An aqueous solution containing 10 g of an optically pure compound was diluted to 500 ml with water and was found to have a specific rotation of −127°. if this solution were mixed with 500 ml of a solution containing 3 g of a racemic mixture of the compound, what would the specific rotation of the resulting mixture of the compound? what would be its optical purity?

Optical purity = 76.9231 %

Specific rotation of mixture = - 97.6923 °

Explanation:

The mass of the racemic mixture = 3 g

It means it contains R enantiomer = 1.5 g

S enantiomer = 1.5 g

Amount of Pure R = 10 g

Total R = 11.5 g

Total volume = 500 mL + 500 mL = 1000 mL = 1 L

[R] = 11.5 g/L

[S] = 1.5 g/L

Enantiomeric excess = = = 76.9231 %

Optical purity = 76.9231 %

Also,

Optical purity =

Optical rotation of pure enantiomer = −127 °

Specific rotation of mixture = - 97.6923 °