Develop a rate law for the HBr reaction that is consistent with the experimental observations given above.  
SolutionIt is customary in discussions of reactions of this sort to let the species formula enclosed in parentheses represent its concentration. In the azomethane reaction, we saw that a rate law of the form 



could account for the change in the apparent reaction order when going from low to high concentration.  
For the HBr reaction  

(CDE71.1)  
where [s_{1}] represents a reaction constant or the concentration of one of the species that will be determined later  
and 
(CDE71.2)  
We see that the concentration dependence of bromine given
in Equation (CDE71.1) is consistent with experimental data. Next consider the HBr dependence. 



One rate expression in which the concentration dependence of HBr is consistent with experimental observation is  
Going to the extremes of high and low concentration 

(CDE71.3) 

Consequently, the concentration dependence of HBr denoted
by Equation (CDE71.31) is consistent with experimental observation. This concentration dependence of the species H_{2}, Br_{2}, and HBr in the rate expression are, respectively, 



Comparing Equations (CDE71.1) and (CDE71.3) we see that [s_{1}] in Equation (CDE71.1) could be (HBr) and that [s_{2}] in Equation (CDE71.3) could beTherefore, Equations (CDE71.1) and (CDE71.3) are combined to give  

(CDE71.5)  
If we now incorporate dependence of the reaction rate on H_{2} [Equation (CDE71.4)] into Equation (CDE71.5), we arrive at the rate expression  

(CDE71.6)  
or, identically,  

(CDE71.7)  
which is consistent with all experimental observations. 