Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 446

If one were to use Eqn (E9-4.41) to correlate experimental data, one would not be able to
distinguish whether it is PSSH model or LHHWwith a rate-limiting step as the parameters
would need to be lumped together. The appeal of the PSSH approach is that it may be able
to approximate the reaction rate in general (i.e. all the fluxes are considered), without
imposing a particular step as the rate-limiting step as illustrated in Fig. E9-4.7 . This approx-
imation is particularly useful when the beginning (reactants) and end (products) are only of
concern.
Based on Fig. E9-4.7 , one can think of the reaction network in analogy to the electric
conduction: 1) the fluxes must be equal at any given point and 2) the total resistance is the
summation of all the resistors in series. If one were to look carefully, these statements could
be detected as both are embedded in Eqn (E9-4.41) .
At this point, one may look back at the full solutions as illustrated in Figs E9-4.3 through
E9-4.5 , especially with Figs. E9-4.3 B and D, E9-4.4 C and D, and E9-4.5 B, that the concentra-
tions of intermediates (in this case, the fractional coverage of A and the fractional coverage of
B) are hardly constant or at “steady state” in any reasonably wide regions where we would
like to have the solutions meaningful. Therefore, the assumption is rather strong. How do the
solutions actually measure up with the full solutions?
To apply the PSSH expression (E9-4.40) or (E9-4.41) , we must first ensure that the reaction
mixture in already in pseudo-steady state to minimize the error may cause in the solution.
This error can be negligible if the amount of catalyst is negligible or for steady flow reactors
where steady state is already reached.
Let us consider again the case where no B is present in the reaction mixture at the start of
the reaction. The concentrations of A and B charged into the batch reactor are C AT0 and
C BT0 ¼ 0. Since there is no B present in the initial reaction mixture, C B0 ¼ 0. Overall mole

balance at the onset of the reaction leads to

C AT0 ¼ C A0 þ q A0 C s þ q B0 C s (E9-4.42)

where q A0 and q B0 satisfy Eqns (E9-4.34) and (E9-4.35) . Since C B0 ¼ 0, substituting

Eqns (E9-4.34) and (E9-4.35) into Eqn (9-4.42) , we obtain

ðK A K C k 1 þ k 1

S

þ k B K B ÞC s C A0

B

C AT0 ¼ C A0 þ (E9-4.43)

K C k 1 þ K A k 1 þ k A þðK A K C k 1 þ k 1

S

þ k B K B ÞC A0

B S B

This quadratic equation can be solved to give

q

ðC AT0 C s aÞ

2

C AT0 C s a þ þ 4aC AT0

C A0 ¼ (E9-4.44)

2

J 1 = r 1 J 2 = r 2 J 3 = r 3

A A .σ B .σ B

r 1 = r net, Ad-A r 2 = r S r 3 = r net, Des-B

FIGURE E9-4.7 A schematic of reaction pathway showing the rates and fluxes between each adjacent inter-
mediates or substances for isomerization of A to B carried out on a solid catalyst.