Learning Resources

Solved Problem - Example CD7-1

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


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

    where [s1] represents a reaction constant or the concentration of one of the species that will be determined later  

andIMAGE 07eq138.gif

    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

IMAGE 07eq140.gifIMAGE 07eq141.gif

    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

    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

    or, identically,  

IMAGE 07eq145.gif

    which is consistent with all experimental observations.