12 1 RADIATION HIOLOGY 



l)()th of which are exothermic. Xoiie of these reactions reduce the total 

 immhcr of atoms present. Therefore the formation of atoms in step (1) 

 must be balanced by their disappearance in atomic combination reactions: 



(5) M+2H-^Br2 + M, 



(6) M + H + Br -^ HBr + M, 



(7) M + 2H -^ H2 + M. 



Since no hydroj^eii atoms arc formed directly and since, furthermore, steps 

 (3) and (4) are much more efficient than the endothermic step (2), the 

 concentration of hydrogen atoms must be much less than that of bromine 

 atoms. Accordingly, the rates of step (6) and (7) must be small com- 

 pared to the rate of step (5). As a working hypothesis, let us assume that 

 only steps (1) through (5) affect the course of the reaction. The corre- 

 sponding mechanism may be written as follows, where the expression for 

 each rate follows its chemical equation: 



(1) Br, + /)i'-^2Br Vi = Us, 



(2) Br + H.2 -^ HBr + H v^ ^ /,-,fH,][Br]. 



(3) H + Br., -^ HBr + Br v^ = A-4Br,][H], 



(4) H + HBr^ H., + Br v^ - A-4[HBr][H], 



(5) M + 2Br-^ Br,, -f- M v, = k,Pc[Br]- = /.{[Br]-. 



Introducing the steady-state assumptions 



^[Br] _ m] _ 



dt ~^ ^'^"^ dt ""' 



then 



2^1 + v-.i + ''4 = ''2 -f 2?'-, 

 and 



V-2 = Vs + ?'4 



may be written. Therefore 



Vl ^ Vr, 



or 



Similarly. 

 and 



[Br] = (J^'- 



/;,[H.,][Br] = {A-.[Br,l + ^•4[HBr]![H] 



k,[BT,] + A-4[HBr] \ /,-.; / 



In terms of the mechanism the rate of formation of hydrogen bromide is 

 given by 



d[HBr] 



-r. — = V2 + V:i — Vi 



dt 



= A-2fH.,l[Br] -f lUBv,] - A^4[HBrl}[H]. 



