Kinetic Models in Heterogeneous Catalysis - ACS Publications

2 Kinetic Models in Heterogeneous Catalysis S O L W. W E L L E R

Downloaded by UNIV OF PITTSBURGH on June 17, 2013 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0148.ch002

Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, Ν . Y. 14214

The

diverse

objectives monly muir,

meanings

used and Freundlich,

concentrations isotherm, reactive

models are reviewed.

theoretically and

derivable

problems

Temkin—attempt

arise

with

apparent

and abnormal

coefficients.

A few procedural

whose primary primary

In the

modelling

suggestions

interest is reaction

surface Langmuir

of

from

adsorption

dependence

approaches

interest is reactor design

com

adsorption

values

temperature

Various

years have been taken to kinetic catalysis.

to relate

enhanced

negative

varied

Three

isotherms—Lang

to gas phase composition.

mixtures,

coefficients, sorption

of "kinetic models" and the

in establishing

in the in

of

ad

past

10

heterogeneous

are offered for

those

and for those

whose

mechanism.

' T ^ h e subject of k i n e t i c m o d e l s i n heterogeneous catalysis is a t r o u b l i n g A

one. A r i g o r o u s t h e o r y of heterogeneous c a t a l y t i c k i n e t i c s is analogous

to a G r e e k t r a g e d y : the p r o t a g o n i s t is d o o m e d to f a i l u r e , a n d t h e course of t h a t f a i l u r e is k n o w n to the observers f r o m the start. T h e roots of t h i s p r e o r d a i n e d d o o m f o r p r a c t i c a l systems are t w o - f o l d . F i r s t , the surface of a p r a c t i c a l catalyst is not u n i f o r m , g e o m e t r i c a l l y or e n e r g e t i c a l l y ; t h e adsorbate m o l e c u l e s m a y i n t e r a c t b o t h to p r o d u c e surface complexes a n d also to g i v e a d s o r p t i o n energies that d e p e n d o n surface coverage;

n e i t h e r of these effects is q u a n t i t a t i v e l y p r e d i c t a b l e

t o d a y f r o m first p r i n c i p l e s f o r a n y a r b i t r a r y system. A s a result, w e h a v e n o w a y of k n o w i n g i n a d v a n c e , for a n y system, w h i c h of s e v e r a l different isotherms is q u a n t i t a t i v e l y v a l i d .

M o r e is s a i d a b o u t different i s o t h e r m s

later, a n d I p o i n t out h e r e o n l y that e a c h of t h e m d e p e n d s o n t h e u n v e r i fiable

a s s u m p t i o n of some m o d e l a b o u t t h e u n i f o r m i t y of t h e surface or

t h e d i s t r i b u t i o n of energies. T h e s e c o n d root of the t r a g e d y lies i n the n e e d to use a d s o r p t i o n isotherms at a l l . I n h o m o g e n e o u s k i n e t i c s , a n d often i n e n z y m a t i c k i n e t i c s , 26 In Chemical Reaction Engineering Reviews; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

2.

WELLER

Kinetic

27

Models

one c a n measure d i r e c t l y the concentrations of the r e a c t i n g species.

With

the a d d e d a s s u m p t i o n that the mass a c t i o n l a w is a p p l i c a b l e to e l e m e n t a r y r e a c t i o n steps, w e c a n t h e n p i e c e out a r e a c t i o n m e c h a n i s m w h i c h c a n b e e x a m i n e d for consistency w i t h the g l o b a l k i n e t i c s . I n heterogeneous catalysis w e g e n e r a l l y are i g n o r a n t of the surface concentrations.

Even

as p o w e r f u l a t o o l as m e a s u r e m e n t of the I R a b s o r p t i o n spectra of a d s o r b e d species, for e x a m p l e , m a y give i n f o r m a t i o n a b o u t entities w h i c h are present i n l a r g e c o n c e n t r a t i o n o n the surface b u t m a y b e i r r e l e v a n t to the r e a c t i o n m e c h a n i s m .

[ T h e c o n c e p t of a "most a b u n d a n t surface


i n t e r m e d i a t e " ( m a s i ) , discussed b y B o u d a r t i n his recent a n d excellent review ( I ) , mediates.]

is c o n c e r n e d

w i t h surface species t h a t are, i n fact, i n t e r -

W e t h e n a d d to this p r o b l e m of i n d i r e c t estimate of surface

concentrations the i m p l i c i t a s s u m p t i o n that the s i m p l e mass a c t i o n l a w a p p l i e s to e l e m e n t a r y surface reactions.

T h e l i t e r a t u r e is r e p l e t e w i t h

c l a i m s of r a t e - l i m i t i n g surface reactions that are t h i r d or f o u r t h o r d e r — a result w h i c h w o u l d m a k e a h o m o g e n e o u s k i n e t i c i s t t r e m b l e . N e v e r t h e l e s s , the reactions occur, w e c a n m a k e some sense out of t h e k i n e t i c s , a n d w e h a v e some f e e l i n g a b o u t t h e g e n e r a l p r i n c i p l e s t h a t u n d r l y heterogeneous k i n e t i c s . W h a t is the r a t i o n a l m a n to do? has b e e n a s p e c t r u m of possible approaches, a l l of w h i c h h a v e a n d examples of w h i c h I w i l l give. those

who

There

advocates,

N e a r one e n d of t h e s p e c t r u m are

c o r r e c t l y c l a i m t h a t f u n d a m e n t a l u n d e r s t a n d i n g is c l e a r l y

p r e f e r a b l e to r a w e m p i r i c i s m a n d w h o also b e l i e v e that there is a d e q u a t e reason to a c c e p t the q u a n t i t a t i v e v a l i d i t y of some i s o t h e r m (say, L a n g m u i r - H i n s h e l w o o d ) a n d of the mass a c t i o n p r i n c i p l e , a n d t h a t i t is possible to establish the r e a c t i o n m e c h a n i s m ( or at least the r a t e - l i m i t i n g s t e p ) t h r o u g h consistency w i t h the o b s e r v e d k i n e t i c s . N e a r the

other

e n d of the s p e c t r u m are those w h o c l a i m t h a t n o n e of t h e theories has q u a n t i t a t i v e v a l i d i t y a n d t h a t t h e i m p o r t a n t t h i n g i n p r a c t i c e is to o b t a i n the most c o n v e n i e n t e m p i r i c a l k i n e t i c e q u a t i o n t h a t p r o v i d e s a d e q u a t e fit to observations a n d that p e r m i t s d e s i g n of c o m m e r c i a l reactors i n t e n d e d to operate w i t h i n the r a n g e of parameters studies.

The

intermediate

positions are n u m e r o u s . O n e p o p u l a r one, at least a m o n g chemists t u r n e d kineticists, is to assert that some i s o t h e r m , say L a n g m u i r - H i n s h e l w o o d , gives correct q u a l i t a t i v e insights a l t h o u g h i t m a y l a c k q u a n t i t a t i v e v a l i d i t y , that u s e f u l forms of the g l o b a l rate expression m a y b e d e d u c e d

on

the basis of this a s s u m p t i o n , b u t t h a t b y n o means is the r e a c t i o n m e c h a n i s m to b e b e l i e v e d as p r o v e d s i m p l y f r o m consistency w i t h k i n e t i c d a t a . A n o t h e r i n t e r m e d i a t e p o s i t i o n , i n t r i n s i c a l l y a t t r a c t i v e , is to say t h a t w e w i l l progressively complicate

(as n e e d e d ) the s i m p l e s t t h e o r e t i c a l ex-

p r e s s i o n {e.g., of the L a n g m u i r - H i n s h e l w o o d t y p e ) , i n c o r p o r a t e

those

changes r e q u i r e d b y heterogeneity or i n t e r a c t i o n , a n d suffer as a necessary e v i l the r e s u l t i n g c o m p l i c a t i o n s i n the final rate l a w . T h e d i f f i c u l t y

In Chemical Reaction Engineering Reviews; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

28

CHEMICAL

REACTION ENGINEERING

w i t h this, of course, is t h a t w e don't k n o w a priori

REVIEWS

what complications

are q u a n t i t a t i v e l y justified for o u r system. P e r h a p s the best w a y to p r o c e e d h e r e is to t r y to a n s w e r s o m e f u n d a m e n t a l questions. ( 1 ) S o m e d e f i n i t i o n of terms is a p p r o p r i a t e . w e mean by "kinetic model"?

