Mobility of chemisorbed molecules on magnesium chromite

Mobility of chemisorbed molecules on magnesium chromite

Mobility of Chemisorbed Molecules on Magnesium Chromite B E R N A R D GILLOT FacultE des Sciences Mirande, Laboratoire de Recherches sur la REaclivit~...

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Mobility of Chemisorbed Molecules on Magnesium Chromite B E R N A R D GILLOT FacultE des Sciences Mirande, Laboratoire de Recherches sur la REaclivit~ des Solides

associ£ au C.N.R.S., 21000 Dijon, France

Received March 16, 1976; accepted May 22, 1976 Alolecules of oxygenand water vapor are highly chemisorbed on magnesium chromite prepared at low temperature (<600°C) and stabilized at a surface area of 35 m2/g. When coverage is low, the mobility of these molecules is solely due to their jump from one site to another; when coverage increases they behave like a two-dimensional gas whose vibration is perpendicular to the surface. Carbon dioxide is perfectly nonlocalized, which is in accordancewith its low adsorption heat and its easy desorption. INTRODUCTION

Gaseous molecules, chemisorbed at the surface of a solid may be regarded as nonlocalized or localized depending on the amount of the thermal energy of the adsorbate relative to superficial energy barriers. In a chemical adsorption, the adsorption heat usually decreases with coverage and therefore the molecules may become nonlocalized when coverage is large. Adsorption isotherm analysis allows the entropy of gas molecules relative to the adsorbate, to be determined and the degrees of freedom loss comparative to a standard state, to be deduced. These data make clearer the bond forces of the gaseous molecules on adsorption sites with respect to such factors as coverage and temperature. Thus, we showed, in a previous investigation (1), that ethylene and propane are adsorbed reversibly on magnesium chromite showing weak bonds between surface and adsorbate; the consideration of the mobility of adsorbed molecules led to results that were similar to those obtained for a physical adsorption: at low coverage, and from a given temperature onward, the molecules are nonlocalized and get localized, owing only to overcrowding.

In the present paper we extended mobility assessment to the chemisorption of the various gases involved in the catalytic oxidation of ethylene and propane on magnesium chromite (2) i.e., carbon dioxide, water vapor, and oxygen. The investigation of the mechanism of adsorption and the isotherm plotting, for the three gases on magnesium chromite stabilized at 35 m2/g, was carried out previously (3) over the temperature range 180 to 450°C. In particular, we showed that these gases depend on the characteristic laws of chemisorption with relatively high adsorption heats varying with coverage. THEORY The method used is based on the determination, through statistical thermodynamics, of the entropy loss associated with the degrees of freedom loss of the molecule passing from the gaseous state to the adsorbed one. The values thus obtained from the various models are compared with the entropy loss determined experimentally from the adsorption isotherms. Following Kemball, de Boer, Guggenheim, and Fowler (4-8) we consider two adsorptions : the localized and the nonlocalized one, and within both domains the presence or absence

166

Journal of Colloid and Interface Science, VoL 59, No. 1, March 15, 1977 ISSN 0021-9797

Copyright ~ 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

CHEMISORBED MOLECULES MOBILITY

167

TABLE I Models Used for Mobility Calculations--Expression of the Various Entropy Localized adsorption

Without interaction

Langmuir's equation P = KI(O/(1 -- 0)) or

Freundlich's equation P = KIO" Thermal entropy Sth = S,~ + S~ + S~= Configuration entropy S~o~e = R In [(1 -- 0)/0]

Nonlocalized adsorption

With interaction

Fowler and Guggenheim's general equation" K2P = [0/(1 -- O)]e(OZW/kr) Configuration entropy S~o~ = R { - (OZW/kT) + in [(1 -- 0)/0]}

Without interaction

Volmer's equation P = Ka[O/(1 - 0)]e[0/(1 - 0)] Translation entropy b S t r = R{ln MTa + in (1/0 - 1) - [1/(1/0 -- 1)] + 1 + in [2rrk/(Noh')]} Entropy of the internal degrees freedom Entropy of vibration perpendicular to the surface S, = R[(hv/kr)e((hv/kr) -- 1)-~ -- In [1 -- e -- (hv/kT)]}

