You have a racemic mixture of (+)-2-butanol and (-)-2-butanol. The (+) isomer rotates polarized light by +13.5∘. What is the observed rotation of your mixture?

The observed rotation of the racemic mixture = 0°

Explanation:

The (+)-2-butanol and (-)-2-butanol are enantiomers of each other.

A (+) isomer rotates polarized light in the clockwise direction and the (-) isomer of similar concentration rotates the polarized light through the same angle as the (+) isomer, but in the anti-clockwise direction.

Therefore, if the (+)-2-butanol isomer rotates polarized light by +13.5°, the (-)-2-butanol will rotate polarized light by -13.5°.

And since the two isomers are given as a racemic mixture (containing equimolar amounts of both enantiomers), the observed degree of rotation of the racemic mixture = +13.5° - 13.5° = 0°.

And this is scientifically correct because a racemic mixture will not rotate polarized light; a racemic mixture is inactive optically.

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