Question

\((\pm)-2\)-bromobutane indicates (A) Meso compound (B) \(80 \%\) (+)-2-bromobutane and \(20 \%(-)-2\)-bromobutane (C) \(75 \%(+)-2\)-bromobutane and \(25 \%(-)-2\)-bromobutane (D) Equal amount of \((+)-2\)-bromobutane and \((-)-2\)-bromobutane

Short answer

(D) Equal amount of \((+)-2\)-bromobutane and \((-)-2\)-bromobutane

Step-by-step solution

Understand the notation

First, let's understand the given notation \((\pm)-2\)-bromobutane. The '\((\pm)\)' symbol is used to indicate that the compound is a racemic mixture, which means it contains equal amounts of both the enantiomers (optical isomers) of a chiral molecule.

Enantiomers

Enantiomers (optical isomers) are pairs of molecules that are non-superimposable mirror images of each other. They have identical physical and chemical properties except for their effect on plane-polarized light. \((+)\) denotes the molecule that rotates plane-polarized light clockwise (dextrorotatory), and \((-)\) denotes the molecule that rotates it counterclockwise (levorotatory).

Analyzing the given options

Now let's analyze the given options: (A) Meso compound: A meso compound is a molecule that has chiral centers but is optically inactive due to an internal plane of symmetry. This is not true for a racemic mixture, so this option is incorrect. (B) \(80 \%\) (+)-2-bromobutane and \(20 \%(-)-2\)-bromobutane: This option suggests an unequal distribution of enantiomers, which is not the case for a racemic mixture. So, this option is incorrect. (C) \(75 \%(+)-2\)-bromobutane and \(25 \%(-)-2\)-bromobutane: Like option (B), this option also suggests an unequal distribution of enantiomers, which is not the case for a racemic mixture. So, this option is incorrect. (D) Equal amount of \((+)-2\)-bromobutane and \((-)-2\)-bromobutane: This option indicates that the compound contains an equal amount of both enantiomers, which is the definition of a racemic mixture. Therefore, this option is correct. So, the correct answer is (D) Equal amount of \((+)-2\)-bromobutane and \((-)-2\)-bromobutane.

Key concepts

Optical Isomers

Optical isomers, also known as stereoisomers, are molecules that have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This difference in spatial arrangement means that, while they may contain the same atoms, those atoms are connected in such a way that the isomers cannot be superimposed onto one another, much like your left and right hands.

These isomers have unique optical properties. When polarized light passes through a substance containing optical isomers, the plane of polarization can be rotated. This effect is fundamental to understanding the behavior of racemic mixtures, as the rotation caused by one isomer will be countered by its optical isomer counterpart, leading to no net change in the plane of polarized light when both are present in equal amounts.

Enantiomers

Enantiomers are a pair of optical isomers that are mirror images of each other but cannot be superimposed, just like left and right hands. In chemistry, the existence of enantiomers is evidence of 'chirality' in molecules. Enantiomers have the same physical and chemical properties in a non-chiral environment—such as melting point, boiling point, and solubility—but they differ dramatically in chiral environments, including biological systems, and when interacting with plane-polarized light.

In a racemic mixture, you have a 1:1 ratio of these two enantiomers, which causes the optical rotations due to each enantiomer to cancel each other out, making the mixture optically inactive. This is an essential concept in the pharmaceutical industry, as different enantiomers of a drug can have very different biological effects.

Chiral Molecules

Chiral molecules are central to the study of enantiomers and optical activity. Chirality in molecules occurs when a carbon atom (or any other tetrahedral atom) is attached to four different groups or atoms. This tetrahedral center is known as a chiral center or a stereocenter. The property of chirality is not just limited to individual molecules; it can also be a property of several atoms within a more complex molecule.

Now, chiral molecules are unique because their mirror images (enantiomers) cannot be superimposed on each other. Importantly, unless they are in a racemic mixture, chiral molecules will rotate plane-polarized light to either the left (levorotation) or the right (dextrorotation), and this property is used to distinguish between the two types of enantiomers. However, for substances with multiple chiral centers, some can be both chiral and symmetrical - these are known as meso compounds, which are optically inactive despite having chiral centers.

Plane-Polarized Light

Plane-polarized light is light that has been filtered so that all of its waves are oscillating in the same plane. Ordinary light is composed of waves oscillating in all directions perpendicular to the direction of propagation. When this light passes through a polarizer, however, it is transformed so that it vibrates in only one direction.

Chiral molecules interact with plane-polarized light by rotating its plane of polarization—a property called optical rotation. Scientists use instruments called polarimeters to measure this effect and thus distinguish between different enantiomers. The direction and degree of rotation are key to identifying specific compounds and their purity. A racemic mixture, having equal amounts of left and right rotating enantiomers, will have no net effect on plane-polarized light, because the rotations due to each enantiomer will negate one another.