PHOTOCHEMISTRY 25 



Introducing the values for the concentrations of the intermediates and 

 simplifying, 



d( ~ A-4[HBr] ■ 



A-.[Br2] 

 The corresponding equation for the quantum yield, 



?t^Hl 



f/[HBr]A// A-f ^ '^ 



<P = - 



labs ji/, I /i:4[HBr: 



^abs I 1 I" 



A::i[Br2] 



is identical in form with the empirical equation. The empirical constant 

 k' corresponding to A-3/A-4 of the theoretical equation is independent of 

 temperature over a wide range. This is consistent with the mechanism 

 since steps (3) and (4) are exothermic reactions of an atom with a dia- 

 tomic molecule and should have small heats of activation. The observed 

 heat of activation for A'^ is 17.6 kcal. This is only slightly greater than 

 the (endothermic) thermochemical heat of step (2). The mechanism has 

 been further tested by investigating the effect of such substances as 

 inert gases on the photochemical rate and by comparing the photo- 

 chemical to the thermal rate. The results of all these tests are consistent 

 with the proposed mechanism. It may be concluded, therefore, that it is 

 very probably correct. 



Limitations of the Method. In the two examples just considered the 

 determination of the mechanism was simplified by rejecting possible reac- 

 tion steps on the basis of thermochemical data. Frequently the necessary 

 thermal data are not available, and there is no a priori reason for rejecting 

 any of the chemically possible steps. Under these conditions the kinet- 

 icist endeavors to find a mechanism consisting of a minimum number of 

 reaction steps which is consistent with the stoichiometry and the kinetics 

 of the reaction. Whenever possible, the rate constants for the individual 

 steps are evaluated in terms of the empirical rate equation. Unless these 

 several constants fall within the (frequently rather wide) range of values 

 permitted by rate theory, the mechanism must be rejected. If the mech- 

 anisms of diff"erent reactions have steps in common, the rate constants 

 for these steps should have the same values regardless of what mechanism 

 they occur in. 



There is no general method by which the mechanism of a reaction may 

 be derived from empirical rate data. The process of devising a mecha- 

 nism is essentially a " cut-and-try " procedure, in some respects similar to 

 the methods used in solving differential equations. As in the latter case, 



