398 Thermodynamics and Biology /2I : 5 



Because catalase acts as a catalyst, these equilibrium constants and 

 AG°'s are related to those for the spontaneous decomposition of hydrogen 

 peroxide as 



K = K X K 2 and AG = AG° + AG° 



If it were possible to measure all four rate constants directly, it would 

 be possible to confirm these last relationships. No one has been able 

 to measure A; 4 for this reaction. However, the free energy change 

 AG 2 can be used to compute £ 4 . This allows a qualitative check on the 

 reaction mechanism, as it shows that A; 4 is so small that it should not be 

 detected experimentally. 



To show this, one must substitute numbers into the formulas above. 

 Referring to Chapter 18, one may use 



k x = 2 x 10 7 sec- 1 

 k 2 = 2 x 10- 4 sec- 1 

 k 3 = 2 x 10 7 sec- 1 



all relative to the standard state 



[O 2 ] (0) = [H 2 Oj,] (0 > = [£] (0) = [E-S] w = 1 mole/liter 



and 



[H 2 O] (0) = 55 moles/liter 



Solving for £ 4 gives 



k k 

 k± = j—-f = 2 x 10 ~ 15 sec -1 , relative to the above standard state 

 ft 2 A 



Similarly, it can be shown that 



K 2 = 10 22 

 K, = 10 11 



both relative to the preceding standard state. 



The foregoing value of K 2 can be used to find the equilibrium concen- 

 tration of hydrogen peroxide in an air-saturated catalase solution. 

 Appropriate concentration ratios relative to the standard state are 



[0 2 ] = 0.24 x 10- 3 

 [E] = 5 x 10~ 6 

 [H 2 0] = 1 



Because only a negligible fraction of the total enzyme exists in complex 

 form, we may write 



[E-S] = [H 2 2 ] = x 