With interaction

Hill's equation c P = K~[O/(1 -- 0)]e{[0/(1 -- 0)] - aO} a = 2a'/b'kT

a Z = number of molecules surrounding each adsorbed molecule, W = energy of interaction between molecule adsorbed on neighboring sites. b ~ = area occupied by a mole at saturation, M = gas molecular mass, h = Planck constant, ~ = Boltzmann constant. c a' and b' = van der Waals' constants. of i n t e r a c t i o n b e t w e e n the molecules will h a v e to be t a k e n into a c c o u n t , w h i c h leads us to consider the f o u r basic m o d e l s of T a b l e I. I n these e q u a t i o n s T, K1, K2, Ka, K4, are c o n s t a n t s a t a g i v e n t e m p e r a t u r e , P expresses t h e e q u i l i b r i u m p r e s s u r e of the a d s o r b e n t a b s o r b a t e s y s t e m and 0 = V~ Vm, the coverage. A. 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 s are identified w i t h one of t h e f o u r e q u a t i o n s ( L a n g m u i r , Fowler, Volmer, Hill) expressing the linear t r a n s f o r m e d c u r v e s in the following form : 0

inK1 + ln---1--0 0

-- i n P

ZW 0+lnKo

in P -- In 1--0 0 In P -- In - 1--0 0 in P

--

[-1]

In - -

1--0

= f(O)

[2-]

kT 0

in K~ = /(0) V3J 1--0 0 m = a O 1--0 +lnK~=

for a = 0, H i l l ' s e q u a t i o n is r e d u c e d to Volmer's. B. T h e a d s o r p t i o n n a t u r e being determined, the t h e o r e t i c a l and e x p e r i m e n t a l e n t r o p y losses are calculated. T h e s t a n d a r d state, a s s u m i n g a nonlocalized a d s o r b e d layer or a localized one, is t h a t p r o p o s e d b y de B o e r (9), i.e., for the localized c o m p l e x P0 = 760 T o r r 0 = ½ and for the nonlocalized complex, the a v a i l a b l e surface A o~ for an a d s o r b e d molecule is 4.08 T . 10 -16 cm 2.

1. Experimental Entropy Loss I t is c a l c u l a t e d f r o m a d s o r p t i o n isotherms. I n t h e nonlocalized m o d e l it is e q u a l to t h e difference b e t w e e n the m o l a r e n t r o p y of t h e t h r e e - d i m e n s i o n a l gas Sg a n d e x p e r i m e n t a l e n t r o p y v a r i a t i o n Se -ASo,

= Sg -- So.

[5]

T o express this difference, we s t a r t f r o m t h e c h e m i s o r p t i o n free e n e r g y AG e q u a l t o :

f(O)

[4]

AG = - - ( U g - - / ~ o ) + r ( S g -- £'o)

[6]

Journal of Colloid and Interface Science, Vol. 59, No. 1, M a r c h 15, 1977

168

BERNARD GILLOT

where no and S0 are the molar, differential entropies and enthalpies of the adsorbed layer, Hg and Sg the values corresponding to the gaseous phase. In order to keep the same reference state as for the calculation of theoretical entropies and by keeping temperature constant, pressure is caused to vary from the standard state to value P which is the equilibrium pressure at temperature T. Gibbs' energy variation is yielded by :

zXG = - - R T In Po/P.

