induce different spatial orientations, known as configurations.

• These unique arrangements do not require the breaking of bonds but simply involve the different possible orientations.
• Understanding these arrangements helps us differentiate between molecular forms, such as enantiomers and meso compounds.

For molecules with multiple stereocenters, stereochemistry becomes vital for predicting how the substance will interact under various conditions.

Chirality

Chirality is a core concept in stereochemistry describing objects or molecules that cannot be superimposed on their mirror images. These objects are said to be chiral, much like left and right hands.
In chemistry, chirality is critical because it affects how molecules react and interact with various biological systems. Our compound has four chiral centers: each of these carbon atoms bonded to a chlorine and differing groups form chiral centers.

• Each chiral center can have one of two configurations, denoted as \(R\) (rectus, or right) or \(S\) (sinister, or left).
• For a molecule to be chiral, it must exist in two non-superimposable mirror image forms called enantiomers.

However, when there is an internal plane of symmetry, chirality may be canceled out, revealing a different type of compound known as a meso compound.

Internal Plane of Symmetry

The internal plane of symmetry is an imaginary plane that bisects a molecule into two mirror-image halves. For our compound, \[ \mathrm{C}_{6}\mathrm{H}_{5}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{CHCl}-\mathrm{C}_{6}\mathrm{H}_{5} \] an internal plane of symmetry would render the chiral centers' effects on optical activity as null.
Identifying this plane is crucial when determining if a compound is a meso compound:

• An internal plane of symmetry suggests that the molecule has symmetric stereocenter arrangements, potentially rendering it achiral overall.
• This symmetry can override local chirality by balancing the different stereocenter configurations.

In essence, the internal plane simplifies the symmetrical interaction between stereocenters, resulting in a molecule that is achiral even though it has chiral centers.

Stereocenter Configurations

Stereocenters are pivotal points within a molecule where the spatial arrangement of substituents can lead to multiple configurations. Each \(\mathrm{CHCl}\) unit in our compound is a stereocenter, and the placement of chlorine atoms can give two possible configurations for each: the \(R\) or \(S\).

• Simply put, a stereocenter's configuration describes the three-dimensional arrangement of its attached groups.
• In compounds with multiple stereocenters, different combinations of these \(R\) and \(S\) configurations produce a wide range of stereoisomers, some of which may be meso forms.

When viewed together, a compound's stereocenters can interact to create a specific overall symmetry, potentially leading to optical inactivity despite having individual sites of chirality. In this context, examining (RSRS) and (SRSR) configuration patterns reveals two meso forms that share a crucial internal symmetry.