Description of Adsorption Equilibria of Vapors on Zeolites over Wide

44 Description of Adsorption Equilibria of Vapors on Zeolites over Wide Ranges of Downloaded by STANFORD UNIV GREEN LIBR on September 23, 2012 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch044

Temperature and Pressure M. M . DUBININ Institute of Physical Chemistry, Academy of Sciences of the U S S S R , Moscow V - 7 1 , U S S R

V. A . A S T A K H O V Bielorussian Technological Institute, M i n s k 50, U S S R

The distinguishing feature of zeolites as microporous adsorbents is the presence of cations in the micropores.

These

cations are centers for the adsorption of molecules with a nonuniform electron density distribution.

An attempt has

been made to develop the theory of volume filling of micropores for approximate description of adsorption of vapors on zeolites over wide temperature

equilibria

ranges.

An

adsorption equation has been obtained which takes into consideration, in the general case, both dispersion forces and the forces of interaction of molecules with ions. This equation describes adsorption on the active centers and the filling of the remainder of the adsorption space of the voids after the blocking of the active centers. Several examples of agreement between the results of calculation and

experimental

data are given.

T h e d e s c r i p t i o n o f a d s o r p t i o n e q u i l i b r i a o n r e a l m i c r o p o r o u s adsorbents A

(3)—i.e., a c t i v e carbons, zeolites, a n d other

fine-pore

mineral ad

sorbents—over

w i d e ranges of t e m p e r a t u r e

objectives:

T h e most accurate possible a n a l y t i c a l expression o f t h e

(1)

a n d pressure m a y h a v e 2

aggregate e x p e r i m e n t a l d a t a , w h i c h is u s e d to d e t e r m i n e t h e constants of t h e a d s o r p t i o n e q u a t i o n . I n this case, t h e n u m b e r of constants is r e l a t i v e l y large, a n d u s u a l l y most of t h e m a c q u i r e a s e m i - e m p i r i c a l n a t u r e . (2)

U t i l i z a t i o n o f m i n i m a l e x p e r i m e n t a l i n f o r m a t i o n — f o r instance, a d 69

In Molecular Sieve Zeolites-II; Flanigen, E., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

70

M O L E C U L A R SIEVE ZEOLITES

Π

Downloaded by STANFORD UNIV GREEN LIBR on September 23, 2012 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch044

s o r p t i o n isotherms at 1 or 2 t e m p e r a t u r e s — f o r a p p r o x i m a t e c a l c u l a t i o n of a d s o r p t i o n e q u i l i b r i a o v e r a sufficiently w i d e r a n g e of t e m p e r a t u r e a n d pressure. I n this case, the a d s o r p t i o n e q u a t i o n has f e w e r e x p e r i m e n t a l constants. T h e f o l l o w i n g d i s c u s s i o n pursues this a i m . It is e x p e d i e n t to base the d e s c r i p t i o n of a d s o r p t i o n e q u i l i b r i a f o r m i c r o p o r o u s adsorbents o n t h e t h e o r y of v o l u m e filling of m i c r o p o r e s . T h i s t h e o r y has b e e n d e v e l o p e d m a i n l y for m i c r o p o r o u s carbonaceous adsorbents—i.e., a c t i v e c a r b o n s — f o r w h i c h the d e c i s i v e role i n a d s o r p t i o n i n t e r a c t i o n is p l a y e d b y d i s p e r s i o n forces (4, 5, 6). T h e t h e o r y is b a s e d o n the c o n c e p t of t e m p e r a t u r e i n v a r i a n c e of the characteristic c u r v e expressing the d i s t r i b u t i o n of the degree of filling, 0, of the v o l u m e of the a d s o r p t i o n space a c c o r d i n g to the d i f f e r e n t i a l m o l a r w o r k of a d s o r p t i o n , A — a n e x p e r i m e n t a l fact w h i c h a c t u a l l y was n o t e d b y P o l a n y i w i t h a different i n t e r p r e t a t i o n . D e t e r m i n i n g the d i f f e r e n t i a l m o l a r w o r k of a d s o r p t i o n as a decrease i n G i b b s ' free energy ( A = —AG): A = RT In ( p . / p ) = 2.303 RT l o g ( p . / p ) where p

is the pressure of t h e saturated v a p o r of the substance

s

(1) under

s t u d y ( s t a n d a r d reference state) at a t e m p e r a t u r e Τ or f u g a c i t y , a n d ρ is the e q u i l i b r i u m pressure.