[7]

Noting that Hg --5q0 is equal to the chemisorption isosteric heat (save factor RT), Eqs. [-5] through [-7~ give:

Po -ZSox~

=

-R

ln--

Q0 -

P

~8]

--

T"

The gaseous phase entropy is given by: Sg = R In M~T~ - 2, 3,

[9]

consider that there is no free rotation loss. We then have/XSrot = 0. In our case, moreover, the vibration frequency is not known with accuracy. Furthermore, the adsorption type being determined from adsorption isotherms, the vibration entropy will be calculated from Eqs. [-8] and r l l ] . I t should, also, be stated that in the calculation of &r, the configuration entropy is taken into account (Table I). (b) Localized adsorption. The entropy of a localized phase includes a thermal entropy Sth independent of the surface coverage but temperature dependent, containing the terms of rotation, internal vibration, molecule vibration and a configuration entropy, Scon,. The latter depends on the distribution of the molecules on a given number of adsorption sites depending on their jumping from site to site. In this model, the translation degrees are lost and the rotations can be prevented. We thus have

where M is the gas molar weight.

Sloc= Sth+Sc,,nr.

2. Theoretical Entropy Loss (a) Nonlocalized adsorption with two degrees of translation freedom. If the adsorbed phase behaves like a system with two degrees of translation freedom along the surface, the system entropy will be the sum of the translation entropy Sm the entropy of internal degrees of freedom including rotation, inhibited rotation and vibration around chemical bonds and finally the entropy resulting from a vibration of the molecule perpendicular to the surface S,. The rotation is considered to be free except for oxygen where there is dissociation. We, thus, have: S m = Sgr -J- Sv± -~ Srot _dr_Svib "~- Selee.

[-10~

The entropy due to the electronic state and that due to internal vibrational movements are usually negligible. The entropy change may be written as: AXm = AStr -~- ~Srot -~ Sv¢.

Vll]

In the case of a nonlocalized adsorption we may

[12]

In this case, it is still difficult to assess the thermal entropy Sth. In fact, the entropy change due to rotation cannot be calculated because we do not know whether one or two degrees of rotation are retained. In addition, the vibration frequency is not well known. I t must, however, be noticed that in the case of a chemical adsorption the vibration frequency is often about 10la sec-1. RESULTS AND DISCUSSION

A. Case of carbon dioxide. The isotherms coincide with Vohner's equation throughout the range of 0 (Fig. 1). From the curve, showing the isosteric heat variation with coverage (3), the variations in the experimental entropy can be calculated from the previous relationship. Table I I shows the gaseous molecule entropy values assuming that the degrees of rotation and internal vibration are maintained during adsorption, the translation entropy values following the two directions of the surface plane and the value of entropy toss through adsorption. I t is always much smaller

Journal of Colloid and Interface Science, VoI. 59, No. 1, March 15, 1977

CHEMISORBED MOLECULES MOBILITY

'169

TABLE Ii ieo ,~oi"

Carbon Dioxide~ T°K

0

Sa

533

0.250 0.312 0.375 0.437 0.506 0.542 0.592 0.637

(e.u.)

o~

a.



m

9

o

o •



0[2

0:3

9

O'4

--aScap

(e.u.)

(e.u.)

30 31.15 32 32.05 31.65 31.20 30.80 30.66

8.40 6.90 6.40 6.35 6.75 7.20 7.60 7,74

19.88 18.09 17.32 16.35 15.34 14.53 13.80 12.78

36o~c



o

Str

So

(e.u.)

0'5-

335aC • 300°c 260~c

0'6

0

FIC. 1. Carbon dioxide; isotherms equation.

38.4

Experimental and theoretical entropy values.

than the degree of translation loss, thereby the CO2 molecule is perfectly nonlocalized at the adsorbent surface, which accounts for its easy desorption. B. Case of water vapor. The various mobility ranges were made clearer by identifying the isotherms with the models listed in Table I and using the linear transformed curves previously established (Fig. 2). For 0.16 < 0 < 0.32, we have a localized adsorption without any interaction (Fig. 2a). Indeed, the isotherms coincide with Freundlich's equation (n = ½). For 0.32 < 0 < 0.46, the chemisorbed molecules are localized with interaction (Fig. 2b); Fowler's transformed curve is a straight line, with a positive slope varying from 4.5 to 3.4 when temperature rises from 360 to 430°C. Repulsion energy equals 0.54-10 -2° calories; this value is close to the adsorption heat at the corresponding coverage. For 0.46 < 0 < 0.62, we have a nonlocalized adsorption without any interaction and with two freedom degrees of translation (Fig. 2c). Table I I I gives the difference between experimental entropy and translation entropy according to the two directions of the plane. This difference varying with 0 corresponds to a vibration of frequency ~, perpendicular to the surface plane; over this range vibration frequencies are more than 10~2sec-k The mean value obtained is close to that reported by McCafferty el al. (10) for the physical adsorption of I-I.oO on aFe203.

