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 −135°. if this solution were mixed with 500 ml of a solution containing 8 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?

Explanation:

The given data is as follows.

Amount of racemic mixture = 8 g

Amount of pure R compound = 10 g

Therefore, total amount of R compound after missing is calculated as follows.

                 = 14 g

Let us assume that the amount of Si isomer is 4 g.

So, [R] = 11.5 g/L

     [S] = 4 g/L

Now, we will calculate the enantiomeric excess as follows.

             =

             = 71.4%

Therefore, optical purity of the compound is 71.4%.

Now, the specific rotation will be calculated as follows.

          Optical purity =

               71.4% =

                         =

Therefore, specific rotation of the resulting mixture of the compound is .

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