Optically pure (S)-3-chloro-3-methylhexane, $CH X_{3} CH X_{2} CH X_{2} - C (CH X_{3}) (Cl) - CH X_{2} CH X_{3}$ , is solvolysed in aqueous acetone via ion pairs, and the 3-methylhexan-3-ol formed is 76% inverted and 24% retained in configuration. Pure (R)-3-methylhexan-3-ol has a specific rotation of $+ 12. 5^{\circ}$ under the conditions used. The specific rotation of the product mixture is

Answer: A

CIP priorities at C-3:

Cl

(or

OH

) > propyl > ethyl > methyl in both chloride and alcohol, so inversion changes (S) to (R). The mixture is 76% (R) and 24% (S), an excess of

76 - 24 = 52

% of (R). The rotation is

12.5 \times 0.52 = + 6. 5^{\circ}

; the descriptor changes on inversion.