The reaction rate of the isotope molecules may be different. This effect is determined by the reaction mechanism, including thermodynamic properties of the transition state, so the kinetic isotope effects can be applied for the study of the mechanism of the chemical reactions.

Table 3.2 Relative Tension of Some Isotope Molecules Relative Partial Pressure At Triple Point At Boiling Point (1 bar) H2(ortho)/HD 3.61 1.81 (NH3/ND3)1/3 1.080 1.036 (H2OID2O)112 1.120 1.026 CH4/CH3D 1.0016 0.9965 3He/4He 7.0 20Ne/22Ne 1.043 128Xe/136Xe 1.006 12COI13CO 1.01 14nh3i15nh3 1.0055 1.0025 h216oih218o 1.01 1.0046 11BF3I10BF3 ^1.01

The kinetic effects are significant in the case of light elements since the mass of the isotopes of these elements has the greatest differences, resulting in relatively great differences in the rotation, vibration, and electron energies of the isotope molecules and the transition state. The reactions of the molecules containing differ­ent H, C, N, O, and S isotopes are important. Obviously, the reactions of such molecules are interesting mainly in organic chemistry.

The kinetic isotope effects can be classified as primary and secondary effects. In the primary effects, the bond that contains the isotope atoms breaks or forms in the rate-determining step. The primary kinetic isotope effects can be divided further in intermolecular and intramolecular effects. In the intermolecular effect, two molecules react with different rates. In the intramolecular effect, the equivalent sites within the same molecules show different rates because the sites have different isotopes.

A primary intermolecular isotope effect is as follows:

AX 1 BY ——! BX 1 AY (3.19)

AX01 BY ———! BX01 AY (3.20)

In Eqs. (3.19) and (3.20), two identical molecules (AX and AX0) contain differ­ent isotopes of the same element (X and X0). When the reaction constants are different (k1 ф k2), the reaction of the two isotope molecules (AX and AX0) with the molecule BY shows a primary intermolecular isotope effect.

A primary intramolecular isotope effect can be observed in the following process:

AXX’ + 2BY -> BX’ + BX + AYY

(3.21)

£3 k4

where k3 and k4 are the rate of the production of BX0 and BX, respectively. An isotope effect occurs when k3 ф k4.

In the secondary isotope effects, the isotope atom does not directly take part in the reaction. For example,

&5

AXX 1 BY —5—— BX 1 AXY (3.22)

AXX01 BY ——— BX 1 AX’Y (3.23)

where k5 ф k6.

A primary isotope effect can be observed in the thermal decarboxilation of oxa­lic acid if one or both carbon atoms are substituted by the 13C isotope:

12COOH k

I -> 12CO2 + H2O + 12CO (3.24)

12COOH
12COOH	12CO2 + H2O + 13CO
k2^,
13COOH	13CO2 + H2O + 12CO
13COOH

-> 13CO2 + H2O + 13CO

k

4

(3.26)

13COOH

An intramolecular isotope effect is found when k2/k3, whereas intermolecular isotope effects can be observed in case of k1/(k21 k3), k1/k4, and (k2 1 k3)/k4, respectively.

As a secondary isotope effect, the reaction of carboxyl groups of malonic acid is mentioned when deuterium is substituted for the hydrogen bonded to the (3-carbon atom. The maximum values of the kinetic isotope effects (shown in Table 3.3) are determined using the thermodynamic properties of the isotope molecules.

The study of the isotope effects can be used to elucidate the reaction mecha­nism, as the following example shows. The oxidation of alcohols to carboxylic acid by bromine is made up of two steps:

CH3 — CH2 — OH 1 Br2 ——— CH3 — CHO 1 2HBr (3.27)

fast

CH3 — CHO 1 Br2 1 H2O———— — CH3 — COOH 1 2HBr (3.28)

The rate-determining step is the oxidation of the alcohol, which results in the formation of aldehyde (Eq.(3.27)), a first-order reaction both for alcohol and

Table 3.3 Maximum Values of Isotope Effects in the Kinetics of Chemical Reactions Isotope Substitution Bond Ratio of Rate Constants Maximum Primary Isotope Effects at 25° C H D 18 H T 60 10B 11B 1.3 12C 13C 1.25 12C 14C 1.5 14n 15n 1.14 16O 18O 1.19 19f 18F 1.25 31P 32P 1.02 32S 35S 1.05 Cl natural 38Cl 1.14 127i 131I 1.02 Maximum Secondary Isotope Effects at 25° C H D C-H 1.74 H T C-H 2.20 H D O-H 2.02 H T O-H 2.74 12C 13C C-C 1.012 12C 14C C-C 1.023

bromine. There are two mechanistic possibilities. The first is that bromine reacts with the hydrogen in the hydroxide group and in a rate-determining step:

CH3 — CH2OH 1 Br2 -—! CH3 — CH2 — OBr 1 HBr (3.29)

fast

CH3 — CH2 — OBr———— ! CH3 — CHO 1 HBr (3.30)

This support for this mechanism is that it resembles the fast reaction of alkyl hypochlorites. If this is the right mechanism, secondary isotope effects should be observed if the alcohol CH2 group is labeled by an isotope of the hydrogen. In the case of H — T substitution, this mechanism can decrease the reaction rate by 2.2 times (Table 3.3).

The second possibility is that bromine reacts with the carbon atom of the alcohol CH2, which would result in a much higher (i. e., primary) isotope effect when substituting one of the hydrogen atoms of alcohol CH2 by tritium. In this case, two types of aldehyde would form, an unlabeled and a labeled molecule:

CH3 + CHO + TBr + HBr

CH3 — CHT — OH + Br2 (3.31)

"IT^ CH3 + CTO + HBr

k

CH3 — CH2 — OH 1 Br2 —% CH3CHO 1 2HBR

Because of the two product molecules of the labeled alcohol, the value of the isotope effect has to be calculated as:

2kH

kx1 1 kx2

Thus, examining the relative rates, it can be determined if the reaction starts with the reaction of CH2 and Br2, or if it proceeds via a hypobromite intermediare.