Question

Total number of isomers and optically active compounds in the isomers of \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br}\) are (a) 6,4 (b) 5,3 (c) 3,5 (d) 8,3

Short answer

There are 5 isomers and 3 optically active compounds.

Step-by-step solution

Determine Types of Isomers

For the given molecular formula \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), consider possible structural isomers including chain isomers, position isomers, and stereoisomers. These types of isomers vary by the arrangement of the carbon backbone, the position of the bromine atom, or the spatial arrangement.

Identify Chain and Position Isomers

The primary carbon backbone structures possible for \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \) are as follows:1. Propene with a bromine substituent: \( \text{Br}-\mathrm{CH}_2\mathrm{CH}=\mathrm{CH}_2 \) - Bromine can be attached at the 1st or 2nd position: 1-bromopropene, 2-bromopropene.2. Cyclopropyl Bromide: Bromine attached to a cyclopropane ring: \( \mathrm{C}_3\mathrm{H}_4\) ring with one Br.This gives us 3 chain and position structural isomers: 1-bromopropene, 2-bromopropene, and cyclopropyl bromide.

Determine Stereoisomers

For stereoisomers, consider the configurational isomers: 1. Trans and cis forms where double bonds exist within the propene structure for 1-bromopropene and 2-bromopropene. Thus, consider cis and trans for propene derivatives if applicable. 1-bromopropene does not have cis/trans isomers due to lack of differentiation between methyl and hydrogen on the end carbon. 2-bromopropene has cis/trans isomers.

Count All Isomers

Now, counting all forms: - 1-bromopropene (1) - 2-bromopropene (cis and trans) (2) - Cyclopropyl bromide (1) Total: 5 isomers.

Identify Optically Active Compounds

Optically active compounds are those which can rotate the plane of polarized light, typically containing a chiral center. Looking at the structures: - Only 1-bromopropene can be analyzed for chirality. However, it has no chiral center without considering special substitutions. - 2-bromopropene exhibits geometric isomerism but no chirality under typical hydrocarbon arrangements. - Cyclopropyl bromide is not chiral. None of the basic structures shows chiral centers under standard expectations, assuming no other hidden complexities.

Key concepts

Structural Isomers

Structural isomers share the same molecular formula yet differ in their structural connectivity. In the context of organic chemistry, these differences arise from varying the arrangement of atoms within a molecule. When exploring the structural isomers of the formula \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), we examine two main groups: chain isomers and position isomers.

• **Chain isomers:** These involve altering the main carbon chain structure without changing the molecular formula.
• **Position isomers:** Here, the position of a functional group changes—such as changing the position of the bromine atom on the carbon chain.

For \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), viable structures include 1-bromopropene, 2-bromopropene, and cyclopropyl bromide, each with distinct structural arrangements.

Stereoisomers

Stereoisomers have the same molecular formula and connectivity of atoms but differ in spatial orientation. They come in two flavors: geometric isomers and optical isomers. Unlike structural isomers, the configuration of atoms differs without altering their sequence along the chain.
Geometric isomers occur in compounds with restricted rotation, typically around double bonds or within ring structures. For \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), stereoisomerism is crucial due to the presence of double bonds in 2-bromopropene, which leads to distinct cis and trans forms. Consequently, stereoisomers help elucidate the versatile nature of organic molecules.

Optical Isomerism

Optical isomerism stems from the presence of chiral centers in molecules, leading to non-superimposable mirror images. Such isomers are known as enantiomers, and they play a vital role in chemistry because they interact differently with plane-polarized light.
For \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), examining optical activity involves searching for chiral centers, a carbon atom bonded to four different groups. As the exercise notes, neither 1-bromopropene, 2-bromopropene, nor cyclopropyl bromide exhibit such asymmetry in their basic structures. Therefore, optical isomerism doesn't apply directly to these molecules without additional complexity, like substituents.

Chirality

Chirality refers to a property of asymmetry where a molecule and its mirror image are not identical. Think of it like your hands; no matter how you arrange them, they do not perfectly align. This asymmetry is crucial for optical activity.
A molecule shows chirality if it contains a chiral center, typically a carbon atom bonded to four non-identical groups. It results in two stereoisomers, known as enantiomers, which can rotate polarized light in different directions.
In the case of \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), despite being analyzed for chirality, typical representations like 1-bromopropene do not have chiral centers due to symmetrical groupings around their carbon atoms. Therefore, without additional influences, these molecules cannot be classified as chiral.

Geometric Isomers

Geometric isomers, a subtype of stereoisomers, are formed from compounds with restricted rotational capabilities like double bonds or ring structures. This constraint leads to molecules that can have different spatial arrangements of atoms.
For \( \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{Br} \), the double bond environment in 2-bromopropene allows for such variation, leading to cis and trans isomers.

• **Cis Isomers:** where substituents are on the same side of the double bond or ring.
• **Trans Isomers:** where substituents are on opposite sides.

Geometric isomers can significantly influence the physical and chemical properties of substances. However, they do not inherently affect chirality unless a chiral center is also present.