Question

$ ( + ) - $ Mandelic acid has a specific rotation of $ + {158^o} $ . What would be the observed specific rotation of a mixture of $ 25\% \;\left( - \right) - \; $ mandelic acid and $ 75\% \left( + \right) - \; $ mandelic acid:

Answer 1

Hint: Mandelic acid is aromatic in nature and is alpha hydroxy acid. It has a molecular formula $ {C_6}{H_5}CH\left( {OH} \right)C{O_2}H $ . It is a chiral molecule and its racemic mixture is known as para mandelic acid. Specific rotation is a property of a chemical compound which is chiral in nature. Now, we will find the observed specific rotation for the mandelic acid.

Complete answer:
So, now we know that Mandelic acid is aromatic in nature and is alpha hydroxy acid. It has a molecular formula $ {C_6}{H_5}CH\left( {OH} \right)C{O_2}H $ . Its structure is:

So we can clearly see that it is a chiral molecule and hence, shows specific rotation.
Specific rotation is defined as the change in the orientation of a monochromatic plane-polarized light as it passes through a sample of compound in the solution.
Formula used to find observed specific rotation is given as:
 $ E.E = \dfrac{{[\alpha ]}}{{\alpha (pure( + )enantiomer)}} $
Here, E.E refers to enantiomeric excess.
 $ [\alpha ] $ is the observed specific rotation.
 $ \alpha $ is the specific rotation of pure $ ( + ) - $ Mandelic acid.
So, now we are given with:
Concentration of $ \;\left( - \right) - \; $ mandelic acid is $ 25\% $ .
Concentration of $ ( + ) - $ Mandelic acid is $ 75\% $ .
Enantiomeric excess of $ ( + ) - $ Mandelic acid is $ 75 - 25 $
 $ = 50\% $
Putting these values in the formula, we get:
 $ 50 = \dfrac{{[\alpha ]}}{{158}} \times 100\% $
 $ [\alpha ] = + {79^o} $
Therefore, the observed specific rotation of the mixture is, $ [\alpha ] = + {79^o} $ .

Note :
Chiral compounds are those compounds in which at least one carbon atom is chiral (have four different groups attached to it). Chiral compounds can rotate monochromatic plane-polarized light. Achiral molecules are those in which there is no chiral carbon present and this type of molecule is not able to rotate the plane-polarized light.