# Question 425ea

Jan 18, 2017

The primary kinetic isotope effect does not affect the reaction mechanism; rather, it gives information on the reaction mechanism.

#### Explanation:

Kinetic Isotope Effect

The kinetic isotope effect (KIE) refers to the change in rate caused by an isotopic substation in a molecule.

Frequently, the KIE refers to the effect of substituting $\text{D}$ for $\text{H}$ (the ${k}_{\text{H"//k_"D}}$ ratio).

The $\text{C-H}$ and $\text{C-D}$ vibrations are quantized per the condition

$E = \left(n + \frac{1}{2}\right) h f$, where n = 0, 1, 2, …

At ordinary temperatures, most of the molecules are in the $n = 0$ state.

We see the maximum KIE when a $\text{C-H}$ bond is being broken in the transition state, because the vibrational mode disappears.

Since ${E}_{0} \left(\text{H") > E_0("D}\right)$, ${E}_{\text{a""(H") < E_"a""(D)}}$ and ${k}_{\text{H" > k_"d}}$.

This is called a primary kinetic isotope effect.

The calculated value of k_"H" // k_"d" ≈ 7.

A secondary KIE occurs when the isotope is substituted at a position next to the bond being broken.

Usually, for a secondary KIE, ${k}_{\text{H"//k_"D}} < 1.5$.

Mechanistic information from KIEs

KIEs give useful information about the rate determining step in a mechanism.

Case 1

${\text{CH"_3"CH"_2"CH"_2"Br" stackrelcolor(blue)( "EtO"^"-", "EtOH"color(white)(m)) (→) "CH"_3"CH=CH}}_{2}$

${\text{CH"_3"CD"_2"CH"_2"Br" stackrelcolor(blue)( "EtO"^"-", "EtOH"color(white)(m)) (→) "CH"_3"CD=CH}}_{2}$

${k}_{\text{H"//k_"D}} = 6.7$

This is consistent with an $\text{E2}$ elimination in which the $\text{C-H/D}$ bond is being broken in the rate determining step.

Case 2

"CH"_3"CH"_2"C"("CH"_3)_2"Br" stackrelcolor(blue)( "H"_2"O", Δcolor(white)(m)) (→) "CH"_3"CH=C"("CH"_3)_2

"CH"_3"CD"_2"C"("CH"_3)_2"Br" stackrelcolor(blue)( "H"_2"O", Δcolor(white)(m)) (→) "CH"_3"CD= C"("CH"_3)_2#

${k}_{\text{H"//k_"D}} = 1.4$

This is consistent with an $\text{E1}$ elimination in which the $\text{C-H(D)}$ bond is not being broken in the rate determining step.