The $(R)$ -enantiomer of a chiral liquid acid is dextrorotatory with specific rotation $[α] = + 36. 0^{\circ}$ (path length in dm, concentration in g/mL). A scalemic sample of $2.50 g$ is dissolved in solvent to give $25.0 mL$ of solution, which in a $20.0 cm$ tube gives an observed rotation of $+ 1.6 2^{\circ}$ . What mass of the $(S)$ -enantiomer does the sample contain?

Answer: C

Concentration

c = 2.50/25.0 = 0.100 g/mL

, path length

l = 2.00 dm

. Observed specific rotation

= 1.62/ (2.00 \times 0.100) = 8.1 0^{\circ}

. Enantiomeric excess

= 8.10/36.0 = 0.225

(

22.5%

in favour of

R

). Mass fractions:

R = (1 + 0.225) /2 = 0.6125

S = (1 - 0.225) /2 = 0.3875

. Mass of

S = 0.3875 \times 2.50 = 0.969 g \approx 0.97 g