40 ORIGIN AND MAINTEN. OF OPT. ACTIVITY 



constant Ki of equilibrium between the /-antipode of the fi- 

 nal substance and the initial product must be equal to the 

 constant K^ of equilibrium between the c/-antipode of the 

 final substance and the initial product. If c is the con- 

 centration of the initial substance, c'l the concentration 

 of the 7-antipode and c'a the concentration of the d-m\ti- 

 pode of the final substance, one has 



c'l/c = K, = c'd/c = Kd (1) 



Condition (1) characterizes a true catalysis. If this con- 

 dition is not fulfilled, the initial substance will be simul- 

 taneously in equilibrium with different concentrations c'l 

 and c\i of the two antipodes and the final product will be 

 partially optically active. But this is thermodynamically 

 impossible in the case of true catalysis. 



Another character of true catalysis is that the value of 

 the equilibrium constant in equation (1) is the same ir- 

 respective of whether a catalyst is used or not. The 

 velocity constant A-,, in the formation of the f/-antipode 

 from the initial material and the velocity constant k'^ in 

 the reverse conversion are increased by the catalyst to 

 the same degree. If the addition of an enzyme would in- 

 fluence the two velocity constants differently and change 

 the equilibrium constant, the reaction would not be a true 

 catalysis and the final product would be optically active. 



Experimentally, as has been said above, it was found 

 that, in the synthesis of the nitrile of mandelic acid, the 

 use of the catalyst does not change the equilibrium 

 constant. 



That both velocities I'a and k'a are accelerated to the 

 same extent by the catalyst has been proved in optically 

 non-specific enzymatic reactions {cf. Borsook, 1935). 



Furthermore, Nordefeldt (1922) has observed that if in 

 the synthesis of mandelo-nitrile, one adds emulsine when 

 the reaction has already proceeded for a while, the enzyme 

 does not change anything in that which has already been 

 transformed, it exerts its asymmetrical effect only on the 

 material yet to be transformed. In a system which has 

 reached the state of equilibrium without enzymes, the ad- 



