In 100 % H2 SO4 the cyclization shown below occurs. If one...

In $100 \% \mathrm{H}_{2} \mathrm{SO}_{4}$ the cyclization shown below occurs. If one of the ortho hydrogens is replaced by deuterium, the rate of cyclization drops from $1.56 \times 10^{-4}$ to $1.38 \times 10^{-4} \mathrm{~s}^{-1}$. Calculate the kinetic isotope effect. The product from such a reaction contains $60 \%$ of the original deuterium. Write a mechanism for this reaction that is consistent with both the magnitude of the kinetic isotope effect and the deuterium retention data.

Key Concepts

Kinetic Isotope Effect

The kinetic isotope effect (KIE) refers to the change in reaction rate caused by the substitution of an atom in the reactants with one of its isotopes, usually hydrogen by deuterium. Because bonds involving the heavier isotope (deuterium) are typically stronger and vibrate at lower frequencies than those with the lighter hydrogen, the transition state energy may be altered, leading to a measurable difference in reaction rate. This effect is used to draw conclusions regarding the involvement of a particular bond (for example, a C–H bond) in the rate?determining step of the reaction mechanism.

Reaction Mechanism

A reaction mechanism details the step-by-step sequence of elementary reactions by which an overall chemical change occurs. Understanding the individual steps, including which step is rate-determining, helps in correlating experimental observations like the kinetic isotope effect and isotopic retention with the underlying process. A mechanism consistent with the observed moderate KIE and partial deuterium retention must account for a step featuring proton (or deuteron) removal that is not entirely irreversible and allows for exchange processes prior to cyclization.

Isotopic Labeling and Retention

Isotopic labeling involves substituting a specific atom in a molecule with its isotope to track its pathway through a chemical reaction. The degree of deuterium retention in the final product provides insight into the reversibility of steps where the labeled atom might exchange with the medium. In this case, the fact that only 60% of the original deuterium is retained suggests that while there is a significant primary isotope effect, there is also an exchange process occurring that partially replaces deuterium with hydrogen during the reaction sequence.

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