402 Thermodynamics of Enzyme Reactions /22 : I 



to be a trivial one. Suppose two molecular species, say hydrogen and 

 oxygen, are mixed together. Under suitable conditions, the reaction 

 goes off with a bang, producing water and heat. By controlling the 

 reaction, one can carry it out at several temperatures and measure AG 

 as mentioned in the last chapter. The simplest assumption would be 

 that each time two hydrogen molecules and an oxygen molecule 

 approached each other, they reacted, giving up energy. 



The obvious oversimplification of this picture can be emphasized by 

 considering what happens at room temperature. One can introduce a 

 considerable concentration of hydrogen into air. Although many 

 oxygen-hydrogen collisions occur, no reactions are noticed unless some 

 local region is heated by a spark or match. This illustrates that the 

 reaction rate rises sharply as the temperature rises. Many studies on 

 reacting gases have confirmed that reaction rates vary much more 

 rapidly with temperature than do collision rates. 



A reasonable explanation of this variation, which was essentially 

 originated by Arrhenius, is as follows: Suppose two molecular types, 

 A and B, are mixed and can react to form a third molecular type C. 

 When far apart, A has an internal energy E A and B has an internal 

 energy E B . The total internal energy of the two molecules is then 



E A + E n = E 



T 



As they approach each other, there are repulsive forces which tend to 

 keep A and B apart. While they were far apart, their internal energy 

 was all in the form of kinetic energy. As they approach each other, 

 this is converted into potential energy. Figure 1 shows the case where 

 E T is less than the height of the energy barrier E a , and the molecules 

 cannot even approach close enough to react. Let us assume that 

 A and B are approaching each other at r 3 ; they will continue toward each 

 other until they are separated by the distance r x . By the time they 

 reach r 2 , their relative motion has been slowed. At r x , they stop moving 

 because E T is completely potential energy. Because there are repulsive 

 forces which are responsible for the energy barrier to the right of r , 

 the molecules will not remain at r x but will move apart again, main- 

 taining the same total internal energy E T . 



Next, consider a case in which a reaction does occur. This is shown 

 in Figure 2, where E T is greater than E a at r 3 . The molecules again 

 move toward each other, this time having a minimum velocity at r . At 

 r_ l5 A and B give up internal energy, dropping down to E' . Now they 

 have become the molecule C within the potential well. The total energy 

 given up E T + E' must appear eventually as heat. If the average 

 temperature is maintained constant, E° will be the average heat 



