Calculate the specific rotations of the following samples taken at 25 °C using the sodium D line.
a. 1.00 g of sample is dissolved in 20.0 mL of ethanol. Then 5.00 mL of this solution is placed in a 20.0-cm polarimeter tube. The observed rotation is 1.25° counterclockwise.

(R)-Limonene is a cyclic terpene responsible for the smell of oranges and other citrus fruits.

(a) Given that (R)-limonene rotates plane-polarized light in the clockwise direction, should it be referred to as (d) or (l)?

(b) Is it (+) or (-)?

(c) What direction (d or l; + or −) would you expect (S)-limonene to rotate plane-polarized light?

Which of the following diastereomers of hexane-2,5-diol is optically inactive? Why?

Draw the structure for a compound with molecular formula C₂H₂I₂F₂

c. that is optically active.

A solution of 0.50 g of (−)-epinephrine (see Figure 5-16) dissolved in 10.0 mL of dilute aqueous HCl was placed in a 20-cm polarimeter tube. Using the sodium D line, the rotation was found to be −5.1° at 25 °C. Determine the specific rotation of epinephrine.

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Calculate the specific rotations of the following samples taken at 25 °C using the sodium D line.

b. 0.050 g of sample is dissolved in 2.0 mL of ethanol, and this solution is placed in a 2.0-cm polarimeter tube. The observed rotation is clockwise 0.043°.

If you had the two enantiomers of carvone in unmarked bottles, could you use just your nose and a polarimeter to determine

a. whether it is the (+) or (−) enantiomer that smells like spearmint

b. whether it is the (R) or (S) enantiomer that smells like spearmint?

c. With the information given in the drawings of carvone above, what can you add to your answers to (a) and (b)?

Draw the mirror images of glucose and fructose. Are glucose and fructose chiral? Do you expect them to be optically active?