Optically pure (R) - 1 - phenylethanol (5 g) was dissolved in methanol ( $100 \mathrm{~mL}$ ). The observed optical rotation of this sample in a cell of $10 \mathrm{~cm}$ length was +2.25 . What is the $[a] D$ of $(R)-1$ - phenylethanol?

Question

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Calculate the specific rotation**: The specific rotation $[\alpha]_D$ is calculated using the observed optical rotation $\alpha$, the length of the cell $l$ in decimeters, and the concentration $c$ in grams per milliliter. The formula is $[\alpha]_D = \frac{\alpha}{l \cdot c}$. ‖ ‖ 2 ⋮ **Apply the formula**: Given that the observed optical rotation $\alpha$ is +2.25, the cell length $l$ is $10 \mathrm{~cm}$ (which is 1 decimeter), and the concentration $c$ is the mass of the compound divided by the volume of the solvent in mL, which is $\frac{5 \mathrm{~g}}{100 \mathrm{~mL}} = 0.05 \mathrm{~g/mL}$, we can now calculate $[\alpha]_D$. ‖ ‖ 3 ⋮ **Perform the calculation**: Using the values from step 2, $[\alpha]_D = \frac{+2.25}{1 \cdot 0.05} = +45$. ‖ ∻Answer∻ ⚹ $[\alpha]_D = +45^\circ$ ⚹ ∻Key Concept∻ ⚹ Specific rotation $[\alpha]_D$ ⚹ ∻Explanation∻ ⚹ The specific rotation $[\alpha]_D$ is a physical property that quantifies the degree of optical rotation a chiral compound produces under standard conditions. It is calculated using the observed rotation, the path length of the polarimeter cell, and the concentration of the solution. ⚹◊What is the specific rotation formula for calculating the specific rotation of a compound in solution?⍭ Generate me a similar question◊

Sia