Problem 80 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

Suppose, a sample of an initially pure single enantiomer of tartaric acid \([\alpha]_{D}^{20}=+12.4^{\circ}\left(\mathrm{H}_{2} \mathrm{O}\right)\) underwent a chemical isomerization reaction which yielded 10 per cent of the other enantiomer and 20 per cent of the meso isomer, in addition to 70 per cent of the unchanged starting compound. If \(1.0 \mathrm{~g}\) of the total mixture (including the meso isomer) was dissolved in \(1 \mathrm{~mL}\) water and the rotation measured in a \(1 \mathrm{dm}\) cell, what value of \(\alpha_{\mathrm{D}}\) would one expect to observe? (a) \(+9.92\) (b) \(+7.44 \mathrm{C}\) (c) \(+12.4\) (d) \(+8.68\)

Step-by-Step Solution

Answer

The value of \(\alpha_{D}\) is \(+7.44^\circ\).

Step 1: Understand the Problem

We need to find the observed optical rotation \(\alpha_{D}\) for a mixture of enantiomers and a meso compound. The process involved an initially pure enantiomer undergoing a partial conversion.

Step 2: Identify Initial Conditions

The pure enantiomer has a specific rotation of \(+12.4^\circ\) in water. The initial mixture consists of 70% of the original enantiomer, 10% of the opposite enantiomer, and 20% meso isomer.

Step 3: Calculate Contribution of Each Enantiomer

Calculate the contribution to optical rotation from each part of the mixture:- 70% of the starting enantiomer: \(0.7 \times 12.4^\circ = +8.68^\circ\)- 10% of the opposite enantiomer (which will have an equal but opposite rotation): \(-0.1 \times 12.4^\circ = -1.24^\circ\)- Meso compound does not contribute to optical rotation as it is achiral.

Step 4: Sum Contributions

Add up the contributions to find the total observed optical rotation:\[\alpha_{D} = 8.68^\circ - 1.24^\circ = 7.44^\circ\]

Step 5: Verify Solution Steps

Verify each contribution and calculation step to ensure the sum results in a correct manipulation of positive and negative rotations.

Key Concepts

Enantiomers

Enantiomers are a fascinating concept in the world of chemistry. They are pairs of molecules that are non-superimposable mirror images of each other. Think of them like your left and right hands. Though they look similar, when you try to place one on top of the other, they don't align perfectly. This unique property is called chirality.

• Enantiomers often have identical physical properties like melting and boiling points.
• However, they can rotate plane-polarized light in opposite directions.
• In the context of the exercise, one enantiomer of tartaric acid rotates light in one direction, while the other does so in the opposite direction.

The challenge in exercises like this often involves calculating the net optical effect of a mixture containing different enantiomers and other forms, such as meso compounds, which we'll explore more next.

Specific Rotation

Specific rotation is a crucial measurement in studying chiral substances. It helps us understand how much a particular enantiomer can rotate plane-polarized light. In the formula,\[[\alpha] = \frac{\alpha}{l \times c}\]- \([\alpha]\) is the specific rotation.- \(\alpha\) is the observed rotation in degrees.- \(l\) is the length of the light path (usually in decimeters).- \(c\) is the concentration of the sample (in grams per mL).

For tartaric acid, this specific rotation is \[\alpha_{D}^{20}=+12.4^{\circ}\] meaning under standard conditions, it rotates light to the right (+). Specific rotation is essential for distinguishing and analyzing mixed substances, especially when compound mixtures, like in this exercise, involve isomerisation reactions.

Isomerization Reaction

Isomerization reactions involve the structural rearrangement of molecules, turning them into an isomer with the same molecular formula but different connectivity or spatial arrangement. In the exercise, an initially pure enantiomer undergoes this type of reaction forming:

• The opposite enantiomer: this alters the optical activity of the mixture.
• A meso isomer: known for not contributing to optical activity.

These reactions are critical in organic chemistry since they can convert active molecules into inactive forms, or vice versa, influencing the overall properties and behavior of the mixture.

Meso Isomer

A meso isomer is a special type of isomer that appears as if it could be chiral due to having multiple stereocenters, yet it is achiral overall. This achirality results from an internal plane of symmetry neutralizing its optical activity. Tartaric acid, used in the exercise, has a meso form expected to result in no net optical rotation: its internal symmetry balances the effects of its stereocenters.

• Meso isomers contribute no optical rotation, making them distinct in mixtures with active enantiomers.
• They help scientists establish unambiguous optical activity measures from multiple-isomer samples.

In exercises, knowing the meso form's impact is crucial for correctly calculating total optical rotation of a mixture.

Chiral Compounds

Chiral compounds are molecules that exhibit chirality, meaning they have a non-superimposable mirror image due to a lack of symmetry. This property of chirality is central to enantiomers and determines the way molecules interact with polarized light. Many organic compounds are chiral due to the presence of a carbon atom bonded to four different groups, often termed a stereocenter.

• Chirality is a foundational concept for enantioselectivity in chemical reactions, especially important in pharmaceuticals where different enantiomers can have vastly different biological effects.
• It plays a key role in understanding optical activity, defined as a chiral compound's ability to rotate polarized light either to the left or right.

This concept underscores the whole exercise as we see how mixtures of chiral and achiral compounds result in specific optical rotations.