Total Number of Sites, C

The surface reaction is rate limiting. We need to further discuss setting (r_{AD}/k_{A})~0 to arrive at C_{C.S}=K_{I}P_{I}C_{v}. We are going to do this by first using the total number of sites, C_{T} [i.e. C_{T}=C_{v}+C_{A.S}+C_{B.S}], and then use the fractional surface coverage [1=f_{v}+f_{A.S}+f_{B.S}].

For steady state operation we have:

where:

NOTE: Strictly speaking, We really cannot compare the magnitudes of k_{A},
k_{S}, and k_{D} directly, because k_{A} has
different units than k_{S} and k_{D}. Consequently, we
must compare the product (k_{A}P_{C}) with k_{S}
and k_{D} to determine which reaction step may be limiting. If
the surface reaction is limiting, we say k_{A}P_{C} and
k_{D} are very large with respect to k_{S}:

Strictly speaking, We only take ratios of quantities that have the same units.

Ifandare the fraction of free sites and the fraction of covered sites, respectively, andis the gas phase mole fraction of species A, then:

and

For surface reaction control:

which is identical to the expression derived in the text, assuming that:

Developing the Rate Law

Now let's consider developing the rate law on the basis of fractional suface coverage, i.e. (r_{AD}/k_{A})~0 and (k_{ADB}/k_{B})~0.

Assume that the surface reaction is limiting, then:

Table 10-4 Irreversible Surface-Reaction-Limited Rate Laws.

NOTE: This is the same rate law we would get by comparing the k's directly. Return to Chapter