Question

Among the many examples of reactions that occur with incomplete racemization, the optically pure tosylate of 2,2-dimethyl-1-phenyl-1-propan(${\left[\alpha \right]}_{\mathbf{D}}$= 230.3) gives the corresponding acetate (${\left[\alpha \right]}_{\mathbf{D}}$= 15.3) when heated inacetic acid. If complete inversion had occurred, the optically pure acetatewould have had${\left[\alpha \right]}_{\mathbf{D}}$= 153.6. What percentage racemization and what percentageinversion occurred in this reaction?

Short answer

Percentage of inversion =$\frac{+{5.3}^o}{+{53.6}^o}\times 100=9.9\%$

Percentage of racemization = 100-9.9 = 90.1 %

Step-by-step solution

Inversion and Racemization

Inversion is defined as the state where absolute configuration and relative configuration of the atom or a molecule is not maintained. Or, we can say that it is the spatial rearrangement of atoms in a dissymmetric molecule, giving rise to a product with a molecular configuration that is mirror image of that original molecule.

Racemization is the process when the enantiomer is converted in to racemic mixture.Racemization also means that half the reactant inversion has taken place. As both are equal in amount, they cancel each other and this is called racemization.

Percentage racemization and percentage inversion in the given reaction

If the reaction had proceeded with complete inversion, the product would have had a specific rotation of +53.6^o.

If the complete racemization had occurred, ${\left[\alpha \right]}_D$would have been zero

The observed rotation was +5.3^o.

Since$\frac{+{5.3}^o}{+{53.6}^o}\times 100=9.9\%$ of the original tosylate was inverted.

The remaining product have been racemized .i.e =100-9.9 = 90.1 %