T h e characteristic

c u r v e e q u a t i o n of

the

t h e o r y m a y b e represented as f o l l o w s : θ = exp [ — kA ] 2

= exp [—{A/E) ] 2

(2)

I n these 2 e q u i v a l e n t forms of E q u a t i o n 2 θ = a/a

(3)

0

w h e r e a is the a d s o r p t i o n at a t e m p e r a t u r e Γ a n d e q u i l i b r i u m pressure p, a n d a is the l i m i t i n g a d s o r p t i o n v a l u e c o r r e s p o n d i n g to the filling of t h e w h o l e v o l u m e of t h e a d s o r p t i o n space W or of the m i c r o p o r e v o l u m e , a n d k or Ε are parameters of the d i s t r i b u t i o n f u n c t i o n ( E = l/y/k). T h e l i m i t i n g a d s o r p t i o n , a , d e p e n d s o n the t e m p e r a t u r e as a result of the t h e r m a l expansion of the substance a d s o r b e d . W e neglect the temper ature changes of W . If p * is the density of the substance a d s o r b e d at a l i m i t i n g m i c r o p o r e filling, w h i c h easily c a n b e c a l c u l a t e d to a g o o d a p p r o x i m a t i o n a c c o r d i n g to M . M . D u b i n i n a n d Κ. M . N i k o l a e v f r o m the p h y s i c a l constants of t h e substance (densities of the b u l k l i q u i d to the b o i l i n g t e m p e r a t u r e , the constant b i n the v a n d e r W a a l s e q u a t i o n c a l c u l a t e d f r o m the c r i t i c a l t e m p e r a t u r e a n d pressure) ( 1 0 ) , t h e n 0

0

0

0

a

0

=

Wo p*

(4)

If i n E q u a t i o n 2, w e express A as i n E q u a t i o n 1 a n d θ as i n E q u a t i o n 3, w e w i l l o b t a i n the a d s o r p t i o n i s o t h e r m e q u a t i o n f o r the g i v e n t e m p e r a t u r e , T . R e f e r e n c e 4 quotes examples of e x p e r i m e n t a l v e r i f i c a t i o n over w i d e ranges of t e m p e r a t u r e a n d e q u i l i b r i u m pressures of these equations


44.

DUBININ AND ASTAKHOV

Adsorption

Equilibria

of Vapors

71

of t h e t h e o r y of v o l u m e filling of m i c r o p o r e s f o r t h e a d s o r p t i o n of v a r i o u s v a p o r s o n active carbons w i t h different parameters of t h e m i c r o p o r o u s structure. Generalization Adsorption

of the Concept of Volume Filling of Micropores to

of Gases and Vapors on Zeolites


T h e g e n e r a l i z a t i o n u n d e r r e v i e w is b a s e d o n a n analysis of a d s o r p t i o n e q u i l i b r i a of v a r i o u s gases a n d vapors over w i d e ranges of t e m p e r ature a n d pressure o n different types of zeolites.

F o r this p u r p o s e , use

is m a d e of t h e authors' o w n e x p e r i m e n t a l d a t a a n d of p u b l i s h e d results of investigations b y other w o r k e r s . T h i s e x p e r i m e n t a l m a t e r i a l is a n a l y z e d a n d d i s c u s s e d f r o m a n e w p o i n t of v i e w . T h e d i s t i n g u i s h i n g feature

of d e h y d r a t e d zeolites as m i c r o p o r o u s

a l u m i n o s i l i c a t e adsorbents lies i n the presence i n t h e i r voids—i.e., m i c r o pores—of

cations.

T h e s e cations

of t h e i r a l u m i n o s i l i c a t e skeletons.

compensate

excess negative

charges

T h e cations f o r m , i n the zeolite m i c r o

pores, centers f o r t h e a d s o r p t i o n of molecules w i t h a n o n u n i f o r m dis t r i b u t i o n of t h e e l e c t r o n d e n s i t y ( d i p o l e , q u a d r u p o l e , or m u l t i p l e - b o n d m o l e c u l e s ) o r of p o l a r i z a b l e molecules. T h e s e interactions, w h i c h w i l l b e c a l l e d , s o m e w h a t c o n v e n t i o n a l l y , electrostatic interactions, c o m b i n e w i t h d i s p e r s i o n interactions a n d cause a c o n s i d e r a b l e increase i n the a d s o r p t i o n energy.

A s a result, the a d s o r p t i o n isotherms of v a p o r s o n zeolites,

as a r u l e , b e c o m e m u c h steeper i n t h e i n i t i a l regions of e q u i l i b r i u m pres sures as c o m p a r e d w i t h isotherms f o r active carbons. T h e t o t a l a m o u n t of N a cations i n d e h y d r a t e d z e o l i t e crystals i n +

p a s s i n g f r o m N a A (x =

Si0 /Al 0 2

2

3

varies f r o m 7.2 to 4.2 m m o l e / g r a m . (x =

=

2 ) to t h e zeolite N a Y (x =

5)

A t y p i c a l e x a m p l e is zeolite N a X

2.96), f o r w h i c h the a m o u n t of cations is e q u a l to 5.9 m m o l e / g r a m .

