21:5/ Thermodynamics and Biology 397 



This extremely large equilibrium constant implies that at equilibrium 

 it will be very difficult to detect any hydrogen peroxide. In fact, if 

 one chooses practical values for the ratios of the oxygen and water 

 concentrations to the standard state concentrations, one may compute 

 the equilibrium hydrogen peroxide concentration as follows 



••• [H 2 2 ] 2 = [H 2 0] 2 [0 2 ]/tf 

 [H 2 0] = 1 

 [0 2 ] = 0.24 x 10 3 (in equilibrium with atmosphere) 



7 [H 2 2 ] 2 = 2.4 x 10" 37 

 or [H 2 2 ] =5 x 10" 19 



This value is so low that it represents, on the average, less than 10 mole- 

 cules of hydrogen peroxide per milliliter. This very low concentration 

 must be interpreted as the probability £hat there will be a molecule of 

 hydrogen peroxide in a milliliter of H s O. 



Anyone can go to a neighboring drug store and buy a bottle of hydro- 

 gen peroxide solution. This is a nonequilibrium solution. It will 

 remain in this nonequilibrium condition in a dark bottle for many 

 years providing there are no catalysts present to speed the attainment 

 of equilibrium. Many substances will accomplish this catalysis, 

 including ferric, ferrous, and cupric ions. Per iron atom, the most 

 effective catalyst is the enzyme catalase. None of these catalysts alter 

 either the value of AG or K, but they do alter the rate at which equi- 

 librium is attained. 



It was shown in Chapter 18 that the reaction catalyzed by catalase 

 could be represented as two successive reactions 



e — p x ki p 



E + S^E-S 



* 2 



E P .S + S^±E + 2H 2 + 2 



where E represents catalase, S represents hydrogen peroxide, and 

 ES is the intermediate complex. For each of these two reactions, there 

 is an equilibrium constant defined as 



tf 1= > and * 2 = (i^iraf[°J 



1 (e - p)x p-x 



Both K's can be represented as quotients of rate constants 



K x = kjk 2 and K 2 = kjk^ 

 or as exponentials involving changes in free energy 



Ki = ee-MllRT and K 2 = e -2 e -AG°IRT 