S p e c i f i c a l l y , w h a t do


( 2 ) W h y do w e w i s h to e s t a b l i s h the k i n e t i c m o d e l ? objectives as engineers or e n g i n e e r i n g scientists?

W h a t are o u r

( 3 ) S i n c e w e n o r m a l l y cannot d i r e c t l y d e t e r m i n e the surface c o n centrations of r e a c t i n g species, w h a t is the r a n g e of v a l i d i t y of the v a r i o u s a d s o r p t i o n isotherms t h a t relate surface concentrations to the o b s e r v a b l e gas-phase p a r t i a l pressures? ( 4 ) T o w h a t extent c a n k i n e t i c s f u r n i s h u n a m b i g u o u s answers to c e r t a i n f u n d a m e n t a l questions c o n c e r n i n g the n a t u r e of the catalyst surface a n d the d e t a i l e d course of the surface reactions w h i c h are a c t u a l l y occurring? Kinetic

Models

T h e r e are at least t w o i n t e r p r e t a t i o n s of this expression to b e f o u n d i n the l i t e r a t u r e : ( a ) T h e a c t u a l m e c h a n i s m , at the m o l e c u l a r l e v e l , b y w h i c h the c h e m i c a l r e a c t i o n occurs. ( b ) A c o n v e n i e n t a n d r e a s o n a b l e r e p r e s e n t a t i o n of the r e a c t i o n w h i c h , a l t h o u g h n o t i n g e n e r a l u n i q u e , is at least consistent w i t h k n o w n d a t a a n d p e r m i t s b o t h i n t e r p o l a t i o n a n d some e x t r a p o l a t i o n . [ K n o z i n g e r et al. (2) h a v e r e c e n t l y d r a w n even m o r e e x p l i c i t d i s t i n c t i o n s i n the f o l l o w i n g d e f i n i t i o n s : " M e c h a n i s t i c m o d e l : a r e a c t i o n s c h e m e w h i c h c a n b e i n t e r p r e t e d as a possible m o l e c u l a r m e c h a n i s m , t h e i n t e r m e d i a t e species a n d active sites of w h i c h c a n b e o b s e r v e d d i r e c t l y or m u s t b e p o s t u l a t e d o n the g r o u n d s of e x p e r i m e n t a l e v i d e n c e . K i n e t i c e q u a t i o n : a r a t e e q u a t i o n t h a t is d e d u c e d for a g i v e n m e c h a nistic model. K i n e t i c m o d e l : a p u r e l y f o r m a l r e a c t i o n scheme w h o s e i n t e r m e d i a t e s a n d a c t i v e sites are not i n t e r p r e t e d as a n y r e a l c h e m i c a l species. F o r m a l k i n e t i c e q u a t i o n : a rate e q u a t i o n that is d e d u c e d for a g i v e n kinetic model."] T h e difference b e t w e e n the t w o i n t e r p r e t a t i o n s is n o t t r i v i a l since i t is a l w a y s d e s i r a b l e i n science to d i s t i n g u i s h b e t w e e n r e a l i t y a n d p l a u s i b i l i t y or, i n other w o r d s , b e t w e e n necessity a n d consistency.

I n o n e case,

e s t a b l i s h i n g the k i n e t i c m o d e l is c o n s i d e r e d the e q u i v a l e n t of e s t a b l i s h i n g a u n i q u e t r u t h c o n c e r n i n g the w a y i n w h i c h the r e a c t i o n a c t u a l l y occurs. I n the other, o n l y consistency a n d c o n v e n i e n c e are i n v o l v e d . B o u d a r t

(3)

has expressed a n extreme p o s i t i o n o n the e n t i r e m a t t e r : " ' M e c h a n i s m ' or ' m o d e l ' c a n m e a n a n a s s u m e d r e a c t i o n n e t w o r k , or a p l a u s i b l e s e q u e n c e of steps for a g i v e n r e a c t i o n , o r a p o s t u l a t e d s t e r e o c h e m i c a l p a t h d u r i n g


2.

WELLER

Models

29

the course of a n i s o l a t e d step.

S i n c e methods of i n v e s t i g a t i o n a n d goals

Kinetic

are so u t t e r l y different i n the s t u d y of n e t w o r k s , sequences a n d steps, the w o r d s ' m e c h a n i s m ' or m o d e l ' s h o u l d be a v o i d e d .

T h e y have acquired

the b a d c o n n o t a t i o n associated w i t h i r r e s p o n s i b l e or v a i n s p e c u l a t i o n , l a r g e l y to describe achievements that v a r y w i d e l y i n s o p h i s t i c a t i o n . " A t this p o i n t i t is u s e f u l to ask w h y w e w i s h to e s t a b l i s h the k i n e t i c m o d e l for a surface r e a c t i o n . I f t h e reason is to p r o v e c o n c l u s i v e l y the m o l e c u l a r m e c h a n i s m b y w h i c h the r e a c t i o n is t r u l y o c c u r r i n g o n the catalyst surface, t h e n t h e response m u s t p r o b a b l y be t h a t ( 1 ) the m e c h a


n i s m of

no

s o l i d - c a t a l y z e d r e a c t i o n is a d e q u a t e l y

m o l e c u l a r l e v e l , e v e n for as s i m p l e a case as H — D 2

2

understood

at

the

exchange, a n d ( 2 ) of

a l l the s o p h i s t i c a t e d approaches t h a t h a v e b e e n a p p l i e d to t h e e s t a b l i s h i n g of c a t a l y t i c r e a c t i o n m e c h a n i s m s , k i n e t i c s is a m o n g the least u s e f u l i n p r o v i d i n g u n a m b i g u o u s answers.

M u c h m o r e u s e f u l , i n different sys

tems, are t e c h n i q u e s s u c h as i s o t o p i c tracer studies, i s o t o p i c r a t e effects, d e t e r m i n a t i o n of s t o i c h i o m e t r i c n u m b e r , i n v e s t i g a t i o n of the stereochemis t r y of c o m p l e x

r e a c t i o n p r o d u c t s , a n d i n f r a r e d a b s o r p t i o n spectra

of

a d s o r b e d species, w h i c h h a v e a l l g i v e n s o m e i n s i g h t as to the r e a c t i o n mechanism. O n the other h a n d , i f w e w i s h a k i n e t i c m o d e l for less a m b i t i o u s reasons—to

b e consistent w i t h r a t e d a t a , to p e r m i t reactor d e s i g n , to

suggest n e w experiments b a s e d o n p r e d i c t i o n s of the m o d e l , to c o n t r i b u t e q u a l i t a t i v e i n s i g h t i n t o a possible r e a c t i o n p a t h — t h e n m a n y