T h e p r i n c i p a l results of a d s o r p t i o n investigations g i v e n b e l o w h a v e b e e n o b t a i n e d b y us a n d b y Α. V . K i s e l e v o n this s a m p l e of zeolite, w h i c h w a s s y n t h e s i z e d b y S. P . Z h d a n o v . I f w e e x c l u d e , f o r this zeolite, cations i n p o s i t i o n S i i n s i d e s i x - m e m b e r e d o x y g e n b r i d g e s , w h i c h are inaccessible to t h e m o l e c u l e s b e i n g a d s o r b e d ( 2 cations p e r large v o i d ) , the a m o u n t of cations i n l a r g e z e o l i t e v o i d s w i l l b e a b o u t 4.7 m m o l e / g r a m . O f this a m o u n t , 2.4 m m o l e / g r a m are l o c a l i z e d i n s i x - m e m b e r e d w i n d o w s of c u b e o c t a h e d r a a n d 2.3 m m o l e / g r a m are n o n l o c a l i z e d .

It is n o t clear y e t

w h e t h e r cations n o t l o c a l i z e d i n large v o i d s c a n b e a d s o r p t i o n c e n t e r s — i.e., l o c a l i z a t i o n centers of t h e m o l e c u l e s a d s o r b e d . T h e r e f o r e , the a m o u n t of a c t i v e centers i n t h e zeolite N a X u n d e r s t u d y is at least 2.4 m m o l e / gram. T h e m a x i m a l a d s o r p t i o n v a l u e , a , a n d t h e average n u m b e r , N, of 0

m o l e c u l e s p e r large v o i d o f zeolite (x =

2.96) d e p e n d o n the size of t h e


72


molecules adsorbed.

T h e e x p e r i m e n t a l values of a

0

Π

a n d the c a l c u l a t e d

values of Ν are g i v e n i n T a b l e I. Table I. Substance


No. 1 2 3 4 5 6 7

Limiting

Adsorption Values

T,°K

Water Oxygen Argon Nitrogen Benzene n-Pentane Cyclohexane

ao,

293 90 90 77 293 293 293

Mmole/Gram

Ν 33.4 18.0 17.0 16.5 5.5 4.2 3.8

20.26 10.72 10.26 9.71 3.30 2.56 2.32

T a b l e I shows that, f o r the s m a l l m o l e c u l e s , substances 1-4, the m a x i m u m n u m b e r of a d s o r b e d molecules c o n s i d e r a b l y exceeds t h e n u m b e r of a d s o r p t i o n centers of the zeolite. F o r the larger m o l e c u l e s ,

substances

5 - 7 , t h e m a x i m u m n u m b e r of a d s o r b e d molecules is close to the n u m b e r of a d s o r p t i o n centers.

T h e r e f o r e , 2 l i m i t i n g cases are t y p i c a l for a d s o r p

t i o n o n zeolites. T h e first case corresponds to the a d s o r p t i o n of r e l a t i v e l y larger m o l e c u l e s (as c o m p a r e d w i t h the v o i d sizes f o r t h e zeolite i n h a n d ) , w h i c h is d e t e r m i n e d to a great extent b y the i n t e r a c t i o n of the molecules a d s o r b e d w i t h the a d s o r p t i o n centers of the zeolite e v e n f o r the m a x i m a l filling

of the zeolite v o i d s . I n the s e c o n d case, after the

filling

of

the

a d s o r p t i o n centers, there m a y r e m a i n a free space i n the zeolite v o i d s f o r a d s o r p t i o n as a result of the m a n i f e s t a t i o n of b o t h d i s p e r s i o n forces (adsorbent—adsorbate i n t e r a c t i o n ) a n d the forces of i n t e r a c t i o n b e t w e e n the m o l e c u l e s a d s o r b e d ( a d s o r b a t e - a d s o r b a t e

interaction).

L e t us first c o n s i d e r the most c o m m o n case. A n analysis of m a n y a d s o r p t i o n isotherms o n zeolites of v a r i o u s vapors w i t h r e l a t i v e l y large molecules has s h o w n that the characteristic curves are expressed b y a n e q u a t i o n s i m i l a r to E q u a t i o n 2, b u t w i t h p o w e r ( d i s t r i b u t i o n o r d e r ,

n)

higher than 2: θ = exp[-(A/Ey]

(5)

w h e r e η are integers f r o m 3 to 6. I n most cases, E q u a t i o n 5 satisfactorily describes e x p e r i m e n t a l d a t a over the range of

fillings,

Θ, f r o m * 0

75

c o n s i d e r i n g the

don

(11)

If n o a d s o r p t i o n space remains f o r a d s o r p t i o n u n d e r the effect of d i s p e r s i o n forces because of the size of the molecules a l r e a d y a d s o r b e d o n the a c t i v e centers—i.e., a

=


o2

0 — w e o b t a i n f r o m E q u a t i o n 10: a

on

=

Wo?*

(12)

A c c o r d i n g to the d a t a of analysis of m a n y a d s o r p t i o n systems,

the

first t e r m i n E q u a t i o n 9 c o r r e s p o n d i n g to the second o r d e r appears o n l y w h e n c o n s i d e r i n g a d s o r p t i o n of r e l a t i v e l y s m a l l molecules.

