A sample of Limonene has a specific rotation of +76.9. What is the % ee and

molecular composition of this sample?

To determine the % ee (enantiomeric excess) and molecular composition of a sample of Limonene based on its specific rotation (+76.9), we need to understand the relationship between specific rotation, enantiomeric excess, and molecular composition.

1. Specific Rotation (α): Specific rotation is a measure of the ability of a chiral compound to rotate the plane of polarization of plane-polarized light. It is denoted by the symbol α and is expressed in degrees per dm per g (°/dm/g).

2. Enantiomeric Excess (% ee): Enantiomeric excess represents the excess or imbalance of one enantiomer over its mirror image in a sample. It is usually expressed as a percentage and indicates the ratio of the difference in the amount of one enantiomer to the total amount of enantiomers in a sample.

3. Molecular Composition: Limonene is a chiral compound that exists in two enantiomeric forms: (+)-limonene and (-)-limonene. The molecular composition refers to the relative amounts of these two enantiomers present in the sample.

To determine the % ee and molecular composition, we can use the following relationship:

% ee = (observed specific rotation / specific rotation of pure enantiomer) x 100

The specific rotation of pure (+)-limonene is +126.9°. Therefore:

% ee = (76.9 / 126.9) x 100
% ee ≈ 60.63%

This means that the sample of Limonene has an enantiomeric excess of approximately 60.63%.

To determine the molecular composition, we need to consider that the enantiomeric excess represents the ratio of the difference in the amount of one enantiomer to the total amount of enantiomers. In this case, the difference corresponds to the excess of (+)-limonene over (-)-limonene.

Assuming the total amount of enantiomers is 100 g, we can calculate the amount of (+)-limonene:

Amount of (+)-limonene = (% ee / 100) x total amount
Amount of (+)-limonene = (60.63 / 100) x 100 g
Amount of (+)-limonene = 60.63 g

The amount of (-)-limonene can be determined as the difference:

Amount of (-)-limonene = total amount - amount of (+)-limonene
Amount of (-)-limonene = 100 g - 60.63 g
Amount of (-)-limonene = 39.37 g

Therefore, the molecular composition of the sample is approximately 60.63% (+)-limonene and 39.37% (-)-limonene.