LOGARITHMIC ORDER OF DEATH 37 



must necessarily be identical in all tubes, as long as 

 the mass law applies. If, in identical test tubes, the re- 

 action would proceed dilTerently, there could be no mass 

 law and no science of chemistry. Thus, if bacteria would 

 die from inactivation of enzymes, all cells should die at 

 the same moment. 



The mass law makes only one assumption, namely, 

 the presence of masses {i.e., of large numbers) of re- 

 acting molecules. This requirement is fulfilled in our 

 case. Estimates by Hand (1933) for catalase in yeast 

 suggest about 2,000 molecules per cell. Haldane and 

 Stern (1932) concluded that the yeast cell contains be- 

 tween 15,000 and 150,000 invertase molecules. The as- 

 sumption of fairly large numbers of enzyme molecules in 

 bacteria, which are in many respects comparable with 

 yeast, seems thus justified, and the logarithmic order 

 of enzyme inactivation cannot explain the logarithmic 

 order of death of bacteria. 



Mass L a IV and Single Molecules. 

 However, if the number of molecules becomes very small, 

 identical cells would not die at the same time. The mass 

 law can not be applied when there is no mass. When a 

 million test tubes, each containing a solution of 1,000 en- 

 zyme molecules, are heated uniformly, it is quite cer- 

 tain that when half of the molecules are inactivated in one 

 tube, the same fraction will be inactivated in all the other 

 tubes. When the same solution is put in much smaller 

 test tubes so that each contains only 10 enzyme mole- 

 cules, it is to be expected that, while 5 molecules are in- 

 activated in most of the tubes, there may be 4 or 6 inacti- 

 vated in some of them. If we choose our tubes so small 

 that each contains only one enzyme molecule, the reac- 

 tion cannot be identical in all the tubes. Yet, the mass 

 law still holds for the entire enzyme solution. By chang- 

 ing the size of the container, the rate of reaction can- 

 not be altered, and, at the same time and temperature, 

 half of the molecules must be inactivated in these small 



