The reaction of H 2 and Br 2 to form HBr occurs through the following sequence of elementary steps involving free radicals:

Use the fact that bromine radicals are in equilibrium with Br to derive a rate expression of the form:

2. Chemical reactions that proceed through free radical intermediates can explode if there is a branching step in the reaction sequence. Consider the overall reaction of A B with initiator I and first-order termination of free radical R:

                             I  R                   initiation  

                       R + A  B + R          propagation

                       R + A  B + R +R    branching

                             R side product termination

The rate constants for the above steps are k1, k2, k3, k4, respectively. Notice that two free radicals are created in the branching step for every one that is consumed.

a.) Find the concentration of A that leads to an explosion. (Hint: compare the rates for the branching and termination steps).

b.) Derive a rate expression for the overall reaction when it proceeds below the explosion limit.

3. The reaction of carbon monoxide with steam to produce carbon dioxide and dihydrogen is called the water gas shift (WGS) reaction and is an important process in the production of dihydrogen, ammonia, and other bulk chemicals. The overall reaction is shown below:

           CO+ H2O =CO2 +H2

Iron-based solids that operate in the temperature range of 360 to 530oC catalyze the WGS reaction. One possible mechanism is of the Rideal-Eley type that involves oxidation and reduction of the catalyst surface. This can be represented by the following steps:

           H2O + * ↔H2 + O*   reversible with k1 and k-1 rate constants

           CO+ O*↔CO2 + *    reversible with k2 and k-2 rate constants

Derive a rate expression using Steady State Approximation.

4. Another mechanism for the WGS (Problem #3) is of the Langmuir-Hinshelwood type that involves reaction of adsorbed surface species. For the following steps:

           CO + * ↔CO*                  Equilibrium constant K1

           H2O + 3* ↔2H* + O*     Equilibrium constant K2

           CO* + O* ↔CO2 + 2*    Rate Determining Step, k3 and k-3 rate constants

                      2H*↔H2 + 2*      Equilibrium constant K4

Derive the rate expression based on this mechanism.