Answer:
a) Specific rotation of pure fructose = - 130°
b) Specific rotation of racemic fructose = 65°
Specific rotation of the racemic mixture = -65°
Optical purity = 50%
Explanation:
specific rotation = observed rotation/ (tube length in decimeters x concentration)
[α] = α/lc
Observed rotation, α = -5.2°
Tube length in decimeters, l = 2 decimeters (1 decimeter = 10cm)
Concentration in g/mL or g/cm³ = 10/500 = 0.02 g/mL
Specific rotation, [α] = -5.2/(2×0.02) = - 130°
b) The racemic fructose would rotate light in the opposite direction. If the two enantiomers have the same concentration, specific rotation of the racemic fructose would be -(-130°) = 130°, but the concentrations are different.
Concentration in g/mL or g/cm³ = 5/500 = 0.01 g/mL
At half of the concentration of optically pure fructose, specific rotation would be 0.5 × 130° = 65°
Total specific rotation of mixture = - 130° + 65° = -65°
Optical purity = (specific rotation of mixture/specific rotation of pure sample) × 100% = [-65/(-130)]× 100 = 50%
Hope this Helps!!!
