A pure, unknown chiral compound () is entirely dissolved in a total solution volume of . When placed — Isomerism and Stereochemistry Chemistry Question
Question
A pure, unknown chiral compound ($20 \text{ g}$) is entirely dissolved in a total solution volume of $200 \text{ mL}$. When placed inside a standard $10 \text{ dm}$ polarimeter tube, it physically rotates the plane of polarized light by an angle of exactly $+30^\circ$. What is the calculated specific rotation $[\alpha]$ of this pure compound?
💡 Solution & Explanation
The mathematical equation defining specific rotation is $[\alpha] = \alpha_{obs} / (l \times c)$, where '$l$' is the optical path length strictly in decimeters (dm) and '$c$' is the concentration strictly in g/mL. The concentration is $C = 20 \text{ g} / 200 \text{ mL} = 0.1 \text{ g/mL}$. Given $\alpha_{obs} = 30^\circ$ and $l = 10 \text{ dm}$, the substitution yields $[\alpha] = 30 / (10 \times 0.1) = 30 / 1 = +30^\circ$.