## 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 (CD7-2) Synthesis of the Rate Law from Experimental Data.An analysis of the experimental rate data shows the following observations. The reaction is: Experimentalobservationsfrom which to deducethe rate law First order with respect to the H2 concentration. Nearly independent of the HBr concentration at low HBr concentrations, and the decreases with increasing HBr concentrations at high HBr concentrations. Three-halves order in Br2 at low Br2 concentrations and one-half-order in Br2 at high Br concentrations. Example CD7-1Deducing 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

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:

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

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

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

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