They include

m o l e c u l e s of l i n e a r shape, s u c h as the d i a t o m i c gases, c a r b o n d i o x i d e , c a r b o n m o n o x i d e , etc.

E x p e r i m e n t a l l y r e a l i z a b l e orders, n, are

integers

f r o m 3 to 6 i n the general case. W i t h larger p o l y a t o m i c m o l e c u l e s ,

no

a d s o r p t i o n space r e m a i n s i n t h e zeolite v o i d s f o r final a d s o r p t i o n u n d e r the effect of d i s p e r s i o n forces. T h e n E q u a t i o n 9 retains o n l y the second term, and a

on

is expressed b y E q u a t i o n 12.

T h e n u m b e r of a d s o r p t i o n centers of z e o l i t e a

on

b y different

methods—for

w a t e r at a t e m p e r a t u r e

instance,

f r o m the

of a b o u t 300 ° C .

c a n be

determined

adsorption isotherm

U n d e r these c o n d i t i o n s ,

of the

c o n t r i b u t i o n of the first t e r m of E q u a t i o n 9 to the total a d s o r p t i o n v a l u e i n the i n i t i a l r e g i o n of t h e i s o t h e r m is n e g l i g i b l y s m a l l . F o r zeolite N a X , w e first a d o p t the average n u m b e r of a d s o r p t i o n centers f o r their pos s i b l e r a n g e estimated a b o v e f r o m the zeolite c o m p o s i t i o n , w h i c h is a b o u t 3.5 m m o l e / g r a m , or a n a d s o r p t i o n v a l u e of about 1.2 m m o l e / g r a m

for

the characteristic p o i n t . F r o m E q u a t i o n 1, w e find a n a p p r o x i m a t e v a l u e of Ε =

A

0

a n d , u s i n g E q u a t i o n 7, w e estimate t h e exponent, n, w h i c h is

close to 4. A s s u m i n g η = proximations, a

on

=

4, w e o b t a i n , b y the m e t h o d of successive a p

2.72 m m o l e / g r a m .

T h i s v a l u e of a

on

w a s a d o p t e d as

the n u m b e r of the a d s o r p t i o n centers of zeolite N a X a n d w a s u s e d w i t h a n i n s i g n i f i c a n t c o r r e c t i o n f o r cases of a d s o r p t i o n of other gases a n d vapors w i t h r e l a t i v e l y s m a l l m o l e c u l e s — f o r instance, Our

C0 . 2

experiments o n the b l o c k i n g of a d s o r p t i o n centers (i.e., zeolite

c a t i o n s ) b y p r e a d s o r b e d w a t e r molecules serve to substantiate the p h y s i c a l m e a n i n g of E q u a t i o n 9.

F o r the a d s o r p t i o n of c a r b o n d i o x i d e o n

d e h y d r a t e d crystals of zeolite N a X , E

2

2.90 m m o l e / g r a m , a n d E

3

=

=

3470 c a l / m o l e , η =

3, α

=

ολ

5200 c a l / m o l e , the second t e r m of E q u a t i o n

9 expressing a d s o r p t i o n o n active centers, w h i c h a m o u n t to 2.90 g r a m . W a t e r is a d s o r b e d energetically o n active centers ( n =

mmole/ 4, E

4

9150 c a l / m o l e ) , a n d as a result o f p r e a d s o r p t i o n of 3.5 m m o l e / g r a m


= of

76

M O L E C U L A R SIEVE ZEOLITES Π

w a t e r v a p o r o n zeolite, a l l t h e active centers are p r a c t i c a l l y b l o c k e d a n d t h e a d s o r p t i o n space o f t h e zeolite is r e d u c e d o n l y b y 1 9 . 5 % . T h e e q u i l i b r i u m pressure of p r e a d s o r b e d w a t e r at 2 0 ° C is of the o r d e r of 0.001 torr a n d p r a c t i c a l l y does n o t affect t h e measurements

o f e q u i l i b r i u m pres

sures i n subsequent a d s o r p t i o n o f c a r b o n d i o x i d e . A s a result o f t h e b l o c k i n g o f a d s o r p t i o n centers, a d s o r p t i o n o f c a r b o n d i o x i d e is expressed o n l y b y t h e first t e r m o f E q u a t i o n 9 at E =

3050 c a l / m o l e .

