The Isotope Effect in a Chemical Equilibrium

The equilibrium constants of the reactions involving isotope molecules may also be different:

AX 1 BYoAY 1 BX (3.34)

AX01 BYoAY 1 BX0 (3.35)

Both X and X0 mean the isotopes of the same element. The equilibrium con­stants are as follows:

K = [AY][BX]

(3.36)

[AX][BY]

K = [AY][BX0]

(3.37)

[AX0][BY]

The ratio of the two equilibrium constants is:

Подпись: (3.38)Подпись: (3.39)K = K = = [BX][AX0]

K0 [BX0][AX]

This ratio gives the equilibrium constant of the isotope exchange reaction:

AX 1 BX0 з AX01 BX

When the equilibrium constant of the isotope exchange is equal to 1, there is no isotope effect—the distribution of the isotopes is the same in both compounds.

The equilibrium constants of some isotope exchange reactions are listed in Table 3.4. The calculated values were obtained from the thermodynamic properties.

As seen in Table 3.4, the equilibrium constants of isotope exchange reactions are close to 1 but frequently not equal to 1. These small differences from 1 have, however, a great theoretical and practical importance because they provide a way to separate isotopes and give important geological information (discussed further in Section 3.4).

Table 3.4 Equilibrium Constants of Some Isotope Exchange Reactions

Isotope Exchange Reaction

Temperature

(K)

Equilibrium Constant

Experimental

Calculated

0.5C16O2 1 H218Oaq3 0.5C18O2 1 H216Oaq

273

1.044

1.044

15NH3 1 14NH3aq3 15NH3aq 1 ^3

298

1.026

H12CN 113CNaq3H13CN 112CNaq

295

1.026

1.030

hc14n 1 CNaq 3 hc15n 1 CNaq

295

1

1.002

12CO2~ 113CO2 313CO32 112CO2

273

1.017

1.016

H12CO3 113CO23H13CO3 1 12co2

298

1.014

34SO2 1 H32SO3 332SO2 1 H34SO3

298

1.019

36SO2 1 H32SO3 332SO2 1 H36SO3

298

1.043

7Li(Hg) 1 6LiCl 3 6Li(Hg) 1 7LiCl

295

1.025

H218O 1 1 /3C16O|2 3 H216O 1 1 /3C18O|2

273

1.022

298

1.0176

H218O 1 1 /4Si16O42 3 H216O 1 1 /4Si18O22

273

1.0204

298

1.0157

H218O 1 1/4S16o423H216O 1 1/4S18o22

288

1.03

413

1.014

H218O 1 1/4S16o423H216O 1 1/4S18o42

273

1.0104

298

1.0037