Learning Resources

Solved Problem - Hydrogen Bromide

       
    One of the most studied chain reaction is that between hydrogen and bromine:  
       
   

H2 + Br2 2HBr

(CD7-1)
       
    In studying this reaction we first deduce the rate law from reaction rate-concentration data and then formulate a mechanism and rate equation that are consistent with experimental observations. The relative rates of the reaction of bromine, hydrogen, and hydrogen bromide are  
       
   

IMAGE 07eq133.gif

(CD7-2)
       
    Synthesis of the Rate Law from Experimental Data.
An analysis of the experimental rate data shows the following observations. The reaction is: 		 
       

Experimental
observations
from which to deduce
the rate law

 
  1. First order with respect to the H2 concentration.
  2. Nearly independent of the HBr concentration at low HBr concentrations, and the decreases with increasing HBr concentrations at high HBr concentrations.
  3. Three-halves order in Br2 at low Br2 concentrations and one-half-order in Br2 at high Br concentrations.
 
       
   

Example CD7-1
Deducing the Rate Law

 
       

The Mechanism
     
    We first postulate that the active intermediates are bromine and hydrogen free radicals Brand H, and . Referring to the denominator of the rate equation and to part 1 in Text Table 7-1, we see that the active intermediates Brand Hcollide with HBr and Br2 o intermediates times two species) delineating these collisions or interactions are
     

Propagation steps

 

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    The last reaction has no effect on the overall reaction because one Br2and one Brare produced for every Br2 and Brthat are consumed. However, it is logical to assume that Br2 and H2 probably react instead of Brand Br2:
     
   

IMAGE 07eq147.gif

     
    Note that our proposed scheme of reactions [Equations (CD7-3) through (CD7-6)] produces one of the active intermediates in each step. Now we only need a reaction yielding the initial formation of Brand H. Experience and, possibly, a good guess tell us that the fractional reaction order of Br2 in the numerator suggests that the primary reactive intermediate is Br? formed from Br2 and terminated by the reaction of two bromine free radicals:
     

Initiation and termination steps

 

IMAGE 07eq148.gif

 

   

 

  As a first approximation we shall assume that the mechanism consists of reactions (CD7-3), (CD7-4), and (CD7-6) through (CD7-8). If this mechanism does not produce a rate equation that is consistent with the experimental observations in Equation (CDE7-1.6), we could propose a different mechanism that might include Equation (CD7-5) together with H22Hand similar reactions. The mechanism we first propose is

 

   

The mechanism

 

IMAGE 07eq149.gif

 

   

 

  The specific reaction rates k1 and k5are defined with respect to Br2.
     

 

 

Example CD7-2
Deriving the Rate Law from the Reaction Mechanism