Question

Composition of mixture at which observed rotation of mixture is maximum is (A) \(100 \%\) racemisation (B) \(20 \%\) racemisation \(+80 \%\) retention (C) \(50 \%\) retention \(+50 \%\) inversion (D) \(20 \%\) retention \(+80 \%\) racemisation

Short answer

The composition of the mixture at which the observed rotation of the mixture is maximum is (B) \(20 \%\) racemisation \(+80 \%\) retention.

Step-by-step solution

Analyzing Each Option

In option (A), a net rotation of zero is observed, because, in the racemic mixture, the rotations by the two enantiomers cancel out each other. Option (B) proposes a composition of a 20% racemic mixture (which contributes zero rotation) and 80% retention product (which holds on to its initial rotation). It means that the net observed rotation would be 80% of the total rotation in the pure compound. Option (C) suggests a 50-50 proportion of the retention and inversion products. Since the inversion process inverts the initial configuration and therefore changes the sign of rotation, the net observed rotation would be zero here. Option (D) proposes a composition of a 20% retention product (contributing 20% of the initial rotation) and an 80% racemic mixture (contributing a net rotation of zero). So, the net observed rotation is 20% of the total rotation in the pure compound.

Comparing The Contributions To Net Rotation In Each Option

Among the four options, (B) mentions a composition that contributes 80% of the initial rotation, which is highest among the provided options. Hence, option (B) must be the correct answer. In option (A), (C), and (D), the net observed rotations contribute 0%, 0%, and 20% of the initial rotation, respectively, which are less than the contribution in option (B). Hence, option (B) provides the mixture composition that gives the maximum observed rotation.

Final Answer

The composition of the mixture at which the observed rotation of the mixture is maximum is (B) \(20 \%\) racemisation \(+80 \%\) retention.

Key concepts

Racemisation

Racemisation is a chemical process by which an optically active compound, or one that rotates plane-polarized light, is converted into a racemic mixture. A racemic mixture is a 50:50 blend of two enantiomers – molecules that are mirror images of each other but cannot be superimposed. Each enantiomer rotates plane-polarized light to the same magnitude but in opposite directions, which means the mixture exhibits no optical activity.

Understanding racemisation is crucial when studying the behavior of optically active mixtures. In the context of our exercise, a solution with a high degree of racemisation would not contribute to the overall optical rotation of the mixture. This is because the equal presence of enantiomers, each rotating the light in opposite ways, results in no net rotation. Thus, racemisation can decrease the observed optical activity in a mixture.

Optical Isomerism

Optical isomerism is a form of stereoisomerism where molecules exist in two isomeric forms that are non-superimposable mirror images of one another, known as enantiomers. These isomers possess the characteristic of rotating plane-polarized light, a phenomenon referred to as optical activity.

An enantiomer that rotates light to the right is known as a 'dextrorotatory' or 'd-form', and one that rotates light to the left is termed 'levorotatory' or 'l-form'. The degree to which these isomers rotate light can be measured using polarimetry, and it's crucial for applications such as determining the purity of a substance and its concentration in a mixture. For students and chemists, understanding optical isomerism is essential for predicting the properties and reactions of chiral molecules in pharmaceuticals and organic reactions.

Enantiomers

Enantiomers are a type of stereoisomer that consist of chiral molecules with non-superimposable mirror images. This chirality results in each enantiomer having different interactions with other chiral molecules and with plane-polarized light. Enantiomers have the same physical and chemical properties in an achiral environment—such as melting point or solubility—but differ in a chiral environment and in their interaction with plane-polarized light.

In our textbook exercise, the distinction between enantiomers is critical for determining the mixture's observed optical rotation. The mixture’s rotation changes depending on the proportion of each enantiomer present. The concept helps explain why option (B) in the exercise yields the most significant observed rotation: it contains a greater proportion of one enantiomer, leading to 'retention' of the original compound's optical rotation, as opposed to the 'inversion' or equal proportions that would negate the rotation.