approaches

are possible a n d p l a u s i b l e . Adsorption

Isotherms

M o s t of us go t h r o u g h the f o l l o w i n g steps i m p l i c i t l y or e x p l i c i t l y , i n d e r i v i n g a rate e q u a t i o n o n the basis of a p a r t i c u l a r k i n e t i c m o d e l f o r a surface-catalyzed reaction: ( a ) C h o o s e a p a r t i c u l a r surface r e a c t i o n as the r a t e - l i m i t i n g step. ( F o r s i m p l i c i t y , this d i s c u s s i o n is l i m i t e d to cases w h e r e s u c h a p r o c e d u r e is justifiable—i.e., w h e r e a l l h e a t a n d mass transfer steps a n d a l l a d s o r p t i o n a n d d e s o r p t i o n processes are r e l a t i v e l y r a p i d ; o n l y one step i n a n o v e r a l l sequence is rate l i m i t i n g , etc. ) A s a n e x a m p l e , i n a r e a c t i o n 2 A -> Β + C , w e m a y w i s h to c o n s i d e r t h e i m p l i c a t i o n of a s s u m i n g t h a t ( 1 ) r e a c t i o n occurs o n l y b e t w e e n m o l e c u l e s of c h e m i s o r b e d A , a n d ( 2 ) t h e r a t e l i m i t i n g step is r e a c t i o n b e t w e e n t w o m o l e c u l e s of A a d s o r b e d o n adjacent sites. ( b ) A s s u m e t h a t a c o n v e n t i o n a l m a s s - a c t i o n l a w applies to s u c h surface reactions, w h e r e the G u l d b e r g - W a a g e " a c t i v e masses" are p r o p o r t i o n a l to the surface concentrations ( o r f r a c t i o n a l c o v e r a g e ) . ( c ) A s s u m e that some i s o t h e r m e q u a t i o n c o r r e c t l y relates the surface c o n c e n t r a t i o n of a n y species to the o b s e r v a b l e p a r t i a l pressures of a l l species i n the a m b i e n t b u l k gas.


30

C H E M I C A L

R E A C T I O N

E N G I N E E R I N G

R E V I E W S

( d ) D e d u c e the c o r r e s p o n d i n g rate e q u a t i o n r e l a t i n g the k i n e t i c s to t h e o b s e r v a b l e p a r t i a l pressures.

global

A l t h o u g h the f o l l o w i n g discussion w i l l focus l a r g e l y o n step c, b r i e f c o m m e n t s a b o u t a a n d b are a p p r o p r i a t e . surface

reactions

L a n g m u i r (4, 5)

i n terms

of

F i r s t , i t is c o m m o n to treat

the f u n d a m e n t a l

and Hinshelwood

concept advanced

that the molecules

(6)—i.e.,

w h i l e a d s o r b e d , w i t h c o v e r a g e not exceeding

a monolayer.

by

react

Langmuir

h i m s e l f , i n his e x t r a o r d i n a r y 1921 p a p e r o n the P t - c a t a l y z e d o x i d a t i o n of C O and H

(5),

2

suggested

a n alternate p o s s i b i l i t y : that r e a c t i o n


o c c u r d i r e c t l y o n c o l l i s i o n of a gas m o l e c u l e w i t h a n a d s o r b e d or a t o m .

T h i s concept was later d e v e l o p e d

may

molecule

b y R i d e a l a n d E l e y (7,

8)

a n d has b e e n v a r i o u s l y l a b e l l e d t h e L a n g m u i r - R i d e a l , R i d e a l - E l e y , E l e y R i d e a l , or " d i v e - b o m b " m e c h a n i s m .

T h e resultant rate equations

significantly f r o m the L a n g m u i r - H i n s h e l w o o d f o r m .

differ

T h e r e are f e w , i f

any, u n a m b i g u o u s examples w h e r e this m e c h a n i s m is operative.

[Never-

theless, S i n f e l t has h a d great p r a c t i c a l success i n a p p l y i n g a m i l d l y c o m p l i c a t e d v e r s i o n of hydrogenolysis

this m e c h a n i s m

i n the treatment of

o v e r s u p p o r t e d metals.

hydrocarbon

H i s m o d e l is d e r i v e d f r o m that

u s e d e a r l i e r b y T a y l o r a n d co-workers at P r i n c e t o n , cf. Réf. 10.1 ever, the M a r s - v a n K r e v e l e n ( 9 ) t r a n s i t i o n m e t a l oxides

How-

a p p r o a c h to o x i d a t i o n reactions

over

does i n fact i n v o k e the n o t i o n of c y c l i c

redox

r e a c t i o n of the catalyst d i r e c t l y o n c o l l i s i o n of a gaseous m o l e c u l e

( sub-

strate or 0 ) 2

w i t h the ( o x i d i z e d or r e d u c e d ) surface.

This

approach

has a c h i e v e d c o n s i d e r a b l e p o p u l a r i t y ; its f u n d a m e n t a l f o r m u l a t i o n a n d l i m i t a t i o n s are c o n s i d e r e d i n some d e t a i l later. W i t h respect to i t e m b , i f the b i n d i n g energies of a d s o r b e d

mole-

cules are n o t i d e n t i c a l , there is no reason to expect e q u a l r e a c t i v i t y of those molecules.

T h e d i r e c t result is that the a s s u m p t i o n of a surface

mass-action rate l a w is w i t h o u t ' t h e o r e t i c a l justification for systems n o n - u n i f o r m energetics.

of

T o p u t the m a t t e r another w a y , the surface rate

constant k, n o r m a l l y a s s u m e d to be o n l y a f u n c t i o n of t e m p e r a t u r e , w i l l also be a f u n c t i o n of surface coverage i n the g e n e r a l case. W e n o w consider i t e m c a n d i n q u i r e : w h a t is the p r o p e r e q u i l i b r i u m a d s o r p t i o n i s o t h e r m to be u s e d i n d e v e l o p i n g a rate e q u a t i o n ?

Again

f o r s i m p l i c i t y , the discussion is l i m i t e d to a d s o r p t i o n w i t h o u t d i s s o c i a t i o n . B e f o r e a t t e m p t i n g a n answer, w e r e v i e w some salient characteristics of t h e L a n g m u i r , F r e u n d l i c h , a n d T e m k i n isotherms a n d the assumptions involved i n their derivation. r e l e v a n c e to m o n o l a y e r Langmuir Isotherm.

These

are s i n g l e d out because of

their

chemisorption. T h e L a n g m u i r isotherm, initially derived

the basis of k i n e t i c arguments (11),

on

c a n b e d e r i v e d e q u a l l y w e l l f r o m the

statistical t h e r m o d y n a m i c s a p p r o p r i a t e to e q u i l i b r i u m i n i d e a l l o c a l i z e d monolayers

(12).

However,

i n either case the v a l i d i t y of the


simple

2.

WELLER

Kinetic

31

Models

i s o t h e r m depends o n the satisfaction of a set of postulates, some of w h i c h are m o r e easily g r a n t e d t h a n others as b e i n g true for r e a l systems.

Re

gardless of a n y questions c o n c e r n i n g t h e q u a n t i t a t i v e v a l i d i t y of a l l t h e postulates, L a n g m u i r ' s concepts are of f u n d a m e n t a l i m p o r t a n c e to a l l subsequent t h e o r e t i c a l w o r k i n the

field.

