## Learning Resources

#### Solved Problem - Example CD7-1

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 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

(CDE7-1.1)

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

and

(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.

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

(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,

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 beTherefore, Equations (CDE7-1.1) and (CDE7-1.3) are combined to give

(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

(CDE7-1.6)

or, identically,

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