2


increase i n t h e a m o u n t o f p r e a d s o r b e d H

2

0 reduces E

2

A further

only slightly.

T h u s , i f a d s o r p t i o n o n cations is e x c l u d e d , t h e zeolite becomes a n a n a l o g u e o f m i c r o p o r o u s carbonaceous

adsorbents to w h i c h E q u a t i o n 2 i s

applicable. E q u a t i o n 5 at η = 2 describes, t o a g o o d a p p r o x i m a t i o n , t h e a d s o r p t i o n o f v a p o r s o n active carbons, f o r instance, t h e a d s o r p t i o n o f b e n z e n e w i t h a v a r i a t i o n o f t h e characteristic e n e r g y E

f r o m 3000 to 6000 c a l /

2

m o l e . H o w e v e r , f o r active carbons w i t h t h e finest m i c r o p o r e s , w h e n E

2

of b e n z e n e s u b s t a n t i a l l y exceeds 6000 c a l / m o l e — f o r e x a m p l e , f o r active c a r b o n o b t a i n e d f r o m p o l y v i n y l i d e n e c h l o r i d e (E

2

=

7240 c a l / m o l e ) —

E q u a t i o n 5 w i t h η = 2 is a p p l i c a b l e o n l y t o θ $C 0.5 w i t h t h e effective

-1.6

-1.2

~0.8

-OA

0

0.4

0.8

1.2

1.6

2.0 log ρ

Zhurnal Fizicheskoi Khimii Figure

1.

Adsorption isotherm of n-hexane vapor on zeolite NaX (x = 2.96) at different temperatures ( 8 )

Solid lines: Equation 5 (using f ), W = 0.226 cm /gram, the values of a were calculated by Equation 4, η = 4, and E/„ = 6642 cal/mole Circles: experimental points 8/

0

3


Q

44.


Adsorption


a mmole I g A

-/

I

ι

Equilibria

77

-20°

ι

0

of Vapors

ι

1

ι

2

δ

Log ρ

Zhurnal Fizicheskoi Khimii

Figure 2. Adsorption isotherms of carbon dioxide on zeolite NaX (x = 2.96) at differ ent temperatures ( 1 ) Solid lines: Equation 9, W = 0.345 cm /gram, E — 3470 cal/mole, η = 3, a a = 2.90 mmole/ gram, and E = 5200 cal/mole Circles: experimental points 3

G

2

0

3

v a l u e of W

0

almost 1.5 times t h e r e a l v o l u m e of t h e c a r b o n m i c r o p o r e s .

But with η =

3, E q u a t i o n 5 a p p r o x i m a t e s q u i t e satisfactorily t h e char

acteristic c u r v e o v e r t h e range θ =

— 0 . 1 - 1 , w i t h t h e v a l u e of W

0

cor

r e s p o n d i n g to the r e a l m i c r o p o r e v o l u m e . T h u s , f o r t h e a d s o r p t i o n of v a p o r s as a result of t h e m a n i f e s t a t i o n of d i s p e r s i o n forces o n active carbons w i t h t h e finest m i c r o p o r e s , t h e o r d e r of t h e characteristic e q u a t i o n b e c o m e s e q u a l to 3. P e r h a p s f o r a s i m i l a r reason, t h e a d s o r p t i o n of acetylene o n m o l d e d zeolite N a A [experiments of t h e L i n d e C o . ( 9 ) J is expressed b y a n e q u a t i o n s i m i l a r to E q u a t i o n 9, b u t w i t h η =

3 for

a d s o r p t i o n c a u s e d b y d i s p e r s i o n forces, i.e. a = azθ + a Q

For

3

on

θ

(13)

η

a d s o r p t i o n o n active centers of zeolite, η =

h y d r a t e d zeolite, E

3

=

4870 c a l / m o l e a n d E

5

=

5. I n this case, f o r d e 8090 c a l / m o l e .

Pread-

s o r p t i o n of 5 . 1 % w a t e r p r a c t i c a l l y b l o c k s t h e a d s o r p t i o n centers, t h e s e c o n d t e r m of E q u a t i o n 13 disappears, a n d t h e e q u a t i o n f o r acetylene becomes a o n e - t e r m e q u a t i o n w i t h E

3

=

4590 c a l / m o l e .

A further i n

crease i n t h e p r e a d s o r b e d a m o u n t of w a t e r to 1 9 . 1 % is a c c o m p a n i e d b y a decrease i n E

3

to 4030 c a l / m o l e .