Some of the k e y assumptions a n d results of the e l e m e n t a r y e q u a t i o n


are: ( 1 ) A d s o r p t i o n occurs o n a finite n u m b e r of e q u i v a l e n t sites o n a u n i f o r m surface. ( 2 ) E a c h site c a n adsorb one a n d o n l y one gas m o l e c u l e , a n d the a d s o r p t i o n is l o c a l i z e d . T h i s i m p l i e s l o c a l i z e d m o n o l a y e r s . If the m o l e cules w e r e t o t a l l y free to m o v e over the surface w i t h n o m u t u a l i n t e r a c t i o n , t h e y w o u l d b e h a v e as a t w o - d i m e n s i o n a l p e r f e c t gas. F r e e d o m to m o v e , b u t w i t h v a r y i n g degrees of m u t u a l i n t e r a c t i o n , w o u l d c o r r e s p o n d to the a p p r o p r i a t e l y i m p e r f e c t , t w o - d i m e n s i o n a l gas. ( 3 ) T h e a d s o r b e d m o l e c u l e s d o n o t i n t e r a c t , a n d t h e i r energies are i n d e p e n d e n t of the presence or absence of a d s o r b e d m o l e c u l e s o n n e i g h b o r i n g sites. ( 4 ) I f t w o or m o r e species of gas m o l e c u l e s are present, t h e y w i l l c o m p e t e for a d s o r p t i o n o n t h e fixed n u m b e r of e q u i v a l e n t sites. ( 5 ) F o r a n y gaseous species i , the c o r r e s p o n d i n g e q u i l i b r i u m a d s o r p t i o n constant K i is the r a t i o of a n a d s o r p t i o n r a t e constant fc a n d a d e s o r p t i o n rate constant k . K is i n t r i n s i c a l l y p o s i t i v e . M o r e o v e r , K i = e x p C - A G i V R T ] = e x p [ + A S i ° / R ] e x p [ - A H ° i / R T ] , w h e r e AG ASi°, a n d ΔΗι° are the free energy, e n t r o p y , a n d e n t h a l p y change o n a d s o r p t i o n . ( 6 ) F o r a n y gaseous species i at a p a r t i a l pressure p the f r a c t i o n of sites c o v e r e d b y a d s o r b e d i (θι) increases l i n e a r l y w i t h p at sufficiently l o w values of p\\ conversely, θι becomes i n d e p e n d e n t of p\ at sufficiently h i g h values of p . in

in

{

U

u

x

{

T h e p r o b l e m s w i t h the q u a n t i t a t i v e , l i t e r a l a p p l i c a t i o n of the s i m p l e L a n g m u i r i s o t h e r m h a v e b e e n presented i n m a n y places.

Only a few

a d d i t i o n a l c o m m e n t s are m a d e here, chiefly i n c o n n e c t i o n w i t h the t e m p e r a t u r e d e p e n d e n c e a n d the s i g n of the constants K i . P a r e n t h e t i c a l l y , L a n g m u i r was one of his o w n most severe critics. I n his 1938 F a r a d a y L e c t u r e (13)

he observes, i n d i s c u s s i n g his w o r k o n the a d s o r p t i o n of

c e s i u m o n tungsten,

. . t h e p h y s i c a l assumptions u n d e r l y i n g this f a c t o r

( 1 — θ ) [ i n the e q u a t i o n for the a d s o r p t i o n rate] are v e r y i m p r o b a b l e . . . . E v e n i f there w e r e n o m o b i l i t y at a l l , w e cannot j u s t i f y the f a c t o r ...

i f the sites are closely adjacent to one another.

I n this case i t is

m o r e r e a s o n a b l e to assume t h a t ( 1 — θ ) s h o u l d b e r e p l a c e d b y ( 1 — β ) 4

B o u d a r t , i n 1956 (14)

a n d since, has p r o p e r l y e m p h a s i z e d the i m

p o r t a n c e of e x a m i n i n g the t e m p e r a t u r e d e p e n d e n c e of the e q u i l i b r i u m a d s o r p t i o n constants K i i n o r d e r to establish t h a t the heats a n d entropies of a d s o r p t i o n are reasonable. H e q u o t e d t h e e x a m p l e of stibine d e c o m p o s i t i o n o n a n t i m o n y , w h e r e the k i n e t i c d a t a are w e l l fitted b y the L a n g m u i r e q u a t i o n for a single site m o d e l , r = kKp/(l

+ Kp).

Experimentally, Κ


32

CHEMICAL

REACTION ENGINEERING

REVIEWS

is essentially i n d e p e n d e n t of t e m p e r a t u r e , i m p l y i n g that AH ~ 0, a n u n reasonable

result.

The

deduced

AS

a

is also unreasonable.

Boudart's

suggestion that the " p a r a d o x of heterogeneous k i n e t i c s " c a n a c c o u n t for the t e m p e r a t u r e i n d e p e n d e n c e of Κ i n v o l v e s the i d e a that, a l t h o u g h the surface coverage decreases w i t h i n c r e a s i n g t e m p e r a t u r e , sites of h i g h e r adsorption energy

( i n a n e n e r g e t i c a l l y heterogeneous system)

o p e r a t i v e at h i g h e r t e m p e r a t u r e .

become

T h e q u a l i t a t i v e a r g u m e n t is p l a u s i b l e ,

b u t there are difficulties i n d e v e l o p i n g q u a n t i t a t i v e r i g o r : ( a ) the a c t u a l d i s t r i b u t i o n of energetics is a l w a y s q u a n t i t a t i v e l y u n k n o w n ; a n d ( b )


w o u l d b e c o i n c i d e n t a l t h a t these t w o effects of opposite

it

sign should

h a p p e n to just b a l a n c e . A n o t h e r e x a m p l e i l l u s t r a t i n g strange b e h a v i o r of a n a d s o r p t i o n c o n stant is the f a s c i n a t i n g d i s p r o p o r t i o n a t i o n of p r o p y l e n e to b u t e n e e t h y l e n e over t u n g s t e n o x i d e - s i l i c a . B o t h L u c k n e r et al. (15) kudur and Thodos

(16)

and

and Hatti-

agree t h a t a d u a l - s i t e surface r e a c t i o n is rate

c o n t r o l l i n g a n d t h a t the i n i t i a l rates are g i v e n b y t h e s t a n d a r d d u a l - s i t e Langmuir-Hinshelwood equation: r

Q

where K

3

and p

3

=

Cp /(1+#3P ) 3

2

3

2

are the a d s o r p t i o n constant a n d p a r t i a l pressure, respec

t i v e l y , of p r o p y l e n e .

T h e w o r k of H a t t i k u d u r a n d T h o d o s is p a r t i c u l a r l y

c o n v i n c i n g because of the u n u s u a l l y large r a n g e of p a r t i a l pressures i n v e s t i g a t e d ( m o r e t h a n 3 0 - f o l d for p r o p y l e n e ) . T h e u n e x p e c t e d result is that, as b o t h sets of investigators agree, K a c t u a l l y increases w i t h i n c r e a s i n g t e m p e r a t u r e whereas expects a decrease.

one

H a t t i k u d u r a n d T h o d o s r e p o r t a v a l u e of Δ Η

+ 12,140 c a l / g - m o l e for the a d s o r p t i o n of p r o p y l e n e . n e r et al. do not f a l l o n a straight l i n e for In K

3

3

normally α

=

( T h e data of L u c k

vs. 1/T.)

Now

endo-

t h e r m i c a d s o r p t i o n is possible ( 1 7 ) , b u t there are v e r y f e w a u t h e n t i c a t e d examples a n d these seem to i n v o l v e either m o l e c u l a r h y d r o g e n or m o l e c u l a r o x y g e n (18).

Since the free e n e r g y of a d s o r p t i o n m u s t be n e g a t i v e ,

endothermic adsorption implies that T A S

a

> ΔΗ . &

Thomas and Thomas

suggest, for h e u r i s t i c purposes, t w o w a y s of h a v i n g a n e n t r o p y increase o n a d s o r p t i o n r a t h e r t h a n the e x p e c t e d decrease. sociative

adsorption

with

complete

T h e first i n v o k e s d i s

two-dimensional

m o b i l i t y of

the

a d s o r b e d fragments; t h e s e c o n d is that for some reason the e n t r o p y of t h e s o l i d itself increases m o r e t h a n t h e e n t r o p y of the a d s o r b e d decreases.

gas

F o r present purposes w e note o n l y t h a t the first suggestion

w o u l d m e a n g i v i n g u p the L a n g m u i r i s o t h e r m , for w h i c h i m m o b i l e a d s o r p t i o n is p o s t u l a t e d ; m o r e o v e r , the p i c t u r e seems i n t u i t i v e l y i m p r o b a b l e for p r o p y l e n e d i s p r o p o r t i o n a t i o n . T h e s e c o n d suggestion raises a difficult t h e o r e t i c a l p r o b l e m , w h i c h I b e l i e v e n o one has q u a n t i t a t i v e l y a t t e m p t e d to date.


