Question

The specific rotation $[\alpha]_D^{25}$ of (S)-2-pentanol is +13.0 degreesA one molar solution of (S)-2-pentanol is mixed with an equal volume of one molar solution of racemic 2-pentanolThe observed rotation, $\alpha$, of the resulting solution, when measured in a polarimeter tube of path length 10 cm is _ _ _ degrees. (rounded off to three decimal places)

Hint:

Observed rotation depends on enantiomeric excessAlways calculate net optical purity before applying $\alpha = [\alpha]lc$

Answer 1

Correct Answer: 0.739

Step 1: Active part of the mixture.
The racemic half contributes no rotation, so only the extra S form from the pure solution rotates light.

Step 2: Net S excess.
After mixing, the S excess gives an enantiomeric excess of one half.

Step 3: Apply the rotation relation.
Using specific rotation, path length and the active concentration, the observed rotation works out to about 0.739 degrees.

Step 4: Answer.
\[ \boxed{0.739} \]