Answer:
- 41.3°
Explanation:
Observed rotation for the mixture can be converted to specific rotation for the mixture through
[α] = α/(lc)
[α] = specific rotation = ?
when written as [α]²⁵D, 25 refers to the temperature at which the optical exercise was carried out, and D indicates that a particular wavelength of Sodium light was used.
α = observed rotation = 25.3°
l = cell length or length of the polarimeter tube in dm = 1 dm (Because 10cm = 1 dm)
c = concentration of the mixture in g/mL = 2.038 g/mL
[α] = 25.3/(1×2.038)
[α] = 12.4°
The mixture contains 65% R enantiomer and automatically 35% S enantiomer.
That is,
Fraction of R = 0.65
Fraction of S = 0.35
Let the predicted specific rotation of the pure S enantiomer be +x
The predicted specific rotation of the pure R enantiomer will automatically be -x
Rotation (R/S Mixture) = [Fraction(S) × Rotation (S)] + [Fraction(R) × Rotation (R)]
12.4° = [0.35x] + [0.65(-x)]
12.4 = 0.35x - 0.65x
12.4 = -0.30x
x = -(12.4/0.3)
x = -41.3°
The predicted specific rotation of the pure S enantiomer = x = - 41.3°.
Hope this Helps!