2.

WELLER

Kinetic

33

Models

T h e last p o i n t to b e m e n t i o n e d relates to the s i g n of the K's.

I n the

s t a n d a r d a p p l i c a t i o n of L a n g m u i r - t y p e isotherms, those k i n e t i c m o d e l s are d i s c a r d e d that l e a d to rate equations for w h i c h a n y K i d e t e r m i n e d f r o m e x p e r i m e n t a l r a t e d a t a turns out to b e significantly negative. years ago it was n o t e d (19)

Some

that the l i m i t e d w o r k a v a i l a b l e o n m i x e d

a d s o r p t i o n f r o m a p o t e n t i a l l y r e a c t i v e gas m i x t u r e i n d i c a t e d t h a t e n h a n c e d , rather t h a n c o m p e t i t i v e , a d s o r p t i o n m i g h t b e a c o m m o n nomenon

a n d t h a t force-fitting of " e n h a n c e d

phe-

adsorption" data into a

L a n g m u i r f o r m guarantees a n e g a t i v e v a l u e for at least one K i i n t h e


r a n g e of c o n d i t i o n s s t u d i e d . I n the i n t e r v e n i n g years m o r e examples of a d s o r p t i o n f r o m r e a c t i v e mixtures h a v e b e e n e x a m i n e d , a n d the e n h a n c e d a d s o r p t i o n b e h a v i o r for at least one ( sometimes b o t h ) of the constituents does seem to b e the g e n e r a l p a t t e r n . T h e b e h a v i o r of H - C O m i x t u r e s 2

o n C o a n d F e F i s c h e r - T r o p s c h catalysts, Z n O , a n d n o b l e metals has b e e n r e c e n t l y r e v i e w e d b y G u p t a et al. (20). adsorption from C H - 0 3

of 0

2

6

2

Gérai et al. (21),

i n a s t u d y of

on C u O and C u 0 , report enhanced adsorption 2

f r o m the m i x t u r e a n d decreased a d s o r p t i o n of C H ; at a l l t e m p e r a 3

6

tures a n d f r o m a l l m i x t u r e s the t o t a l a d s o r p t i o n was m o r e t h a n a d d i t i v e for b o t h C u O a n d C u 0 . 2

I n t u i t i v e l y w e c a n u n d e r s t a n d the reason f o r e n h a n c e d

adsorption,

w h e n i t occurs, i n terms of t h e f o r m a t i o n of a surface c o m p l e x w h i c h is m o r e strongly a d s o r b e d t h a n either c o m p o n e n t s i n g l y . D i r e c t e v i d e n c e , f r o m I R spectra, c a l o r i m t e r y , a n d other t e c h n i q u e s , is a v a i l a b l e for s u c h complexes i n a n u m b e r of cases (see,

for e x a m p l e , R e f s .

21-24).

It has b e e n suggested t h a t i f a l l the other c r i t e r i a r e q u i r e d f o r q u a n t i tative v a l i d i t y of t h e L a n g m u i r - H i n s h e l w o o d t h e o r y w e r e satisfied, w e c o u l d t a k e i n t o a c c o u n t e x p l i c i t l y the f o r m a t i o n of s u c h surface complexes, w i t h the a d d i t i o n of another e q u i l i b r i u m constant, a n d m a i n t a i n the f o r m of the L a n g m u i r expressions.

U n f o r t u n a t e l y , i t is difficult e x p e r i m e n t a l l y

to establish the existence, n a t u r e , a n d surface e q u i l i b r i u m constants for s u c h complexes i n a q u a n t i t a t i v e w a y , a n d v e r y f e w kineticists i n t e r e s t e d i n m e c h a n i s m h a v e t a k e n the t r o u b l e to investigate this p r o b l e m . Freundlich and Temkin Isotherms. S i n c e the several d e r i v a t i o n s of the F r e u n d l i c h a n d T e m k i n isotherms are s u m m a r i z e d i n v a r i o u s reports (25, 26, 27, 28),

the details are not r e p e a t e d here. R e a d e r s n o t f a m i l i a r

w i t h S i p s ' elegant p a p e r m a y b e interested to k n o w that h e has u s e d Stieltjes transforms to solve the i n v e r s e of the u s u a l p r o b l e m — i . e . , to d e d u c e the p o s s i b l e d i s t r i b u t i o n functions f o r a d s o r p t i o n energy t h a t are consistent w i t h the e x p e r i m e n t a l i s o t h e r m Θ

(ρ).

A U d e r i v a t i o n s of these isotherms u t i l i z e the L a n g m u i r result f o r a d s o r p t i o n o n surface sites of one p a r t i c u l a r a d s o r p t i o n energy, a n d i n this sense the L a n g m u i r i s o t h e r m is a f u n d a m e n t a l starting p l a c e . w i s h to m a k e a f e w p o i n t s :


I do

34

CHEMICAL

REACTION ENGINEERING REVIEWS

(1) T h e F r e u n d l i c h a n d T e m k i n isotherms a r e n o less ( a n d n o m o r e ) t h e o r e t i c a l l y justified t h a n t h e L a n g m u i r i s o t h e r m . T h e b a s i c c o n c e p t of l o c a l i z e d , m o n o l a y e r c h e m i s o r p t i o n is r e q u i r e d for a l l . D i f f e r ent isotherms r e s u l t a c c o r d i n g to t h e assumptions m a d e a b o u t t h e heat of a d s o r p t i o n , Δ Η , a n d t h e site d i s t r i b u t i o n f u n c t i o n , Ν(ΔΗ ), among other things. T h e L a n g m u i r i s o t h e r m r e q u i r e s the a s s u m p t i o n t h a t —ΔΗ = constant. T h e F r e u n d l i c h i s o t h e r m c a n b e d e d u c e d f r o m t h e a s s u m p tions that Ν = ae~ o a n d t h a t θ ( o r ρ ) is s m a l l ; [cf. the c o m m e n t b y T h o m a s a n d T h o m a s ( R e f . 18, p . 44): " T h e F r e u n d l i c h e q u a t i o n is . . . n o l o n g e r to b e r e g a r d e d as m e r e l y a c o n v e n i e n t f o r m of r e p r e s e n t i n g t h e L a n g m u i r e q u a t i o n at i n t e r m e d i a t e values of Θ. M o r e o v e r , t h e m e t h o d of d e r i v a t i o n disposes of t h e c r i t i c i s m that the F r e u n d l i c h e q u a t i o n p r e dicts a p r o g r e s s i v e l y i n c r e a s i n g coverage w i t h i n c r e a s i n g p r e s s u r e : the i s o t h e r m is e x p e c t e d to b e v a l i d o n l y at l o w coverages."] T h e T e m k i n e q u a t i o n is o b t a i n e d i f t h e a d s o r p t i o n heat decreases l i n e a r l y ( b e t w e e n m a x i m u m a n d m i n i m u m v a l u e s ) w i t h surface coverage θ a n d i f θ is i n a m i d d l e range. α

