Problem 73 - Advanced Problems in Organic Chemistry for Competitive Examinations

Question

The enantiomeric excess and observed specific rotation of a mixture containing \(6 \mathrm{~g}\) of \((+)-2\) -butanol and \(4(\mathrm{~g})\) of \((-)-2\) -butanol are respectively (If the specific rotation of enantiomerically pure \((+)-2\) -butanol is \(+13.5\) units) (a) \(80 \%\), \(+2.7\) unit (b) \(20 \%,-27\) unit (c) \(20 \%,+2.7\) unit (d) \(80 \%\), \(-27\) unit

Step-by-Step Solution

Answer

(c) 20%, +2.7 unit

Step 1: Determine Total Mass

Calculate the total mass of the mixture, which is the sum of the masses of \( (+)-2 \ ext{-butanol} \) and \( (-)-2 \ ext{-butanol} \). Total Mass = 6 g + 4 g = 10 g.

Step 2: Calculate Mole Fraction of Each Enantiomer

Determine the mole fraction of each enantiomer by dividing their respective masses by the total mass. Mole fraction of \( (+)-2 \ ext{-butanol} \) = \( \frac{6}{10} = 0.6 \). Mole fraction of \( (-)-2 \ ext{-butanol} \) = \( \frac{4}{10} = 0.4 \).

Step 3: Compute Enantiomeric Excess (ee)

The enantiomeric excess is the absolute difference between the mole fractions of the enantiomers, then presented as a percentage.\[ ee = \left| 0.6 - 0.4 \right| \times 100\% = 20\% \]

Step 4: Calculate Observed Specific Rotation

The observed specific rotation is calculated using the formula \( [\alpha]_{\text{obs}} = ee \times [\alpha]_{\text{pure}} \).Since \( (+)-2 \ ext{-butanol} \) is in excess:\[ [\alpha]_{\text{obs}} = \frac{0.2}{1.0} \times (+13.5) = +2.7 \] units.

Step 5: Identify Correct Answer

From the calculations, the enantiomeric excess is \( 20\% \) and the observed specific rotation is \( +2.7 \) units. Therefore, the correct answer is option (c) \( 20\%, +2.7 \) unit.

Key Concepts

Understanding Specific Rotation

Specific rotation is a fundamental concept in understanding how certain substances interact with polarized light. It refers to the measure of how much a chiral compound can rotate the plane of polarized light as it passes through it. When polarized light enters a solution containing these chiral substances, it rotates either to the right, called dextrorotatory

• expressed as a positive value

or to the left, called levorotatory

• expressed as a negative value

The magnitude of this rotation depends on several factors:

• the nature of the compound itself
• the concentration of the compound in the solution
• the length of the path through which the light travels

Understanding specific rotation helps chemists determine the composition and purity of optical isomers in a mixture, as it provides insights into the predominance and configuration of enantiomers present.

Deciphering Enantiomers

Enantiomers are fascinating chemical structures that are mirror images of each other, much like your left and right hands. These molecules share the same molecular formula and sequence of bonded atoms but differ in three-dimensional orientation. This unique characteristic gives rise to different configurations known as optically active isomers. Enantiomers can exert a profound effect in various chemical and biological environments, mainly because they can interact with other chiral entities differently because of their spatial arrangement. In nature and synthetic chemistry, differentiating between enantiomers can be crucial because they might possess distinct chemical properties, react differently with various enzymes, or have different effects in biological systems. Recognizing the importance of enantiomers in a chemical mixture is part of determining enantiomeric excess, which describes how much one enantiomer is present in greater proportion than the other. This directly influences the observed optical activity of the solution where the enantiomer concentration imbalance is quantified.

Exploring Optical Activity

Optical activity is a property of chiral substances, where these substances have the ability to rotate the plane of polarized light. This concept is central to not only chemistry but also fields like pharmacology and materials science. When a compound is optically active, it means that the interaction of chiral molecules with polarized light results in optical rotation, which can be measured and analyzed. This rotation can be measured using a polarimeter, and it provides invaluable information about the purity and concentration of enantiomers in a sample. Optically active compounds are categorized based on their rotation behavior:

• Dextrorotatory compounds rotate light to the right, denoted by a positive sign.
• Levorotatory compounds rotate light to the left, denoted by a negative sign.

These measurements help identify unknown compounds and check the quality of synthesized chiral products. The degree of optical activity can also indicate disparities in enantiomeric compositions, providing clues about the enantiomeric excess of mixtures.