42 ORIGIN AND MAINTEN. OF OPT. ACTIVITY 



corresponding to these two cases and studied the dynamics 

 of the change of optical activity in terms of time. 



In the case of the splitting up of a racemate (2), if 

 ki/k,, >> J , and K >> 1, the substance Bj will be obtained 

 almost exclusively at the beginning; its concentration 

 might approach c„/2 (if c,, is the concentration of the initial 

 substance) ; later, A^, will be transforming itself into B,i 

 till, finally, the concentrations Bj and Ba are equalized. At 

 the initial and final states the solutions will be optically 

 inactive. 



In the case of asymmetric synthesis (3), assuming again 

 that ki/ka >> 1 and K >> 1, there will be, at the begin- 

 ning, an accumulation of the /-form, B,-, the whole initial 

 material (c,,) will be practically transformed into this 

 /-antipode, since the velocity constant A",, is supposed to be 

 very low as compared to k,. The concentration of the initial 

 substance A will approach cjK. A will also change very 

 slowly into B,j and, as a result of this change, its concentra- 

 tion will be reduced and the equilibrium between A and Bi 

 will be disturbed: consequently, a certain quantity of B, 

 will be transformed into A. This will cause a further 

 transformation of the initial substance into B,i. The pro- 

 cess will continue as long as the initial substance A is in 

 equilibrium simultaneously with Bj and B,i or, in other 

 words, until the racemic state is obtained. So the same 

 catalyst which, at first, brought about the transformation 

 of A into practically pure antipode B, later causes a com- 

 plete racemization of the product. 



It is of interest to inquire what is the difference in the 

 stability of the temporary state of optical activity in the 

 case of the splitting up of a racemate and in that of asym- 

 metric synthesis. Kuhn showed that the ratio H between 

 the time T^ necessary for racemization and the time Ti 

 necessary for the attainment of maximal activity is 

 H = ki/ka ■ K/2 in the case of asymmetric synthesis and 

 H = ki/kf, in the case of the splitting of the racemate. The 

 factor K/2 is absent in the second equation. Since the 

 constant K is large, it is evident that the stability of the 



