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7/30/2019 Oyeah Assignment

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(2-2) Example of a chain reaction having a complicated rate law - The formation of HBr

from hydrogen and bromine.

As we had seen in the introductory section of chemical kinetics, although the stoichiometric

equation for the reaction between hydrogen and bromine to give HBr looks very simple, the rate

law is very complicated indicting a complex mechanism (see fig 1) i.e.:

Fig. 1: The A schematic representation of the mechanism of the reaction between hydrogen and

bromine. Note how the reactants and products are shown as arms to the circle, but the

intermediates (H and Br) occur only within the circle. Similar diagrams are used to depict the

action of catalysts.

The proposed mechanism for this reaction (see Fig. 1.) is:


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Note regarding step (d), termination: The third body M removes the energy of recombination.

Other possible termination steps include the combination of H atoms to form H2 and the

combination of H and Br atoms to from HBr. However it turns out that only Br atom

recombination it important.

Through this mechanism, it may be deduced that the net rate of formation of HBr (product) is

given by:

where the concentrations of the intermediates may be determined by invoking the steady stateapproximation, i.e.:

and:

i.e. from (ii) + (i) we obtain:

i.e.:

which substituted back in (i) gives:

i.e.:

i.e.:


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or: dividing 'top' and 'bottom' by k`b:

Thus, the net rate of formation of HBr may be written solely in terms of reactants, i.e.:

which simplifies to:

as predicted by the empirical rate law:

where:


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and:

Note:

(1) The presence of [HBr] in the denominator is a sign that HBr is acting as an inhibitor, and

reducing the rate of formation of product. Likewise, the presence of [Br2] stems from the role ofBr2 in the removal of the reactive hydrogen radicals from the chain.

(2) In the examples we have considered, the observed rate laws are reproduced by the

mechanisms. In the past, that used to be essentially the end of the calculation (but not of theexperimental investigation). However, we can make use of computers to integrate the

approximate rate law numerically, and hence predict the time dependence of the HBr

concentration. (See Fig. 2). Mathematical software may also be used to integrate the originalcoupled rate laws without needing to invoke the steady-state approximation.

Fig. 2: The numerical integration of the the HBr rate law, can be used to explore how theconcentration of HBr changes with time. These runs began with stoichiometric proportions of

hydrogen and bromine; the curves are labelled with the value of 2k'-1.


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(3) HBr may also be produced through in a process where the initiation step is photochemical. In

this case, the initiation step is of the form:

whilst the other steps are as in the thermal process (b-d).

where represents the rate at which photons of the appropriate frequency are absorbed bythe volume in which the reaction occurs. In this case, the rate of formation of HBr in this case is

given by:

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