C. Case of oxygen, The identification of the isotherms by means of Volmer's equation leads to the curves plotted in Fig. 3. The large evolution of the mobility ranges With temperature should be noticed. For 0 > 0.2, and depending on temperature, we have a nonlocalized adsorption without any interaction (t > 400°C) fo]lowed by a nonlocalized adsorption with interaction (t < 400°C) and ~ > 0. The transformed curve from Hill's equation is a straight line whose slope decreases from 2 to 1.6, when temperature rises from 345 to 400°C. For 0 < 0.2, we have a localized adsorption (Fig. 4) which is without interaction for t > 400°C and with interaction for t < 400°C. The positive slope of Fowler's transformed curve passes from 4 to 3.1 when temperature rises from 345 to 400°C. The calculation of entropy 10ss through adsorption was made; taking into account

~!,

(a)

S [

(c)

(b)

~ a e ~

o

362% . •* . " -11 .0,5

,__

0

°'0

log P

. . . .

04

0 0,5 0',5

~--0 0,6 0

FIG. 2. Water vapor; isotherms equation,

.7ou'nal of CollQ~d and lnle~iface Science, Vol. 59, No. 1, M a r c h 15~ 1977

170

BERNARD GILLOT TABLE I I I Water Vapor ~ T ®K

0

.Sf

38.32

0.490 0.540 0.580 0.608 0.625 0.650 0.665 0.682

633

(e.u.)

Str (e.u.)

11.23 12.12 13 14.06 14.60 14.91

27.09 26.20 25.32 24.26 23.72 23.41

18 17.40 15.90 15.21 14.80 14.71

17.20 17.50 17.87

21.20 20.80 20.45

14.50 14.30 14.10

17.91 17.54 17.31 17.14 17.17 17.22 17.19 17.20

20.41 20.78 21.01 21.18 21.15 21.10 21.13 21.12

13.84 13.19 12.40 11.84 11.40 10.90 10.43 10.30

(e.u.)

0.100 0.160 0.200 0.250 0.275 0.300 0.370 0.415 0.465

-- AS---e~p

SO

(e.u.)

S~ (e.u.)

~, (see-~)

Seo~8 (e.u.) 4.60 3.29 2.74 2.19 1.92 1.67

4.07 4.35 4.91 5.30 5.77 6.32 6.76 6.90

4.60 4.02 3.04 2.51 2.02

1.48 1.19 1.12

X X X X X X X X

10 TM 1012 10 TM i0 ix 10 I~ 10 TM 10~2 1012

" Experimental and theoretical entropy values.

the molecule dissociation, especially internal rotation, entropy disappears when the oxygen atom is considered. This entropy may be formulated as follows: S~ot = R[-log Z~ot + 1.5J.

[13]

Log Zrot may be calculated from : Log Zro~ = 1.5 log T -- 4.794.

F14]

At 678 K calculation gives: S~ot = 12.15 e.u.

For the localized range, the configuration entropy must take into account the oxygen molecule dissociation into two identical atoms. Chang (11) formulated this configuration entropy from statistical calculation using a factor z which is a nearest neighbor for a given atom and ~ the symmetry number equal to two, when both atoms cannot be distinguished from each other. For oxygen, we shall take = 2 and z = 4 or 6. For z = 4 , the configuration entropy value calculated in this way is approximately twice that of the molecule. Table IV shows the values of this entropy

,el

orZ

~"'o

o t-

~ , c . "l~ ~ .

Z

-0,5

c

- ".....

2 o

2 .

