The reaction that is expected to show a primary kinetic isotope effect for the indicated H‐atom (C‐H) is

Concept:-

• The kinetic isotope effect (KIE) describes the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes.
• It is the ratio of the rate constant of reactions involving the light (k_L) and the heavy (k_H) isotopically substituted reactants.
• A primary kinetic isotope (PKI) effect may be found when a bond to the isotopically labeled atom is formed or broken at the rate-limiting step.
• The difference in bond strength will be reflected in different rates of breaking of the two bonds under comparable conditions.
• Quantum mechanical calculation suggests a maximum rate difference observed when,

\({{{{\rm{k}}_{\rm{H}}}} \over {{{\rm{k}}_{\rm{D}}}}}{\rm{ = 7}}\)

Explanation:-

• Out of these four reactions, only the bromination of acetone in presence of acid (reaction C) involves the breaking of the C-H bond in the rate-limiting step of the reaction.
• The mechanism of bromination of acetone in presence of acid is given by,

​

• The first step involves acid-catalyzed enolization followed by the electrophilic attack of the bromine molecule on the nucleophilic carbon of the enol.
• As the rate-limiting step involves the breaking of the C-H bond,  this reaction is expected to show a primary kinetic isotope effect.

​Conclusion:-

Hence, the reaction that is expected to show a primary kinetic isotope effect for the indicated H‐atom (C‐H) is