16 The observed rotation of 10.0 g of \( (R)-2 \)-methyl -1-butanol in 50 ml . of sotution in a 20 cm potarimeter tube is \( +2.3^{\circ} \) at \( 20^{\circ} \mathrm{C} \), what is the specific rotation of the compound? \( [a]_{D}^{20^{\circ} \mathrm{C}}=\frac{a}{l \times c}=\frac{2 d \mathrm{~m} \times \frac{10.0 \mathrm{~g}}{50 \mathrm{ml}}}{2}=5.75 \)

To calculate the specific rotation of \( (R)-2 \)-methyl-1-butanol, we first take into account the measurements provided. The observed rotation \( \alpha \) is \( +2.3^{\circ} \). Then, we know that the path length \( l \) of the polarimeter tube is 20 cm (or 2 dm), and the concentration \( c \) in grams per milliliter is \( \frac{10.0 \text{ g}}{50 \text{ ml}} \), which simplifies to \( 0.2 \text{ g/ml} \). Plugging these values into the formula for specific rotation gives us: \[ [\alpha]_{D}^{20^{\circ}C} = \frac{+2.3^{\circ}}{2 \text{ dm} \times 0.2 \text{ g/ml}} = \frac{+2.3^{\circ}}{0.4} = +5.75 \] Specific rotation is a characteristic property of chiral compounds and can help in identifying and quantifying them in various mixtures. It's fascinating to note that specific rotation is not just a fancy mathematical concept; it's used extensively in industries like pharmaceuticals and food to determine the purity and concentration of chiral substances, ensuring that products meet regulatory standards as well as consumer expectations! In the lab, a common mistake is to not account for the correct units. Always ensure your path length is in decimeters and concentration is in grams per milliliter for specific rotation calculations. Miscalculating these units can lead to incorrect interpretation and results!