(+)-mandelic acid has a specific rotation of +158^∘. What would be the observed specific rotatio

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(+)-mandelic acid has a specific rotation of +158^∘. What...

(+)-mandelic acid has a specific rotation of $+158^{\circ}$. What would be the observed specific rotation of a mixture containing $25 \%$ (-)-mandelic acid and $75 \%$ (+)-mandelic acid?
(a) $+79^{\circ}$
(b) $-118.5^{\circ}$
(c) $-79^{\circ}$
(d) $+118.5^{\circ}$

Key Concepts

Mixture Calculation of Optical Rotation

In a mixture of enantiomers, the observed optical rotation is calculated as the weighted sum of the contributions of each enantiomer. The overall rotation depends on both the specific rotation of each enantiomer and their relative proportions, allowing one to determine the net effect when they are combined.

Optical Activity

Optical activity refers to the ability of a chiral substance to rotate the plane of polarized light. This property occurs because the asymmetrical arrangement of atoms in a chiral molecule causes it to interact with polarized light uniquely, leading to a measurable rotation whose direction and magnitude depend on the structure and concentration of the substance.

Specific Rotation

Specific rotation is a standardized measure of the optical rotation exhibited by a pure substance, expressed under defined conditions of concentration, path length, temperature, and wavelength of light. It allows for the comparison of the intrinsic optical activity of different chiral compounds.

Enantiomers

Enantiomers are stereoisomers that are non-superimposable mirror images of each other. They possess identical physical properties except for the direction in which they rotate plane-polarized light and interact differently with other chiral environments, such as biological systems.

Enantiomeric Excess

Enantiomeric excess is a quantitative measure of the purity of a chiral compound in a mixture of enantiomers. It represents the difference in proportion between the two enantiomers and is directly related to the net optical activity observed in a sample.

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