78 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



some relationship of the k values: (A:i2 — kn)/ki2, k^/kn, or k^/ku. It 

 was shown that ku/ki2 = 0.8889 for the above reactions carried out at 

 0°C. Thus, in a sample of C^^-labeled formic acid undergoing removal of 

 H2O, the CO2 evolved at first will have a lower specific activity than that 

 of the carboxyl carbon of the acid. However, it is important to note that, 

 if the reaction is carried to completion, the specific activity of all the CO2 

 evolved will be equal to that of the parent carboxyl carbon, and there will 

 be no observed isotope effect. This "disappearance " of the isotope effect 

 if the measurements are made at completion is characteristic of inter- 

 molecular reactions. 



An example of intramolecular isotope effects is the well-known decar- 

 boxylation of malonic acid: 



Ci^OOH 



CH2 ^ Ci^02 + CHsC^^OOH 



Ci^OOH (2-9) 



CH2 -^ C12O2 + CHaC^OOH 



\ 



As the decarboxylation of singly labeled malonic acid proceeds, the con- 

 centration of C^* in the CO2 is less than that in the original label, and the 

 concentration of C^"* in the carboxyl of the acetic acid is greater. This 

 may be expressed by the statement that the C^- — C^- bonds are broken 

 with a frequency 1.12 times greater than are the C^" — C^^ bonds. It 

 should be noted that the maximum isotope effect is measured if the reac- 

 tion goes to completion. This is characteristic of the intramolecular as 

 contrasted with the intermolecular processes. In general, the molecule 

 bearing the heavier isotope will react more slowly. The reverse of this 

 behavior was reported for the decomposition of urea by urease (58). 

 However, more recent experimental data indicated that the kn/kn value 

 was 1.032 at 30°C. An excellent general review of isotope effects in chem- 

 ical reactions has been presented by Yankwich (59). 



A few generalizations may now be stated. Isotope effects may be 

 anticipated in experiments involving diffusion-like processes, especially 

 when lighter elements are used and accurate measurements are made. 

 Effects may also be seen in processes based on organic reactions of the 

 intermolecular type if these cannot be forced to essential completion. 

 With intramolecular reactions, these effects may also be of significance 

 regardless of the degree of completion of the reaction. On the optimistic 

 side, it should be recalled that the magnitude of the effect, depending 

 upon the isotopic composition and the system, will most probably be less 



