An optically active compound () is dissolved in a solution. When placed in a polarimeter tube, it ro — Isomerism and Stereochemistry Chemistry Question
Question
An optically active compound ($20 \text{ g}$) is dissolved in a $200 \text{ mL}$ solution. When placed in a $10 \text{ dm}$ polarimeter tube, it rotates the plane-polarized light by exactly $30^\circ$. If this exact solution is subsequently diluted to a total volume of $1 \text{ Litre}$, what will be the new observed angle of rotation in degrees?
💡 Solution & Explanation
Initial concentration $C_1 = 20 \text{ g} / 200 \text{ mL} = 0.1 \text{ g/mL}$. The specific rotation $[\alpha] = \frac{\alpha_{obs}}{l \times c} = \frac{30^\circ}{10 \times 0.1} = +30^\circ$. Upon dilution to $1 \text{ L}$ ($1000 \text{ mL}$), the new concentration $C_2 = 20 \text{ g} / 1000 \text{ mL} = 0.02 \text{ g/mL}$. The new observed rotation $\alpha_2 = [\alpha] \times l \times C_2 = 30^\circ \times 10 \times 0.02 = 6^\circ$.