Problem 79 - 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. What is the enantiomeric excess (ee.) of the major enantiomer relative to the minor enantiomer? (a) 70 per cent (b) 700 per cent (c) 75 per cent (d) \(87.5\) per cent

Step-by-Step Solution

Answer

The enantiomeric excess of the major enantiomer is 75%.

Step 1: Understand Enantiomeric Excess

Enantiomeric excess (ee) is calculated by the formula: \( ee = \frac{|R - S|}{R + S} \times 100 \% \), where \( R \) and \( S \) are the percentages of the two enantiomers (R and S). In this problem, you have a reaction mixture containing 70% of the original enantiomer, 10% of its opposite enantiomer, and 20% of a meso compound.

Step 2: Calculate Total Enantiomer Percentage

Since the meso form is achiral, we focus only on the enantiomers. Therefore, the total percentage of enantiomers present is the sum of the enantiomer percentages: \( 70\% + 10\% = 80\% \).

Step 3: Determine Absolute Difference

The absolute difference between the two enantiomers is calculated as \( |70\% - 10\%| = 60\% \). This difference will help us calculate the enantiomeric excess.

Step 4: Calculate Enantiomeric Excess

Use the formula for enantiomeric excess: \[ ee = \frac{|70\% - 10\%|}{70\% + 10\%} \times 100 \% = \frac{60\%}{80\%} \times 100 \% = 75\% \]. Thus, the enantiomeric excess of the major enantiomer is 75%.

Key Concepts

Tartaric Acid

Tartaric acid is an important organic compound, widely used in various chemical and industrial applications. Its molecular formula is \((C_4H_6O_6)\), and it is naturally occurring, most commonly found in plants such as grapes and bananas. Tartaric acid is a key component in winemaking, as it contributes to the acidity and stability of wine.
This compound is also notable for its chiral properties, which means it never appears in a single molecular configuration. Instead, it can exist in various stereoisomeric forms, most commonly in its dextro (d-) and levo (l-) enantiomers, and the meso form. The optical activity of tartaric acid is pivotal in understanding its applications and reactions, particularly in stereochemistry and catalysis.

Chiral Compounds

Chiral compounds are molecules that lack an internal plane of symmetry, allowing them to exist in two non-superimposable mirror images called enantiomers. Each enantiomer of a chiral compound will rotate plane-polarized light to the same degree but in opposite directions.
These properties make chiral compounds particularly significant in the field of organic chemistry. They are crucial in pharmaceuticals, as each enantiomer of a drug may have different biological effects, making the study of these compounds vital for drug efficacy and safety.

• Enantiomers rotate the polarized light equally but in opposite directions, one clockwise and the other counterclockwise.
• The presence of chirality is often due to a carbon atom bonded to four different groups.
• Examples include amino acids, sugars, and certain acids like tartaric acid.

Chirality profoundly influences molecular interactions, making it a fundamental aspect of molecular biology and chemistry.

Isomerization Reaction

Isomerization reactions are processes where a molecule is transformed into another molecule with the same atoms but a different arrangement, thus changing its properties. This can create structural isomers, stereoisomers, or other forms, affecting the molecule's physical and chemical characteristics.
In the context of tartaric acid, the isomerization reaction resulted in a change in the distribution of its stereoisomers: converting a percentage of one enantiomer into its opposite, and forming a meso compound.

• Isomerization does not change the empirical formula of the molecule.
• It can significantly impact the compound's reactivity and interaction with other molecules.
• Such reactions are reversible, allowing conversion between different isomers under specific conditions.

These reactions are crucial in various industrial applications, ranging from the synthesis of pharmaceuticals to the optimization of chemical processes.

Optical Activity

Optical activity refers to the ability of certain substances to rotate the plane of polarized light. This property is a hallmark of chiral molecules and is measured using a device called a polarimeter. The angle by which the light is rotated is known as the optical rotation, denoted as \([\alpha]_D^{20}\) for specific conditions.
For tartaric acid, its optical activity is largely due to the presence of chiral centers within its molecular structure. Different enantiomers will rotate light by varying degrees.

• The degree of rotation depends on the concentration of the compound, the length of the sample cell, and the wavelength of light used.
• Dextrorotatory compounds rotate the light clockwise, while levorotatory ones rotate it counterclockwise.
• Optical rotation is a fundamental property used to characterize chiral substances and distinguish between enantiomers.

Understanding optical activity is essential in many scientific fields, including analytical chemistry and pharmacology.