η

α


AII/AII

( 2 ) W e d o n o t k n o w , f o r a n y a r b i t r a r y system, w h i c h assumptions a b o u t t h e d i s t r i b u t i o n functions for e n e r g y are t r u e or w h i c h isotherms are therefore t h e o r e t i c a l l y v a l i d . [ I n this context, C l a r k ( R e f . 26, p . 57) has c l e a r l y stated a d u a l d i f f i c u l t y : " I t s h o u l d b e e m p h a s i z e d . . . t h a t agreement b e t w e e n t h e t h e o r e t i c a l isotherms w i t h d i s t r i b u t i o n functions d e t e r m i n e d b y t h e v a r i o u s procedures . . . a n d e x p e r i m e n t a l isotherms does n o t guarantee that t h e true p h y s i c a l p i c t u r e has b e e n d i s c o v e r e d . . . . A n o t h e r difficulty is t h e i n h e r e n t i n s e n s i t i v i t y of the t h e o r e t i c a l iso t h e r m to the f o r m of the d i s t r i b u t i o n f u n c t i o n w i t h i n the a c c u r a c y of experimental data."] (3) R e s t r a i n t is therefore a p p r o p r i a t e i n insistence that a n y one i s o t h e r m has u n i q u e q u a n t i t a t i v e v a l i d i t y i n a p p l i c a t i o n s to c a t a l y t i c kinetics. Rate Equations and Kinetic Models: An Eclectic

Review

T h i s section contains a s a m p l i n g f r o m the enormous

literature on

c a t a l y t i c k i n e t i c s p u b l i s h e d d u r i n g t h e last 10-15 years.

T h e samples

w e r e chosen

p a r t l y to i l l u s t r a t e the s p e c t r u m of approaches

u s e d to

i n t e r p r e t k i n e t i c d a t a a n d p a r t l y to i n d i c a t e some areas of s u b s t a n t i a l disagreement. Ammonia Synthesis: an Example of Ambiguity.

B o u d a r t ' s 1972 r e

v i e w ( 1 ) contains a n excellent discussion of this system as e x e m p l i f y i n g "two-step

c a t a l y t i c reactions."

M y p u r p o s e here is o n l y to a d d to t h e

v a r i o u s l y p r o p o s e d rate equations some recent results of B r i l l (29) a n d to i n d i c a t e t h e difficulty, even i n this m o s t - s t u d i e d of c a t a l y t i c reactions, of d r a w i n g conclusions about s u c h b a s i c questions as ( a ) is t h e surface o f a n i r o n catalyst u n i f o r m or heterogeneous, a n d ( b ) i f the surface is u n i f o r m , is Ho a d s o r b e d m o l e c u l a r l y o n a single site or d i s s o c i a t i v e l y o n d u a l sites.


2.

WELLER

Kinetic

35

Models

T h e classic T e m k i n - P y z h e v e q u a t i o n uses the T e m k i n i s o t h e r m ( i m p l y i n g a heterogeneous surface ) for the surface c o n c e n t r a t i o n of n i t r o g e n as r e l a t e d to the

fictitious

n i t r o g e n p a r t i a l pressure t h a t w o u l d b e i n

e q u i l i b r i u m w i t h the a c t u a l h y d r o g e n a n d a m m o n i a p a r t i a l pressures. F o r the rate of the f o r w a r d r e a c t i o n , the T e m k i n - P y z h e v treatment gives: / P H , ' V

7

VPNIII / 2

T h e constant i m u s t b e d e t e r m i n e d ; to agree w i t h e x p e r i m e n t , i t is often Downloaded by UNIV OF PITTSBURGH on June 17, 2013 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0148.ch002

chosen to be b e t w e e n 0.5 a n d 0.6. T h e 1942 p a p e r of B r u n a u e r et al. (27), its

w h i c h is m o r e e x p l i c i t i n

d e r i v a t i o n s , also starts w i t h the a s s u m p t i o n of

l i n e a r decrease i n

a d s o r p t i o n heat w i t h i n c r e a s i n g c o v e r a g e ( h e t e r o g e n e i t y )

a n d ends w i t h

a g e n e r a l i z e d " T e m k i n i s o t h e r m " t h a t is v a l i d for the e n t i r e r a n g e

of

a d s o r p t i o n , whereas the o r i g i n a l T e m k i n i s o t h e r m is v a l i d o n l y i n the m i d d l e range. Temkin-Pyzhev.

D i s s o c i a t i v e a d s o r p t i o n of No is a g a i n a s s u m e d , as i n F o r the f o r w a r d r e a c t i o n o n l y the rate expression at

l o w surface coverage (0 )

becomes:

N

k pyi

=

2

V If a =

Vu^

)

1 ( a r b i t r a r y c h o i c e ), this reduces to : r

=

k ps αα Κ 2

/

B o u d a r t has s h o w n (14, 30)

ρχηλ

2

that the a s s u m p t i o n of a h o m o g e n e o u s

surface ( L a n g m u i r m o d e l ) a n d dissociative a d s o r p t i o n of n i t r o g e n as the r a t e - d e t e r m i n i n g step leads to the synthesis e q u a t i o n : r

which

is i d e n t i c a l w i t h

=

kp __ N2

the e q u a t i o n

deduced

by

the p r o c e d u r e

B r u n a u e r et al. for a heterogeneous surface ( p r o v i d e d a =

of

1 ).

S t i l l m o r e r e c e n t l y , B r i l l a n d co-workers h a v e r e p o r t e d i n t e r e s t i n g results : ( a ) F i e l d e l e c t r o n m i c r o s c o p i c studies s h o w that N adsorption occurs p r e f e r e n t i a l l y o n (111) faces of i r o n a n d v e r y m u c h less o n (100) a n d (110) faces (31). 2


36

CHEMICAL

R E A C T I O N ENGINEERING REVIEWS

( b ) O n the basis of field i o n mass s p e c t r o m e t r i c studies, N H a p pears to be the first p r o d u c t f o r m e d o n exposure of i r o n to N — H (32). 2

2

2

( c ) I R studies of F e - M g O catalyst exposed to N - H at 4 1 0 ° C i n d i c a t e the p r e s e n c e of p a r t i a l l y h y d r o g e n a t e d N m o l e c u l e s (i.e., u n d i s s o c i a t e d ) h a v i n g b o n d s s i m i l a r to those h y d r a z i n e ( 3 3 ) . 2

2

2

O n this basis, B r i l l d e r i v e d a rate expression for a m m o n i a synthesis u n d e r the assumptions t h a t the surface is h o m o g e n e o u s b u t t h a t the r a t e - d e t e r m i n i n g step

is the n o n - d i s s o c i a t i v e

a d s o r p t i o n of

molecular

n i t r o g e n o n a s i n g l e site (-29). F u r t h e r m o r e , he shows t h a t a set of exp e r i m e n t a l i n t e g r a l c o n v e r s i o n d a t a t a k e n at 340 ° C is satisfied b y this Downloaded by UNIV OF PITTSBURGH on June 17, 2013 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0148.ch002

rate expression w i t h a s t a n d a r d d e v i a t i o n of db 1.5% i n the rate constant. T h e same d a t a , fitted b y the e q u a t i o n of O z a k i et al. for d i s s o c i a t i v e a d sorption on

d u a l sites, gives

a n almost i d e n t i c a l s t a n d a r d d e v i a t i o n ,

± 1.4%, i n the c o r r e s p o n d i n g rate constant. H o p e f u l l y f u r t h e r i n g e n i o u s experiments w i l l s h e d f u r t h e r l i g h t o n the reaction mechanism

( a l t h o u g h after 40 years one m a y

p e s s i m i s m ) b u t i n this s p e c i a l case, at least, the expressions

fitting

approach

of g l o b a l rate

seems u n l i k e l y to differentiate k i n e t i c m o d e l s

that

differ

r a d i c a l l y i n t h e i r assumptions. The

P a r a - O r t h o - H y d r o g e n Conversion: an Example of Simplicity.

p a r a m a g n e t i c m e c h a n i s m for the p a r a - o r t h o - h y d r o g e n shift r e a c t i o n at l o w temperatures s h o u l d constitute the simplest c h e m i c a l e x a m p l e of a c a t a l y z e d r e a c t i o n . H u t c h i n s o n et al. (34)

c o n d u c t e d a c a r e f u l s t u d y of

the a p p r o a c h to e q u i l i b r i u m , f r o m b o t h sides of the e q u i l i b r i u m c o m p o s i t i o n , over f e r r i c oxide g e l at 7 6 ° K . T h e results are d i s c o n c e r t i n g .

