Question

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

Short answer

The answer is (a) 6 total isomers, 4 optically active.

Step-by-step solution

Understand the formula and identify possible structures

The molecular formula given is \( \mathrm{C}_3\mathrm{H}_3\mathrm{Br} \). This suggests we need to consider possible isomers for a three-carbon chain with a bromine atom and unsaturation that fulfills the degree of unsaturation. With 3 carbon atoms, we can consider structures that have double bonds or rings.

Calculate the degree of unsaturation

The degree of unsaturation can be calculated as follows: \[ \text{Degree of Unsaturation} = 1 + \frac{1}{2}(2n_4+n_3-n_1+n_2) \] where \( n_4=3 \) (C), \( n_3 = 1 \) (Br), \( n_1 = 3 \) (H) and \( n_2 = 0 \) (X, where X is any extra group not included, \( \text{e.g., N, O} \)). This results in one degree of unsaturation, allowing either a double bond or a ring in the compound.

Identify possible isomers with given components

Based on the formula and a degree of unsaturation of 1, potential isomers include linear alkenes \((\mathrm{bromo}-\mathrm{propene})\), cyclic structures \((\text{bromocyclo-propane})\), and its configured analogs such as terminal alkene with variations in the position of bromine attachment. This gives: 1-bromo-1-propene, 2-bromo-1-propene, 3-bromo-1-propene, bromocyclopropane, and its sterically distinct forms if applicable based on side configurations.

Determine the optical activity of each isomer

Identify chiral centers in each structural isomer to determine its optical activity. For example, bromocyclopropane doesn't have a chiral center unlike 2-bromo-1-propene which can show chirality depending on its stereochemical structure as it can be arranged in a configuration that isn't superimposable mirror images, revealing at least two optically active isomers.

Count the total number of isomers and optically active compounds

With all configurations counted, four optically active compounds can be deduced from the structural possibilities in alkenes like the 2-bromo-1-propene isomer with capable stereochemistry, and there are total 6 potential isomers, including the cyclic structure, fulfilling two configurations in bromopropene: 2-bromo-1-propene and 2-bromocyclopropane.

Key concepts

Optical Activity

Optical activity refers to the ability of a compound to rotate the plane of polarized light. This property is observed in compounds that possess chiral centers. When light passes through a sample of an optically active compound, its plane of polarization is rotated either clockwise or counterclockwise.

To determine if a molecule is optically active, we need to look for chiral centers. Chiral centers are atoms in a molecule that are bonded to four different substituents, leading to non-superimposable mirror images, also known as enantiomers. For example, in the compound 2-bromo-1-propene, a chiral center could lead to different configurations that are optically active.

• Enantiomers: They possess opposite optical rotations.
• Diastereomers: They may or may not be optically active depending on their specific geometric arrangement.

In the given exercise, identifying the possible chiral centers in the isomers helped determine which forms are optically active. The presence of such centers in some configurations results in optical activity.

Degree of Unsaturation

The degree of unsaturation is a key concept in determining possible structures of a given molecular formula. It indicates how many rings or multiple bonds are present in a molecule.

The formula for calculating the degree of unsaturation is:\[\text{Degree of Unsaturation} = 1 + \frac{1}{2}(2n_4+n_3-n_1+n_2)\]where:

• \( n_4 \) = number of carbon atoms
• \( n_3 \) = number of monovalent atoms like hydrogen and halogens (e.g., Br)
• \( n_1 \) = number of hydrogen atoms
• \( n_2 \) = number of divalent atoms (extra elements like oxygen or nitrogen)

For the molecular formula \( \mathrm{C}_3\mathrm{H}_3\mathrm{Br} \), plugging into the formula gives a degree of unsaturation of 1. This tells us that the compound could have either a double bond or a ring structure.
Understanding the degree of unsaturation allows chemists to visualize what types of isomers may exist for a given molecular setup.

Chiral Centers

Chiral centers are pivotal in organic chemistry as they determine the stereochemistry and resultant optical activity of a compound. A chiral center is typically a carbon atom bonded to four different groups. The resulting spatial arrangement makes two possible non-superimposable mirror-image forms, called enantiomers.

In organic molecules, especially those with potential optical activity, identifying chiral centers is crucial. For instance, in 2-bromo-1-propene, the second carbon can potentially serve as a chiral center depending on the surrounding substituents. The arrangement leads to distinct isomers with different optical activities.

• Chirality results in distinct stereoisomers known as enantiomers.
• Molecules with one or more chiral centers often show different physical properties even though they share the same molecular formula.

Chiral centers greatly influence both the physical properties and the chemical behavior of compounds, making their identification essential in stereochemistry.

Structural Isomers

Structural isomers are compounds that share the same molecular formula but differ in the connectivity of the atoms. This difference can greatly affect the chemical properties and reactivity of the molecules.

In the context of \( \mathrm{C}_3\mathrm{H}_3\mathrm{Br} \), a variety of structural isomers can be constructed, each with a unique arrangement of carbon, hydrogen, and bromine atoms. Key structural isomers for this formula include:

• Bromo-alkenes such as 1-bromo-1-propene and 2-bromo-1-propene with different bromine placements.
• Cyclic structures such as bromocyclopropane, where the atoms form a ring.

Understanding these different types of structural isomers is critical to grasp the diverse chemical possibilities that can arise from a single set of atoms. These variations can lead to differences in boiling points, stability, and reactivity between isomers.