Question

the aldrich chemical company once manufactured a technical(low purity) grade of pinene that contained 85%(+)- alpha pinene and had a specific rotation of +43. is the 15% (by mass) impurity in this product more likely to be (-)-alpha-pinene, (-)-beta-pinene, or some optically inactive substance? justify your answer with calculations.

Answer 1

The technical(low purity) grade of pinene that contained 85% (+)- alpha pinene had a specific rotation of +43^o.

It has 15% (by mass) impurity in this product more likely to be (-)-alpha-pinene, (-)-beta-pinene, or some optically inactive substance?

(+)- alpha pinene = +50^o

(-)-alpha-pinene = -41^o

(-)-beta-pinene = -22^o

Thus when there is a mixture, 15% impurity by mass of (-)-alpha-pinene, (-)-beta-pinene with opposite rotation the specific rotation value decrease.

For 15% (-)-alpha-pinene as impurity, specific rotation of the mixture is:

(50*85-41*15)/100 = +36.3^o

For 15% (-)-beta-pinene, specific rotation of mixture is: +39.2^o

However, the impurity is not an optically active compound, then,

specific rotation is directly proportional to concentration,

Observed specific rotation = 50 * (85/100) = +42.5^o

Thus, for all the cases the observed specific rotation will decrease. As the observed specific rotation (=43^o) is close to the observed specific rotation for an optically impure impurity (+42.5^o), the impurity is achiral.