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Question: \( ( + ) - \) Mandelic acid has a specific rotation of \( + {158^o} \) . What would be the observed ...

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

Explanation

Solution

Mandelic acid is aromatic in nature and is alpha hydroxy acid. It has a molecular formula C6H5CH(OH)CO2H{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 C6H5CH(OH)CO2H{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=[α]α(pure(+)enantiomer)E.E = \dfrac{{[\alpha ]}}{{\alpha (pure( + )enantiomer)}}
Here, E.E refers to enantiomeric excess.
[α][\alpha ] is the observed specific rotation.
α\alpha is the specific rotation of pure (+)−( + ) - Mandelic acid.
So, now we are given with:
Concentration of   (−)−  \;\left( - \right) - \; mandelic acid is 25%25\% .
Concentration of (+)−( + ) - Mandelic acid is 75%75\% .
Enantiomeric excess of (+)−( + ) - Mandelic acid is 75−2575 - 25
=50%= 50\%
Putting these values in the formula, we get:
50=[α]158×100%50 = \dfrac{{[\alpha ]}}{{158}} \times 100\%
[α]=+79o[\alpha ] = + {79^o}
Therefore, the observed specific rotation of the mixture is, [α]=+79o[\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.