Learning Resources

Solved Problem - Example CD9-1

    Develop a rate law for the HBr reaction that is consistent with the experimental observations given above.  
       
   

Solution

It is customary in discussions of reactions of this sort to let the species formula enclosed in parentheses represent its concentrationIMAGE 07eq132.gif. In the azomethane reaction, we saw that a rate law of the form
 
       
   

IMAGE 07eq134.gif

 
       
    could account for the change in the apparent reaction order when going from low to high concentration.  
       
    For the HBr reaction  
       
    IMAGE 07eq135-36.gif  
   

IMAGE 07eq137.gif

(CDE7-1.1)
       
    where [s1] represents a reaction constant or the concentration of one of the species that will be determined later  
       
   

andIMAGE 07eq138.gif

(CDE7-1.2)
       
    We see that the concentration dependence of bromine given in Equation (CDE7-1.1) is consistent with experimental data.
Next consider the HBr dependence.
 
       
   

IMAGE 07139a.gif

 
       
       
    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
 

IMAGE 07eq140.gifIMAGE 07eq141.gif




(CDE7-1.3)
       
    Consequently, the concentration dependence of HBr denoted by Equation (CDE7-1.31) is consistent with experimental observation.

This concentration dependence of the species H2, Br2, and HBr in the rate expression are, respectively,
 
       
   

IMAGE 07eq142.gif

 
       
    Comparing Equations (CDE7-1.1) and (CDE7-1.3) we see that [s1] in Equation (CDE7-1.1) could be (HBr) and that [s2] in Equation (CDE7-1.3) could beIMAGE 07eq142a.gifTherefore, Equations (CDE7-1.1) and (CDE7-1.3) are combined to give  
   

IMAGE 07eq143.gif

(CDE7-1.5)
       
    If we now incorporate dependence of the reaction rate on H2 [Equation (CDE7-1.4)] into Equation (CDE7-1.5), we arrive at the rate expression  
       
   

image 07eq144.gif

(CDE7-1.6)
       
    or, identically,  
   

IMAGE 07eq145.gif

(CDE7-1.7)
    which is consistent with all experimental observations.