They

m a y b e s u m m a r i z e d as f o l l o w s : (1) W i t h expression has face r e a c t i o n , T h i s simplifies

the L a n g m u i r - H i n s h e l w o o d a p p r o a c h , the o v e r a l l rate the same f o r m regardless of w h i c h step ( a d s o r p t i o n , suror d e s o r p t i o n ) or c o m b i n a t i o n of steps is rate l i m i t i n g . c r i t i c a l testing of the a p p r o a c h .

( 2 ) T h e d e d u c e d L a n g m u i r - H i n s h e l w o o d rate constant is different d e p e n d i n g o n w h e t h e r one approaches e q u i l i b r i u m f r o m the o r t h o - r i c h or p a r a - r i c h side. T h i s result w o u l d v i o l a t e the p r i n c i p l e of m i c r o s c o p i c r e v e r s i b i l i t y a n d indicates that no s i m p l e L a n g m u i r - H i n s h e l w o o d m o d e l c a n be a p p l i c a b l e i n this system. (3) T h e discrepancy between theory and experiment can be res o l v e d q u a l i t a t i v e l y i f one postulates that the a c t i v a t i o n energies for a d s o r p t i o n a n d d e s o r p t i o n c h a n g e w i t h coverage of the catalyst surface. H o w e v e r , s u c h a postulate is t a n t a m o u n t to g i v i n g u p the q u a n t i t a t i v e v a l i d i t y of the L a n g m u i r - H i n s h e l w o o d m o d e l . Dehydration of Ethanol to Ether. O n e of the most g r a t i f y i n g p u b l i c a t i o n s i n c a t a l y t i c kinetics is the p a p e r of K a b e l a n d J o h a n s o n ( 3 5 )

on

the v a p o r - p h a s e d e h y d r a t i o n of e t h a n o l to d i e t h y l ether over the a c i d f o r m of D o w e x 5 0 — a s u l f o n a t e d s t y r e n e - d i v i n y l b e n z e n e c o p o l y m e r .

The

authors f o u n d t h e i r k i n e t i c d a t a to b e consistent w i t h the e q u a t i o n p r e -


2.

Kinetic

WELLER

37

Modek

d i e t e d f r o m a s i m p l e L a n g m u i r m o d e l i n w h i c h the r a t e - l i m i t i n g step is a surface r e a c t i o n b e t w e e n a d j a c e n t l y a d s o r b e d e t h a n o l m o l e c u l e s :

7'

=

[l+K P +K Pw+K P ]> A

A

w

Fl

F

the subscripts A , W , a n d Ε r e p r e s e n t i n g e t h a n o l , w a t e r , a n d ether, r e s p e c t i v e l y . T h i s itself is p l a u s i b l e , b u t i t is not the reason f o r the e x c e p t i o n a l


interest of the w o r k . T h e authors p r o c e e d e d to do that w h i c h is s e l d o m d o n e — n a m e l y , to d e t e r m i n e K , K , a n d K A

w

E

directly and independently

f r o m a d s o r p t i o n isotherms ( L a n g m u i r ) of the i n d i v i d u a l p u r e c o m p o nents. T h e e x t r a o r d i n a r y result was the agreement b e t w e e n the t w o sets of a d s o r p t i o n constants—one set d e t e r m i n e d b y fitting of t h e k i n e t i c d a t a , the other set f r o m the i n d i v i d u a l isotherms. A t 1 2 0 ° C , for e x a m p l e , K , A

K , and K w

E

d e t e r m i n e d f r o m the k i n e t i c s w e r e 3.4, 7.0, a n d ~ 0.

The

c o r r e s p o n d i n g values f r o m the isotherms w e r e 2.5, 7.6, a n d ~ 0. T h e experience w i t h D o w e x 50 does not p e r m i t extension to another c o m m o n catalyst for a l c o h o l d e h y d r a t i o n — a l u m i n a . K n o z i n g e r a n d P i n e s h a v e c o n d u c t e d the most extensive research o n the m e c h a n i s m of a l c o h o l reactions over a l u m i n a . K n o z i n g e r et al. earlier d a t a (36) method.

have recently analyzed

(2)

o n the k i n e t i c s of ether f o r m a t i o n b y a g r i d search

T h e e x p e r i m e n t a l d a t a c o u l d not b e fitted b y equations

based

o n the e x p e c t e d m e c h a n i s m . O n the other h a n d , five f o r m a l k i n e t i c e q u a tions w e r e d e v e l o p e d w h i c h describe the d a t a e q u a l l y w e l l ( w i t h m e a n error i d e n t i c a l to the m e a n e x p e r i m e n t a l e r r o r )

a n d w h i c h cannot

d i s t i n g u i s h e d . A l l five give c o m p a r a b l e a c t i v a t i o n energies.

be

T h e authors

c o n c l u d e : " A t least for the ether f o r m a t i o n o n a l u m i n a . . . . , it therefore seems u n r e a l i s t i c to use k i n e t i c analysis for the e l u c i d a t i o n of the m o l e c u lar m e c h a n i s m of the r e a c t i o n . T h e o n l y possible result is a p u r e l y f o r m a l d e s c r i p t i o n of the r e a c t i o n rate as a f u n c t i o n of the p a r t i a l pressures of a l c o h o l , ether, a n d w a t e r . " Hydrogénation of Cyclopropane.

A s e c o n d e x a m p l e of a r e a c t i o n

i n w h i c h agreement is c l a i m e d b e t w e e n the a d s o r p t i o n constant f r o m a rate e q u a t i o n

(Langmuir form)

deduced

and that measured from

a d s o r p t i o n i s o t h e r m is the recent p a p e r of S r i d h a r a n d R u t h v e n

the (37).

T h e k i n e t i c s for c y c l o p r o p a n e hydrogénation over f o u r s u p p o r t e d n i c k e l catalysts at 6 0 ° C w e r e f o u n d to be best fitted b y the s i m p l e e x p r e s s i o n : r =

k K

cVc

w h e r e s u b s c r i p t c represents c y c l o p r o p a n e . determined K

c

(l+K )cPc

1

T h e values of the k i n e t i c a l l y

for the four catalysts r a n g e d f r o m 2.12 to 3.71 a t m " ; the


1

38

CHEMICAL

v a l u e of K

REACTION ENGINEERING REVIEWS

c a l c u l a t e d f r o m the i s o t h e r m data of B e n s o n a n d K w a n

c

(38)

was r e p o r t e d to be 2.5 a i m , i n g o o d agreement. - 1

S e v e r a l aspects of the w o r k l e a d one to b e less t h a n t o t a l l y s a n g u i n e a b o u t the r e s u l t s : ( 1 ) T h e a c t u a l plots of r vs. p are s i g m o i d a l — a result w h i c h , as the authors a p p r e c i a t e d , is not t r u l y c o m p a t i b l e w i t h the a b o v e rate e q u a t i o n . c

( 2 ) N o t e r m i n v o l v i n g p appears i n the " a d s o r p t i o n d e n o m i n a t o r " despite the fact ( w h i c h the authors note ) that h y d r o g e n is m o r e s t r o n g l y a d s o r b e d o n n i c k e l t h a n is c y c l o p r o p a n e . n

( 3 ) T h e c o m m e r c i a l N i - S i 0 - A L 0 catalyst s t u d i e d b y B e n s o n a n d K w a n was o b t a i n e d f r o m a different source ( A t l a n t i c R e f i n i n g C o . , vs. H a r s h a w ).


