A chemist finds that the addition of (+)-epinephrine to

Solution 13P :

Step 1:

Given :

Observed specific rotation of butan-2-ol = +0.45°.

Percentages of (+)-butan-2-ol and (-)-butan-2-ol formed in this reaction = ?

The rotation of pure butan-2-ol = +13.5 %

We know formula for optical purity :

                Optical purity(o.p) = 100 %

        Hence , o.p for butan-2-ol  = 100 %

                                            = 3.33 % 

Therefore, the o.p of butan-2-ol is 3.33 % which also means that the enantiomeric excess(e.e) is 3.33 % excess  (+) enantiomer over (-) enantiomer.

Step 2:

Now, let’s calculate the percentages of (+) and (-) enantiomer in the mixture :

Let’s put it in the equation from and solve it :

                (+) + (-) = 100 %          -------------- (1)

                (+) - (-) = 3.33 %          -------------- (2)

We can rewrite equation (1) as :

                (-) = 100 % - (+)         ----------- (3)

Using equation (3), we can rewrite equation (2) as :

                (+) - (100 % - (+)) = 3.33 %

        The above equation can be simplified as :

                2 (+)  = 3.33 % + 100 %

                2(+)  = 103.33 %

                       (+) =

                       (+)         = 51.66 %

Hence, the percentages of (+)-butan-2-ol formed in the reaction is 51.66 %