Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 435

TABLE 9.3 Some Examples of LHHW Rate ExpressionsdCont'd

Mechanism/
controlling step Overall reaction Rate expression

C A C B C C C D =K eq
K A K 1

5) Bimolecular
(Dual site)
A

A þ s 1 % A $s 1

r ¼ k A C s 1

eq C C C D þð

1 þ K C C C ÞC B

þ B C þ D

%

C A C B C C C D =K eq
K B K 1

B þ s 2 % B $s 2 r ¼ k B C s 2

eq C C C D þð

1 þ K D C D ÞC A

C A C B C C C D =K eq

A $s 1 þ B $s 2 % C $s 1 þ D $s 2

r ¼ k s K A K B C s 1 C s 2

ð 1 þ K A C A þ K C C C Þð 1 þ K B C B þ K D C D Þ

K eq C A C B C C C D
K eq K C C A C B þð

r ¼ k C C s 1

C $s 1 % C þ s 1

1 þ K A C A ÞC C

K eq C A C B C C C D
K eq K D C A C B þð

r ¼ k D C s 2

D $s 2 % D þ s 2

1 þ K B C B ÞC D

C A C B C C =K eq
K A K 1

6) Bimolecular
(Eley-Rideal)
A

A þ s % A $s

r ¼ k A C s

eq C C þð

1 þ K C C C ÞC B

þ B % C

C A C B C C =K eq

A $s þ B % C $s

r ¼ k s K A C s

1 þ K A C A þ K C C C

K eq C A C B C C

r ¼ k C C s

C $s % C þ s

1 þ K A C A þ K eq K C C A C B

The desorption of B (Eqn 9.1c) is also a rapid equilibrium step,

0 ¼ r B;desad ¼ k B q B C s k B C B qC s (9.104)

which gives

k B
k B qC B ¼ K B C B q

q B ¼ (9.105)

The total active site balance leads to

q þ q A þ q B ¼ 1 (9.106)

Substituting Eqns (9.103) and (9.105) into Eqn (9.106) , we obtain after rearrangement

1

q ¼ (9.107)

þ K B C B þ K 1 1

S K B C B

and the fraction of sites occupied by A and B are given by

K B C B

q B ¼ K B C B q ¼ (9.108)

þ K B C B þ K 1 1

S K B C B