78


Π


a mg/g

Figure 3. Adsorption isotherms of water va por on zeolite NaX (x = 2.96) at different tem peratures ( 7 ) ; densities of water in adsorbed state p* were calculated after Ref. 7 Solid lines: Equation 9, W == 0.365 cm /gram, E = 3660 cal/mole, η = 4, a = 2.72 mmole/ gram = 49.0 mg/gram, and = 9150 cal/mole Circles: experimental points 3

G

2

oi

a mg/g

too γ

Figure 4.

Adsorption isotherms of acetylene on pellets of zeolite NaA [experiments of the Linde Co. ( 9 ) ]

Solid lines: Equation 13, W = 0.172 cm /gram, E = 4870 cal/mole, η = 5, a = 2.23 mmole/gram = 58.1 mg/gram, and E = 8090 cal/mole Circles: experimental points 0

o5

3

s

5


44.


Adsorption

Examples of Description of Adsorption

Equilibria

of

Equilibria

79

Vapors

on Xeolites

W i t h the a i d of a c o m p u t e r , a b o u t 40 a d s o r p t i o n systems h a v e b e e n a n a l y z e d f o r e q u i l i b r i u m . T y p i c a l examples are presented i n the graphs of F i g u r e s 1 to 4, w h e r e the s o l i d curves represent c a l c u l a t e d a d s o r p t i o n isotherms a n d the circles denote e x p e r i m e n t a l p o i n t s . T h e

temperatures

are expressed i n degrees c e n t i g r a d e a n d pressures i n m m of H g ( t o r r ) .


F r o m a b o v e - c r i t i c a l temperatures, f o r instance, n-hexane a n d acetylene (t

c

=

(t

c

=

235°C)

3 6 ° C ) , effective values h a v e b e e n o b t a i n e d b y extra

p o l a t i n g the l i n e a r d e p e n d e n c e of p * o n t a c c o r d i n g to E q u a t i o n 5 for the temperatures i n d i c a t e d . E f f e c t i v e values of p

for t >

s

t were calculated c

b y the v a n d e r W a a l s e q u a t i o n , w h i c h m a y b e w r i t t e n i n the f o r m ( 12 ) p

s

= Pc exp [γ (Τ -

T )/T]

(14)

c

the v a l u e f o r n-hexane a n d acetylene b e i n g y =

7.00

a n d 6.61

respec

t i v e l y . T h i s e q u a t i o n shows g o o d agreement w i t h e x p e r i m e n t a l d a t a i n the r a n g e of p f r o m 1 a t m to

p.

s

For

c

a n u m b e r of systems, for instance, for c a r b o n d i o x i d e a n d acety

lene i n the examples q u o t e d , E /n n

T h e examples

^

constant.

a b o v e demonstrate

satisfactory

the c a l c u l a t e d results a n d the e x p e r i m e n t a l d a t a . i n i t i a l a p p r o x i m a t e assumptions are reasonable.

agreement

between

T h i s shows that

the

I n most cases, the one-

t e r m E q u a t i o n 5 is a p p l i c a b l e f o r the d e s c r i p t i o n of a d s o r p t i o n e q u i l i b r i a on zeolites, p a r t i c u l a r l y for zeolites w i t h s m a l l v o i d s ( z e o l i t e L , c h a b a site, erionite, m o r d e n i t e ) for w h i c h , i n a d s o r p t i o n of h y d r o c a r b o n s , η 3 as a r u l e . T h e c o n c e p t of the v o l u m e

filling

=

of m i c r o p o r e s makes it

possible to d e s c r i b e a d s o r p t i o n e q u i l i b r i a over sufficiently w i d e ranges of temperatures a n d pressures ( u s i n g f

8

i n s t e a d of p ) s

w i t h the use of

only 3 experimentally determined (usually from 1 adsorption isotherm f o r the average t e m p e r a t u r e )

constants, W , 0

A , a n d n . T h e constant

η

r e q u i r e s o n l y a tentative e s t i m a t i o n , since it is expressed b y a n integer. Literature (1) (2) (3) (4) (5) (6) (7)

Cited

Avgul, Ν. N . , Aristov, B. G., Kiselev, Α. V., Kurdyukova, L. Ya., Zh. Fis. Khim. 1968, 42, 2678. Bering, B. P., Zhukovskaya, E . G., Rahmukov, B. H . , Serpinsky, V. V., Ιzυ. Akad. Nauk SSSR, Ser. Khim. 1967, 1662. Dubinin, M . M . , Advan. Colloid Interface Sci. 1968, 2, 217. Dubinin, M . M . , "Chemistry and Physics of Carbon," 2, 51, Marcel Dekker, New York, 1966. Dubinin, M . M . , J. Colloid Interface Sci. 1967, 33, 487. Dubinin, M . M . , Symposium on Surface Area Determination, Bristol, 1969. Dubinin, M . M . , Kadlec, O., Czech. Chem. Commun. 1966, 31, 406.


