Question

An aqueous solution containing 10g of an optically pure compound was diluted to 500 mL with water and was found to have a specific rotation of -133 degrees. If this solution were mixed with 500mL of a solution containing 6g 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?

Answer 1

Initially, we have 10 g of optically pure (-) compound with specific rotation of -133 degrees.

Then, we added 6 g of racemic mixture of the compound.

Hence, the 6 g of racemic mixture must contain 3 g each of both the (+) and (-) optical isomer.

Hence, total (-) isomer,

total (+) isomer,

Hence, the optical purity, ee of the solution can be calculated as

Now, the optical purity is also given by

Since we know that the specific rotation of the pure sample is -133 degrees, putting the value of ee=62.5, we get

Hence, the observed rotation of the solution is -83.125 degrees.

As calculated before, the optical purity(ee) of the solution is 62.5.