2

3

( 4 ) B e n s o n a n d K w a n fitted t h e i r o w n rate d a t a for c y c l o p r o p a n e h y d r o g e n to a p o w e r rate l a w , fitted t h e i r o w n a d s o r p t i o n d a t a to F r e u n d l i c h isotherms a n d p r o p o s e d t h a t the r a t e - d e t e r m i n i n g step was a surface reaction between adsorbed cyclopropane and an adsorbed hydrogen atom. Statistical Model Building. I n 1962 a s e m i n a l p a p e r b y B o x a n d H u n t e r (39)

described an extremely powerful, iterative m o d e l - b u i l d i n g

m e t h o d i n v o l v i n g m i n i m i z a t i o n of the residuals of a d i a g n o s t i c p a r a m e t e r . H u n t e r a n d M e z a k i (40),

i n a p p l y i n g this a p p r o a c h , discussed the results

of a n e x p e r i m e n t a l s t u d y of m e t h a n e o x i d a t i o n over P d - A l 0 . 2

3

A frac-

t i o n a l f a c t o r i a l d e s i g n was u s e d for the e x p e r i m e n t a l r u n s . A n a l y s i s of these d a t a w a s c o m p l e t e d i n a subsequent a r t i c l e b y K i t t r e l l et al.

(41).

T h e rate expression ( H o u g e n - W a t s o n t y p e ) d e v e l o p e d to fit the e x p e r i m e n t a l d a t a of H u n t e r a n d M e z a k i a d e q u a t e l y was Pan,

Voi

K i t t r e l l et al. w e r e c a r e f u l to p o i n t out that . . . "no c l a i m is m a d e

con-

c e r n i n g the m e c h a n i s m of the r e a c t i o n or e v e n the uniqueness of the m o d e l w h i c h has b e e n set f o r t h as a d e q u a t e l y d e s c r i b i n g the e x p e r i m e n t a l data."

T h i s caveat seems a p p r o p r i a t e since one w o u l d h a v e difficulty

b e l i e v i n g i n the p h y s i c a l r e a l i t y of the r e a c t i o n m e c h a n i s m w h i c h , b y a s t r a i g h t f o r w a r d L a n g m u i r - H i n s e l w o o d a p p r o a c h for a t h i r d - o r d e r r e a c tion between a methane molecule and two adsorbed oxygen

molecules,

w o u l d l e a d to the p r o p o s e d rate e q u a t i o n . Some d i c h o t o m y

of t h i n k i n g nevertheless appears to exist

the p r o p o n e n t s of this a p p r o a c h .

B o x a n d H i l l (42),

among

i n a paper entitled

" D i s c r i m i n a t i o n A m o n g M e c h a n i s t i c M o d e l s , " p r o p o s e to " d i s c o v e r mechanism

the

for a p a r t i c u l a r p h e n o m e n o n l e a d i n g to a specific m a t h e m a t i -

cal model. . . .

T o d i s c r i m i n a t e a m o n g these

[possible m e c h a n i s m s ]

a

s e q u e n t i a l p r o c e d u r e is d e v e l o p e d i n w h i c h c a l c u l a t i o n s m a d e after e a c h e x p e r i m e n t d e t e r m i n e the most d i s c r i m i n a t o r y process c o n d i t i o n s for use i n the next e x p e r i m e n t . "


2.

WELLE R

Kinetic

39

Models

T h e p r o p o s e d use of s o p h i s t i c a t e d c o m p u t e r analysis to establish or to d i s p r o v e a m e c h a n i s m has b e e n the subject of c o n s i d e r a b l e criticism.

recent

B o u d a r t ( I ) , for e x a m p l e , i n c o m m e n t i n g o n a s t a t i s t i c a l r e -

analysis b y L o g a n a n d P h i l i p (43)

of m e c h a n i s t i c d a t a b y O z a k i et

al.

o n a m m o n i a synthesis, observes " T h e r e is a l w a y s a r e a l d a n g e r i n kinetics to treat d a t a w i t h a p o w e r f u l m e t h o d of analysis w h i c h m a y be far better t h a n the d a t a themselves." A l l a r a a n d E d e l s o n (44) stronger

position

i n a discussion

of

have taken an even

p a r a m e t e r i z a t i o n techniques

in

k i n e t i c s : " T h e a b i l i t y to fit a set of n u m b e r s to a f u n c t i o n a l f o r m r e s e m -


b l i n g c h e m i c a l k i n e t i c equations cannot of itself establish the v a l i d i t y of the m o d e l . . . . W e

believe

that it is most

i m p o r t a n t to d i s t i n g u i s h

b e t w e e n the c o r r e l a t i v e v a l u e of p a r a m e t e r fits as o p p o s e d to the p r e d i c t i v e c a p a b i l i t i e s of a t r u l y f u n d a m e n t a l m o d e l . . . . W e

especially

object to the p u b l i c a t i o n of these parameters as rate constants, a t e r m w h i c h i m p l i e s a f u n d a m e n t a l p r o p e r t y of the reaction, since this o n l y f u r t h e r aggravates a n a l r e a d y c o n f u s e d s i t u a t i o n i n the l i t e r a t u r e . " A s a p a r e n t h e t i c c o m m e n t , the a u t h o r feels that a f u n d a m e n t a l diffic u l t y is not that statistical analysis is a n i n a p p r o p r i a t e l y p o w e r f u l t o o l for d i s c r i m i n a t i n g b e t w e e n a n u m b e r of p o s t u l a t e d models.

T h e difficulty is

i n d e c i d i n g w h e t h e r a n y of the models has a s o u n d t h e o r e t i c a l basis. C h a r l e s W a r e (45)

has c a l l e d the author's attention to the a p p l i c a t i o n

of a m o d i f i e d B o x - H u n t e r a p p r o a c h to p r o c e e d f r o m s t a t i s t i c a l l y d e s i g n e d , i s o t h e r m a l l a b o r a t o r y d a t a to successful p r e d i c t i o n of the

performance

a n d t e m p e r a t u r e d i s t r i b u t i o n i n a d i a b a t i c units. I n b r i e f , a p o w e r rate l a w suggested b y l i t e r a t u r e i n f o r m a t i o n is used as a first a p p r o x i m a t i o n . T h e analysis of l a b o r a t o r y d a t a indicates a possible n e e d for m o d i f y i n g the f o r m of the rate l a w , a n d i t e r a t i o n of the entire process finally results i n a rate l a w s a t i s f y i n g the statistical c r i t e r i a i m p o s e d . T h e e m p i r i c a l rate l a w is satisfactory for d e s i g n i n g c o m m e r c i a l units o p e r a t i n g w i t h i n the range of variables s t u d i e d , a n d m e c h a n i s t i c conclusions are not d r a w n . Hydrogénation of

Propylene and Isobutylene.

An

exceptionally

c a r e f u l a n d fine s t u d y of olefin hydrogénation over P t - A l 0 2

l i s h e d b y Rogers et al. (46)

3

was p u b -

i n 1966. T h e e x p e r i m e n t a l k i n e t i c d a t a h a v e

b e e n a n a l y z e d not o n l y b y the authors b u t also i n at least three subseq u e n t papers. T h e final rate e q u a t i o n of Rogers et al. w a s :

= r

aK K PiV2 (i+K +K y 1

lPl

/

2

2V2

,

βΚ Κ

Kinetic Models in Heterogeneous Catalysis - ACS Publications

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