80 (8) (9) (10) (11) (12)


(13)


II

Garkavenko, L . G., Dzhigit, Ο. M . , Kiselev, Α. V., Mikos, Κ. N . , Zh. Fiz. Khim. 1968, 42, 1033. Linde Co., Isotherm Data, Sheet No. 43, Acetylene-Molecular Sieve Type 4A Pellets. Nikolaev, Κ. M . , Dubinin, M . M . , Izv. Akad. Nauk SSSR, Otd. Khim. Nauk 1958, 1165. Polstyanov, E. F., Dubinin, M . M . , "Zeolites, Their Synthesis, Properties, and Application," p. 109, Publ. Sci. USSR, Moscow, 1965. Van der Waals, J. D., Koninkl. Akad. Belg. Kl. Wetenshap. Verhandel. 1896, 5, 248. Weibull, W., J. Appl. Mech. 1951, 18, 293.

R E C E I V E D January 23,

1970.

Addendum S y n t h e t i c zeolites of v a r i o u s types differ i n the n u m b e r of cations i n t h e i r v o i d s w h i c h are accessible f o r d i r e c t i n t e r a c t i o n w i t h the m o l e cules a d s o r b e d . T a b l e I lists, f o r t y p i c a l examples of zeolites, the n u m b e r s of accessible cations N

a

p e r zeolite v o i d a n d t h e i r n u m b e r Ζ i n m m o l e /

g r a m f o r d e h y d r a t e d zeolites. W h e n p a s s i n g f r o m zeolite N a A to zeolite L , the n u m b e r of accessible

cations Ζ—i.e., the n u m b e r of a d s o r p t i o n

centers i n the v o i d — d e c r e a s e s almost b y a factor of 10. T h e r e f o r e , i n the case of zeolite L , the r e l a t i v e role of interactions a m o n g cations

and

molecules a d s o r b e d , c o n v e n t i o n a l l y c a l l e d electrostatic, w i l l be a p p r o x i m a t e l y one o r d e r l o w e r t h a n f o r zeolite N a A . I n a d s o r p t i o n o n this zeo lite of substances w i t h s l i g h t l y p r o n o u n c e d n o n u n i f o r m i t y of d i s t r i b u t i o n of electron d e n s i t y i n m o l e c u l e s — f o r instance, saturated h y d r o c a r b o n s — one m a y expect that electrostatic interactions w i l l not p l a y the decisive role.

A s a result, w e o b t a i n the l i m i t i n g case of a d s o r p t i o n o n zeolites

l i k e zeolite L a n d erionite w i t h a w e a k electrostatic i n t e r a c t i o n . E x a m p l e s are a d s o r p t i o n e q u i l i b r i a o n zeolite L of methane w i t h i n the t e m p e r a t u r e range f r o m — 1 1 7 ° to — 3 0 ° C s t u d i e d i n a w o r k of B a r r e r

Table I.

Basic Data on Cations in Zeolites Si0 AW,

2

Zeolite NaA Na-Faujasite Na, K-Chabazite Na, K-Erionite Na-Mordenite Na, K-Zeolite

2 2.2-.5 4 6.6 10 6

Cations per

Void

Total Ν

Accessible N

12 11.4-6.9 4 4 4 9

12 9.4-4.9 3 2 2 2

a

M

mole/Gram 7.1 5.7-2.9 3.8 1.7 1.3 0.81


44.


Adsorption

Equilibria

of

Vapors

81

and

L e e ( I ) . T h i s case is also of g e n e r a l interest because the c r i t i c a l

t e m p e r a t u r e of m e t h a n e , — 8 2 . 5 ° C , lies i n this i n t e r v a l . If w e neglect t h e difference b e t w e e n electrostatic a n d d i s p e r s i o n i n t e r a c t i o n energies, then, i n a c c o r d a n c e w i t h the c o n c e p t of v o l u m e

filling

of m i c r o p o r e s d e s c r i b e d p r e v i o u s l y , the e q u a t i o n of a d s o r p t i o n of m e t h a n e on z e o l i t e L w i l l b e expressed b y R e f . 3 as a = a e x p [-(Α/Ε)"]

(1)


0

w h e r e Ε is t h e characteristic a d s o r p t i o n energy, t h e exponent of E q u a t i o n 1, η =

3 f o r a n adsorbent w i t h fine m i c r o p o r e s , a n d A t h e d i f f e r e n t i a l

m o l a r w o r k of a d s o r p t i o n A

= RT\n(f /p)

(2)

s

e q u a l ( w i t h a m i n u s s i g n ) to the v a r i a t i o n i n G i b b s ' free energy.

