Answer:
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.
