A solution of pure (S)-2-iodobutane ([α] = +15.90° ) in acetone is allowed to react with radioactive iodide, 131I-, until 1.0% of the iodobutane contains radioactive iodine. The specific rotation of this recovered iodobutane is found to be +15.58°. a. Determine the percentages of (R)- and (S)-2-iodobutane in the product mixture.

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Identify the initial specific rotation of pure (S)-2-iodobutane, which is given as +15.90°.

Recognize that the specific rotation of the recovered iodobutane is +15.58°, indicating a mixture of (R)- and (S)-2-iodobutane.

Use the formula for enantiomeric excess (ee): ee = (observed specific rotation / specific rotation of pure enantiomer) * 100% to find the enantiomeric excess of the mixture.

Calculate the percentage of the major enantiomer (S)-2-iodobutane using the enantiomeric excess: %S = (ee + 100) / 2.

Determine the percentage of the minor enantiomer (R)-2-iodobutane: %R = 100 - %S.

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주요 개념

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Optical Activity and Specific Rotation

Optical activity refers to the ability of chiral compounds to rotate plane-polarized light. The specific rotation, denoted as [α], quantifies this rotation and is defined as the observed rotation divided by the concentration and path length. In this question, the specific rotation values of the pure and recovered iodobutane are crucial for determining the composition of the product mixture.

Chirality and Enantiomers

Chirality is a property of molecules that are non-superimposable on their mirror images, leading to the existence of enantiomers—two compounds that are mirror images of each other. In this case, (S)-2-iodobutane and (R)-2-iodobutane are enantiomers, and their relative proportions in the product mixture can be inferred from the specific rotation measurements and the extent of racemization during the reaction.

Racemization and Reaction Kinetics

Racemization is the process by which one enantiomer is converted into its mirror image, resulting in a mixture of both enantiomers. The reaction kinetics, influenced by factors such as solvent and temperature, can affect the rate of racemization. In this scenario, the introduction of radioactive iodide and the resulting specific rotation provide insights into the extent of racemization and the final enantiomeric composition of the product.