Chemical Reactions on Solid Surfaces - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 452

power-law terms of the coverage function are negligible as compared with the exponential
variations, the kinetic expressions derived is not expected to be valid in as wide ranges as
one would expect from LHHW expressions. In most cases, the expressions derived from
this approach are merely comparable to LHHW expressions. Table 9.4 shows a comparison
of some examples where both LHHW and power-law form correlations have been made.
Tables 9.5 and 9.6 show some of the rate expressions based on the ExLand and UniLan
adsorption isotherms when surface reaction is limiting. One can observe that when ExLan
and UniLan are employed to derive the rate expressions, the reaction rate expressions are
quite similar to those of the LHHW expressions.

TABLE 9.5 Some Examples of Rate Expressions with ExLan Adsorption Where Surface Reaction is the
Rate-Limiting Step

Overall reaction Rate expression

1) Isomerization A % B b ¼ K A C A þ K B C B

þ b 1 r ¼ k s K A C s ðC A C B =K eq Þ ln ð 1 Þ

ln 2 þ b 1

r ¼ k s K A K B C 2 2) Bimolecular A þ B % C þ D

s ðC A C B C C C D =K eq Þ

ð 1 Þ

b ¼ K A C A þ K B C B
þK C C C þ K D C D

r ¼ k s K 1=2

s ðC 1=2

A 2 K B C 2

ln 2 þ b 1

3) Bimolecular (dissociative)
1
2 A 2 þ

1
2

1
2

A 2 C B C C C D =K eq Þ

ð 1 Þ

b ¼ K

A 2 þ K B C B
þK C C C þ K D C D

A 2 C

B C þ D

%

þ b 1

4) Bimolecular (Eley-Rideal)
A

b ¼ K A C A þ K C C C r ¼ k s K A C s ðC A C B C C =K eq Þ ln ð 1 Þ

þ B C

%

TABLE 9.6 Some Examples of Rate Expressions with UniLan Adsorption Where Surface Reaction Is the
Rate-Limiting Step

Overall reaction Rate expression

þ bexp E max
RT

1) Isomerization A B b ¼ K A C A þ K B C B

%

1

RT
E max b

r ¼ k s K A C s ðC A C B =K eq Þ ln

1 þ b

þ bexp E max
RT

2) Bimolecular
A

b ¼ K A C A þ K B C B
þK C C C þ K D C D

C A C B RT

E max b

2

ln 2 1

þ B C þ D

% C C C D

K eq

r ¼ k s K A K B C 2

s

1 þ b

þ bexp E max
RT

1
2 A 2 þ K B C B
þK C C C þ K D C D

1
2 A 2 C

3) Bimolecular
(dissociative)
1
2 A 2 þ

C RT

E max b

2

1

b ¼ K

2 2

A 2 C B

C C C D
K eq

ln 2

A 2 K B C 2

r ¼ k s K

s

1 þ b

þ

B % C D

þ bexp E max
RT

1

RT
E max b

b ¼ K A C A þ K C C C r ¼ k s K A C s ðC A C B C C =K eq Þ ln

4) Bimolecular (Eley-
Rideal) A

1 þ b

þ

B % C