194 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



tants. The same is true of the reverse reaction. Thus, if 



aA + bB^ cC + dD 



where k ] is the measure of inherent attraction A and B have for each other, 

 the over-all rate of reaction in the forward direction of a moles of A with 

 b moles of B (i.e., i\ = -d[A]/dt, or -d[B]/dt, where [ ] denotes concen- 

 tration), is: 



,, = k,[A][A] ••• x [B][B] ••• = k,[A]"[Bf 



Similarly 



v 2 = k 2 [C]'[DY 



This first principle, that of mass action in reaction kinetics, was demon- 

 strated quantitatively by Wilhelmy in 1850. 



At equilibrium the over-all reaction ceases. Therefore i 1 , = v 2 at equi- 

 librium: 



k.imBY = k 2 [C\[DY 



[CYiDY = k L = K 



[A]"[BY " k 2 ' eq 



where K is the equilibrium constant. This form of the Law of Mass Action 

 was stated thus by Guldberg and Waage in 1863. For any reaction 

 -AF° = RT\n K eq , which states that the free energy change per mole (eg., 

 refer to sucrose oxidation) is a measure of the position of equilibrium. 



Steady State 



Consider again the consecutive process discussed above and consider 

 specifically the case in which the supply of A is unlimited, so that the con- 

 centration of A, [A], never changes. If£, > k 2 , A will be converted into B 

 faster than B will be removed into C, and B will accumulate. Since the rate 

 of the reaction B — ► C is 



v 2 = k 2 [B] 



as we saw above, as B accumulates, v 2 increases until it reaches the value 

 of v { . At this point B will have reached its steady-state concentration be- 

 cause the concentration B neither increases nor decreases further. The same 

 is true of the other steps. 

 In the steady-state then 



»1 = V 2 = V i = V 4 



or 



k t [A] = k 2 [B) = k,[C] = k 4 [D] 



