Question

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

Short answer

Question: Explain the loss of optical activity in (R)-2-butanol when left standing in an aqueous acid. Answer: The loss of optical activity in (R)-2-butanol when left standing in an aqueous acid occurs due to racemization. Racemization is a reaction in which (R)-2-butanol is converted to a mixture of equal amounts of (R)-2-butanol and (S)-2-butanol (its enantiomer) through a protonation-deprotonation process. Since these two enantiomers have equal and opposite rotations of plane-polarized light, they cancel each other out when present in equal concentrations, resulting in an optical rotation of zero. This leads to the loss of optical activity in the racemic mixture.

Step-by-step solution

Identify the chiral center in \((R)-2\)-butanol

The molecular formula of \((R)-2\)-butanol is C\(_4\)H\(_{10}\)O, and its structure is CH\(_3\)CH(OH)CH\(_2\)CH\(_3\). The chiral center is the carbon atom (C2) that is connected to the hydroxyl group (OH), as it is connected to four different groups: hydrogen (H), hydroxyl group (OH), methyl group (CH\(_3\)), and ethyl group (CH\(_2\)CH\(_3\)). This chiral center gives the molecule its optical activity.

Write the reaction of \((R)-2\)-butanol with aqueous acid

When \((R)-2\)-butanol is left standing in aqueous acid, it undergoes a reaction called racemization. In this reaction, \((R)-2\)-butanol is converted to a mixture of equal amounts of \((R)-2\)-butanol and \((S)-2\)-butanol (its enantiomer) through a protonation-deprotonation process: CH\(_3\)CH(OH)CH\(_2\)CH\(_3\) + H\(_3\)O\(^+\) \(\rightleftharpoons\) CH\(_3\)C(OH\(_2$$^+\))CH\(_2\)CH\(_3\) \(\rightleftharpoons\) CH\(_3\)CH(O\(^-\))CH\(_2\)CH\(_3\) + H\(_3\)O\(^+\) Here, the \((R)-2\)-butanol initially forms a protonated intermediate that is achiral, as the hydroxyl group loses its priority (replaced by a positive charge), and then deprotonates to form the \((S)-2\)-butanol.

Explain the loss of optical activity

The racemization of \((R)-2\)-butanol to a mixture of \((R)-2\)-butanol and \((S)-2\)-butanol under aqueous acidic conditions results in the loss of optical activity. Since these two enantiomers have equal and opposite rotations of plane-polarized light, they cancel each other out when present in equal concentrations, resulting in an optical rotation of zero. Thus, the mixture of enantiomers is called a racemic mixture, and it has no optical activity.