See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

# Solution: Specific Rotation of Mandelic Acid Mixture **Given Information:** - $(+)$-mandelic acid: specific rotation $= +158°$ - Mixture: 25% $(-)$-mandelic acid + 75% $(+)$-mandelic acid **Step 1: Find specific rotation of $(-)$-mandelic acid** The $(-)$ and $(+)$ enantiomers have equal but opposite rotations: $$[\alpha]_{(-)} = -158°$$ **Step 2: Apply the additivity rule for optical rotation** For a mixture, the observed specific rotation is the weighted average: $$[\alpha]_{\text{obs}} = (w_1 \times [\alpha]_1) + (w_2 \times [\alpha]_2)$$ where $w$ represents the weight fraction of each component. **Step 3: Calculate** $$[\alpha]_{\text{obs}} = (0.25 \times (-158°)) + (0.75 \times (+158°))$$ $$[\alpha]_{\text{obs}} = -39.5° + 118.5°$$ $$[\alpha]_{\text{obs}} = +79°$$ **Answer: (D) $+79°$** The mixture is enriched in the $(+)$ enanomer (75%), so the net rotation is positive. The dextrorotatory component dominates, giving a positive observed specific rotation of $+79°$.