Tutorials Manual

Chapter 5: Chemical Mechanism Analysis
Tutorials Manual
which we call the “uniform-dimensional” rate constant. Regardless of the order of
reaction, it will have units of mole • cm -3 •sec -1 for a gas-phase reaction or
mole • cm -2 •sec -1 for a surface reaction. In this expression, k f is the rate constant for
the forward reaction, [G] is the total concentration of gas-phase species determined at
the bath gas conditions (in mole • cm -3 ), g is the sum of the stoichiometric coefficients
of all gas-phase species appearing as reactants in the reaction, [Sn] is the total site
density of surface phase n determined at the bath gas conditions, Sn is the sum of the
stoichiometric coefficients of all surface species in phase n participating as reactants
in this reaction.
Using the usual rate constant, one calculates the forward reaction rate as k f times the
product of the concentrations of the reactant species (in mole • cm -3 for gas species,
or mole • cm -2 for surface species) raised to the power of their stoichiometric
coefficients. With the uniform-dimensional rate constant, one calculates the same
*
reaction rate as k f multiplied by the (dimensionless) species mole fractions (gasphase
reactants) or site fractions (surface species) raised to the power of their
stoichiometric coefficients. Thus, independent of the molecularity of the reaction, the
*
reaction rate is k f times quantities that have maximum values on the order of unity
(the mole and site fractions), and it is easier to compare one reaction to another.
*
The quantity k f just discussed can point out which reactions are fast relative to one
another. It can also be of interest to know if a reaction is “fast” relative to a competing
process like molecular transport. The Damköhler number for gas-phase reactions, Da,
allows for such a comparison.
Equation 5-2
Da =
k f
*
----------------------
DG [ ] ⁄ L 2
In Equation 5-2, D is a diffusion coefficient and L is a characteristic length scale for
diffusion; for example, a boundary-layer thickness or a characteristic reactor
dimension. The Damköhler number is a dimensionless number that is a measure of
the relative importance of gas-phase kinetics versus molecular mass transport. If Da
is much greater than 1, then a reaction is fast relative to transport; if it is much less
than 1, then transport processes occur on a shorter time scale than kinetic processes.
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