268 BIOLOGICAL EFFECTS OF RADIATION 



plied by 2.303/ (a - h) gives the specific reaction rate k. Third-order 

 reactions are known in which the rate is proportional to the product of 

 three different substances, but these third-order reactions are uncommon. 

 Zero-order reactions are reactions which are entirely independent of the 

 concentration, as given by equation (13). 



-^ =k (tS) 



at 



They are frequently found among photochemical reactions. 



Chain Reactions.— \N hen the products of reaction are formed with the 



liberation of sufficient energy to activate additional reactants, a chain 



reaction results. An energy chain is defined as one in which the series 



of reactions are continued simply by the transfer of energy. Stoichio- 



metrical chain reactions are, however, much more common. In the case 



of a stoichiometrical chain it is possible to write a series of chemical 



reactions in which a product, such as an atom, combines with reactants 



and again produces the product which can react with more material 



and continue in a manner such as is illustrated for the hydrogen-chlorine 



chain given below. 



CI2 + light = 2C1 



CI -F H2 = HCl + H 



H + CI2 = HCl + CI 



Cl-f H2 = HCl + H 



etc. 

 These chain reactions can involve few or many molecules, depending on 

 conditions. The hydrogen and chlorine chain reaction may involve up 

 to about a million molecules for each molecule of chlorine which is 

 dissociated. Other chain reactions are of much shorter length. 



Temperature Effect. — Aside from finding the order of the reaction 

 and, if possible, a mathematical relationship connecting concentration 

 with time, one of the most important studies in chemical kinetics involves 

 the finding of the temperature coefficient. The fundamental formula 

 which relates the velocity constant with the temperature is given by 



equation {14)- 



dink E 



dT RT^ 

 On integration equation (15) is obtained. 



(U) 



k_, _ E(T, - T,) .^^. 



^^fci 2.303/^(^2 X T,) 

 The nature of this equation is such that when the logarithm of the 

 velocity constant k is plotted against the reciprocal of the absolute 

 temperature a straight line is obtained and the slope of this line multiplied 

 by 2.303 and by the gas constant R (2 cal.) gives the energy of activation 

 for the reaction. Obviously, if two or more reactions are involved, the 