α

Figure 1. I , -117.2°;

Adsorption 2, -94.8°;

isotherms of methane on zeolite L for temperatures: 3, -80.6°; 4, -61.4°; 5, -30°C fa, Cm NTP/G; p, Ton)


3

82


A =

-AG

II

(3)

W e take, as a s t a n d a r d reference state, the state of the b u l k l i q u i d m e t h ane of the same t e m p e r a t u r e Τ i n e q u i l i b r i u m w i t h a v a p o r of f u g a c i t y f.

F o r s u p e r c r i t i c a l temperatures,

s

values of f u g a c i t y

w e assumed extrapolated

effective

f. s

T h e i n i t i a l c o m p u t a t i o n a l data—i.e., the characteristic e n e r g y Ε a n d the l i m i t i n g a d s o r p t i o n v a l u e a

Q

=

a °—were 0

d e t e r m i n e d f r o m the g r a p h


of a single e x p e r i m e n t a l a d s o r p t i o n i s o t h e r m f o r a m e a n t

0

=

temperature,

— 8 0 . 6 ° C , represented i n the l i n e a r f o r m of E q u a t i o n 1: log a = log a

0

0

100

BOO

-

(0.434/# )A 3

580

(4)

3

400

Ρ

Figure 2. Adsorption isotherms of carbon dioxide on Κ,Να-erionite temperatures: 1, 20°; 2, 40°; 3, 60°; 4, 80°; 5, 100°; 6, 120°; 7, (a, %; p, Torr)


for 140°

44.


W e obtained Ε = =

46.8 c m

3

Adsorption

Equilibria

of

Vapors

83

2350 c a l / m o l e a n d the l i m i t i n g a d s o r p t i o n v a l u e ,

N T P / g , at t

a

=

-

80.6°C.

T h e values of a

a° 0

for other t e m

0

peratures w e r e c a l c u l a t e d w i t h the use of the coefficient of t h e r m a l ex p a n s i o n of the adsorbate, a =

1.51 Χ 10" 1/deg, c o m p u t e d a c c o r d i n g to 3

the scheme of the D u b i n i n - N i k o l a y e v m e t h o d o n the basis of the p h y s i c a l constants of methane

(4).


αο =

a ° exp [ — z(t — t )] 0

(5)

0

In F i g u r e 1, the c o n t i n u o u s curves d e p i c t a d s o r p t i o n isotherms c a l c u l a t e d f r o m E q u a t i o n 4.

E x p e r i m e n t a l points are d e n o t e d b y circles.

T h e c a l c u l a t i o n a n d e x p e r i m e n t a l results are i n g o o d agreement.

A sim

i l a r e x a m p l e is i l l u s t r a t e d i n F i g u r e 2, s h o w i n g e x p e r i m e n t a l a n d c a l c u lated

( f r o m E q u a t i o n 4)

a d s o r p t i o n isotherms

of c a r b o n

N a , K - e r i o n i t e . T h e data u s e d i n c a l c u l a t i o n w e r e Ε = a° 0

=

12.4%

at t

0

=

80°C.

dioxide on

5250 c a l / m o l e a n d

T h u s , the g e n e r a l nature of gas a n d v a p o r

a d s o r p t i o n on zeolites at w e a k electrostatic

interactions

a d s o r p t i o n on active carbons w i t h the finest m i c r o p o r e s

is s i m i l a r to

(3).

In the case of a d s o r p t i o n i n m i c r o p o r e s , w h e n the c o n d i t i o n of t e m p e r a t u r e i n v a r i a n c e of the characteristic c u r v e is f u l f i l l e d , the net differ e n t i a l m o l a r heat of a d s o r p t i o n , q, a n d the d i f f e r e n t i a l m o l a r e n t r o p y of a d s o r p t i o n , A S , m a y be expressed ( 2 )

as

and

S u b s t i t u t i n g into E q u a t i o n s 6 a n d 7 the values of the d e r i v a t i v e a n d A c a l c u l a t e d f r o m E q u a t i o n 1, w e o b t a i n e d the f o l l o w i n g expressions d i f f e r e n t i a l e n t r o p y a n d d i f f e r e n t i a l heat of a d s o r p t i o n q = Ε [\ln α /αΥ'*

+

0

ψ

(In a » ~

2

/

3

for

(2):

J

(8)

and A.S =

-

^

(In α / α ) - * β

2 /

(9)

ο N o t e that the degree of filling of the l i m i t i n g a d s o r p t i o n space is: 0 =

a/a-o


(10)

84


ο LsosieiLc heat -so' α -0φ - y ~" a -^,

Description of Adsorption Equilibria of Vapors on Zeolites over Wide

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