Question

When \((R)\)-2-butanol is left standing in aqueous acid, it slowly loses its optical activity. Account for this observation.

Short answer

Short Answer: The loss of optical activity in (R)-2-butanol when left in an aqueous acid occurs due to the formation of a racemic mixture. The acidic environment causes protonation of the hydroxyl group, forming a 2-butanolium ion. The positively charged ion is then attacked by water molecules, producing new (R) and (S) isomers. As the reaction reaches equilibrium, a racemic mixture containing equal amounts of (R) and (S) isomers is formed. These two isomers have equal and opposite effects on plane-polarized light, resulting in the loss of optical activity.

Step-by-step solution

Introduction of (R)-2-butanol

(R)-2-butanol is an optically active molecule due to the presence of a chiral carbon, which is a carbon atom bonded to four different groups. The chiral carbon in (R)-2-butanol is bonded to a hydroxyl group (-OH), an ethyl group (-CH2CH3), a methyl group (-CH3), and a hydrogen atom (-H).

Understand the acidic environment

When (R)-2-butanol is placed in an aqueous acid solution, the acidic environment would cause a protonation of the hydroxyl group (-OH) in (R)-2-butanol. This process is reversible and forms a 2-butanolium ion, an oxonium ion with a positively charged oxygen atom.

Rearrangement of 2-butanolium ion

The positive charge on the oxygen atom makes the 2-butanolium ion susceptible to nucleophilic attack by water molecules. The water molecule attacks the chiral carbon and results in the formation of a new (R) and (S) isomers. This process is also reversible.

Formation of a racemic mixture

As both the formation of 2-butanolium ion and the nucleophilic attack by water are reversible processes, the reaction will reach equilibrium, and both the (R) and (S) isomers will be present in the reaction mixture. This will result in a racemic mixture - a 50:50 mixture of (R) and (S) isomers of 2-butanol.

Loss of optical activity

Due to the formation of a racemic mixture containing equal amounts of (R) and (S) isomers, the optical activity of (R)-2-butanol is lost when it is left standing in aqueous acid. This is because the (R) and (S) isomers have an equal and opposite effect on the plane-polarized light; thus, the overall effect is a loss of optical activity.

Key concepts

Optical Activity

Optical activity is a fascinating phenomenon exhibited by certain molecules, which relates to their ability to rotate the plane of polarized light. When polarized light passes through a solution containing an optically active compound, the direction of the light's polarization is twisted. This rotation can occur in either a clockwise direction (referred to as dextrorotary or (+)) or counterclockwise (levorotary or (-)).

The degree of rotation depends on the molecular structure of the compound, the concentration of the compound in solution, and the length of the path that the light travels through the solution. The presence of chiral centers, typically carbon atoms with four different substituents, is one of the primary reasons certain molecules are optically active.

Chiral Carbon

A chiral carbon is central to the concept of optical activity. It is a carbon atom that is bonded to four different atoms or groups of atoms. The unique arrangement causes the molecule to be asymmetrical, making it impossible to superimpose on its mirror image, much like our left and right hands. This property defines chirality in organic chemistry.

Chiral carbons are responsible for the existence of enantiomers—non-superimposable mirror images of each other. Each enantiomer exhibits optical activity but in opposite directions. Therefore, if a solution contains equal amounts of both enantiomers, the net optical activity will be zero, as the rotations cancel each other out, creating what is known as a racemic mixture.

Racemic Mixture

A racemic mixture is an equimolar mixture of two enantiomers, which are molecules that are mirror images of each other but cannot be superimposed. In the context of optical activity, such a mixture displays no net rotation of plane-polarized light because the optical activities of the individual enantiomers cancel each other out.

In practice, the production of a racemic mixture can occur during a chemical reaction if there is an equal opportunity for the formation of both enantiomers. As the solution contains equal amounts of the left and right-handed forms, it is optically inactive. This phenomenon is critical in areas like pharmaceuticals, where the effectiveness and safety of a drug can depend on its chirality.

Nucleophilic Attack

Nucleophilic attack is a cornerstone of organic reaction mechanisms, where a nucleophile, an electron-rich species, targets a positively charged or electron-deficient carbon. This carbon, often a chiral center, can be found within a variety of functional groups such as alcohols, carbonyls, or alkyl halides.

In the case of racemization, the nucleophilic attack introduces a change in the configuration of the chiral carbon, converting an enantiomer into its mirror image. This could occur as part of a reaction within an acidic environment, where a chiral molecule like (R)-2-butanol can be converted into a racemic mixture, losing its original optical activity because the new configuration (S)-2-butanol is produced at an equal rate to the original (R)-2-butanol.