It's also called " isotope fractionation".
In a mole simple way we can tell KIE is change in rate of a reaction caused by isotopic reactant.
A KIE involving hydrogen and deuterium is represented as,
KIE = κH
κD
κH, κD = Reaction rate constants.
Advantage :-
The magnitude of KIE is used to elucidate the reaction mechanism and to predict the type of bond breaking in the rate determining step.
TYPES :-
KIE is of two types,
(1) Primary kinetic isotopic effect
(2) Secondary kinetic isotopic effect
Primary kinetic isotopic effect :-
If the bond to the isotopically labeled atom is broken during rate determining step, then it's known as primary kinetic isotopic effect.
Secondary kinetic isotopic effect :-
In the rate determining step, bond other than isotopically labeled atom is broken, it's called secondary kinetic isotope effect.
Kinetic isotopic effect is more pronounce when the relative change in masses of the atom and the isotope is greatest.
Example :-
Changing H atom to 'D' represent a 100 % increase in mass whereas changing C¹² atom to C¹³ represents only 8% increasing mass.
Therefore KIE is more pronounced in deuterium than C¹³.
MATHEMATICAL DETAILS IN A DIATOMIC MOLECULE :-
The zero point energy of the chemical bond is defined as,
ZpE = hʋ ( n+ 1/2)
The ʋ is defined as
ʋ = 1 √ R
2π μ
R represents the bond - strength (or) force constant of a bond.
μ represents the reduced mass and is defined as,
μ = m1m2
m1+m2
Consider the cleavage of C-H and C-H bond in rate determining step.
The corresponding reduced masses will be 12/13 and 24/14. In C-D. Since the reduced mass is higher, the frequency and the ZpE will be lesser.
Therefore more amount of energy will be required to break C-D bond, therefore the rate constant will be lesser.
With a lower ZpE, more energy will be required to cleavage the bond.
Therefore between C-H and C-D a rate constant for a C-H cleavage will be more between C-H and C-D.
μc-H < μc-D
⇒ ZpEc-H > ZpEc-D
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