"~

~

41,5°c c

- - _ _

40

. -C

-~-

o:,

0:2

-

-

=,

oc

-I

c

°c

0;

o;

o

Fro. 3. Oxygen; isotherms equation for 0 > 0, 2.

-2

015

log P

oi~

0 02

FIG. 4. Oxygen; isotherms equation for 0 < 0, 2.

Journal of Colloid and Interface Science, Vol. 59, No. i, March 15, 1977

CHEMISORBED MOLECULES MOBILITY

171

TABLE IV Oxygen~ T°K

676

0

Sg

(e.u.)

5;-o

S,o~

(e.u.)

(e.u.)

So -- ,~e + Srot

St,

(e.u.)

(e.u.)

Sv

(e.u.)

Seoa~

(e.u.)

0.027 0.041 0.069

12.35 12.55 18.15

40.30 40.10 34.50

27 25.20 22.12

12.50 12.15 10.40

0.120 0.158

26.30 34.55

26.35 18.10

20.50 19.24

8.10 6.30

13.43 12.02 11.67 11.15 10.94

17.82 17.06 16 15.43 15.10

0.258 0.305 0.388 0.416 0.452

40.5

39.22 40.43 41 41.50 41.68

12.15

3.56 6.31 9 10.64 11.48

Sm (e.u.)

5.52 4.87 4.35 4.02 3.14

a Experimental and theoretical entropy values. close to 12 Kcal mole -1 and, therefore, for the localized range, the thermal entropy is zero. For the nonlocalized range the translation loss m a y be considered as being replaced by a vibration of frequency ~. CONCLUSION As previously found out, for ethylene and propane, carbon dioxide is loosely linked to the surface of magnesium chromite as soon as the coverages are equal to or higher than 0.1 and the chemisorbed gas is to be considered as constituting a superficial, perfectly mobile layer. I t is, thus, possible to admit a nondissociating adsorption, which is confirmed elsewhere b y conductivity measurements between 200 and 600°C (3). On the contrary, water vapor molecules are still partially localized at 0 = 0.2 and become a nonlocalized layer only when coverages are higher than 0.4. I t is noticed, for oxygen, that for a coverage lower than 0.1, adsorption is localized but the calculation accuracy does not allow choice between molecular or atomic adsorption, the values obtained being close to each other. W h e n coverage increases (8 > 0.5), the ad-

sorbate behaves like a perfect nonlocalized gas, according to both surface plane directions. Experimental entropy loss corresponds to the loss of a freedom degree of translation perpendicular to the surface, replaced by a vibration of frequency v. I t is, furthermore, possible to anticipate for the degree freedom of rotation loss. REFERENCES i. GILLOT, B. AND DELAI~0SSE, D. C. R. Acad. Sci. (Paris) 270C, 1057 (1970). 2. GILLOT,B. Bull. Soc. Chim. France No. 6, 2382

(1968). 3. GILLOT, B., 1V~oREAU,M., AND DELA:FOSSE,D., Bull. Soc. Chim. France No. 4, 1330 (1970). 4. DE BOER, J. H. AND KRUGER, S., Proc. Akad. Sci. Amsterdam 5SB, 451 (1952). 5. KEMBALI,C., Advan. Catal. 2, 233 (1950). 6. GARDEN,A., KLINGTON,G. L., AND LAING, W., Trans. Faraday Soc. 51, 1558 (1955). 7. FOWLER,R. H. AND GUGGE~HEI~,E. A., "Statistical Thermodynamics," Cambridge University Press, 1939. 8. HILL, T. L., J. Chem. Phys. 15, 767 (1947). 9. DEBOE~, J. tt., "The Dynamical Character of Adsorption," Clarendon Press, Oxford, 1953. 10. McCA~'FERTY, E. AND ZETTLEraOYER, A. C., Y. Colloid Interface Sci. 4, 452 (1970). 11. CHANG,T. S., Proc. Roy. Soc. London A169, 512 (1939).

Journal of Colloid and Interface Science, Vol. 59. No. 1. March 15. 1977