712
KEITH J. L.IIDLER
T H E lIECHA4KISMSOF SOME E L E N E S T A R Y SURFACE REACTIOKS’ KEITH J . L.-\IDI,ER Department o j C h e m i s t r y , T h e Calholic C n i c e r s i l y o j A m e r i c a , W a s h i n g t o n , D . C . ReceiLed .lugus1 27, 1948
A process occurring in one stage, by a smooth passage over a single free-energy bar1 ier, is conveniently spoken of a5 “elementary.” The calculation from first principles of the rate of such a reaction involves first the construction, by quantum-mechanical methods, of the potential-energy surface relevant to it, and secocdly the calculation of the rate with \I hich the system moves over the surface. In changing from the initial to the final state most reaction systems pass through a configuration for which the flee energy is a maximum: the structure having this configuration is knoivn as the activated complex for the reaction. The calculation of the absolute rates of elementary processes was greatly simplified when it was realized that to a good approximation the activated complex can he considered to be in statistical equilibrium with the reactants, and when in 1935 H. Eyring (6; c.f. 5 , 18, 2G) formulated a simple yet accurate method of calculating the rate with n-hich an activated complex decomposes into the reaction products. According to this treatment, the essential problem in the absolute calculation of rates is the determination of the structuie of the activated complev and of its energy with respect to the reactants. V%en this is done the concentration of the activated comples can be calculated, by statistical mechanics, in terms of the initial concentrations, and the rate of reaction can then be written down. Since the structure of the activated complex controls not only the rate of’ the reaction but also its dependence upon the concentrations of reactants, it is of the greatest importance to define it correctly. In principle this can be done by quantum mechanics, but unfortunately the calculations can be carried out accurately only for the simplest of systems. However, in many cases the configuration of the activated complex can be estimated on the basis of a general knon-ledge of molecular structure, I\ hile its energy level xith respect to the reactants (Le., the energy of activation) can be determined from the experimental variation of the rstte ith the temperature. Although this treatment is not as fundamental as is to be desired, it is convenient and accurate and in many cases has contributed considerably to our understanding of the mechanisms of reactions. I t is important to realize that the manner in which the activated complex is formed is irrelevant to the study of reaction rates. The procedure outlined above has been carried out for a large number of reactions of different types (see Glasstone, Laidler, and Eyring (9)), and in every case it lias been found possible to formulate a mechanism, i.e., define an activated complex, leading t o a calculated rate which varies correctly with the initial concentrations and is in good numerical agreement with experiment. Frequently it is possible to formulate plausible alternative mechanisms for a reaction, and
* Presented on June 8, 1948 at the Pittsburgh International Conference on Surface Reactions.
MECHAPilSJfS O F SOME ELEMENTARY SURFACE REACTIOSS
7 13
in such cases all of the mechanisms except one can usually be excluded as giving poor agreement ; sometimes a decision can be made on mechanisms betiveen ivhich the experiments are unable t o distinguish. The treatment has been applied to adsorption and desorption processes by Laidler, Classtone, and E y i n g (13; rl. 11, 25) and by the same aiit,hors to a number of chemical reactions occiit-ring on surfaces (14); particularly in the latter case \vas it possible to distinguish bet\veen alternative mechanisms. A4napplicat,ion of the treatment to the paraortho hydrogen coniversion on surfaces has been made Ijy Eley and Rideal (3). In the present paper the basic rate and equilibrium equations for adsorption m d desorption processes \vi11 be developed in a somewhat different manner from previously. The treatment \vi11 then be extended to the production and recomi n a t i o n of atoms and free mdicals at, surfaces. processes important in connection ivith free-radical mechanisms and \vith the mechanism of overvoltage, n-hich will 3e referred to briefly later. The question of adsorption with surface penetration s also taken up, in view of its significance in connection with problems of mrrosion. ADSORPTIOS APiD D E S O R P T I O S
SThen a gas is brought into contact n-ith a surface it is frequently found t'hat ;here is a practically instantaneous uptake, follon-ed by a slow process of sorp;ion. The rapid process corresponds to van der ST'aals adsorption in which the nolecules are held to t'he siirface by iveak, non-specific forces; this process repii,es no energy of activation and occurs a t every collision in which certain :ntropy requirements are realized. The slow uptake corresponds to one or both If tivo processes which involve an activation energy; these are activated adsorpion (24) and permeation through the solid. I t is not difficult t'o devise experiments t-hich woiild determine ivhich process in a given case is the slo\ver and therefore ,ate-determining, but in only a few cases have these been carried out. There to, hoiverer, esist a number of systems in which solution in the solid is not probtble, and in irhich the rate of uptake is therefore that of the activated adsorption. :n other cases, in ivhich penetration of the surface does actually occur, it may be lifficult to establish irhether the slo~vstep is the initial adsorption process or the ,ubsequent diffusion through the solid; an example is the sorption of hydrogen ) y palladium, in ivhich solution of' the hydrogen certainly occurs. The problem )f the kinetic laws \vhich are follo\ved \\-hen adsorption is accompanieJ by peneration ivill be treated else\vhere from the present point of view (12), and will iere be discussed only very briefly; in the discussion ivhich now follows it will )e assumed that surface penetration is of' no importance. In some cases of chemisorption, molecules become dissociated and exist on he surface a s atoms or radicals; the chief evidence for this, as \vi11 be discussed tter, is that the adsorption isotherm involves the square root of the pressure. 'hese processes of adsorption involve the breaking of a chemical bond and the xmation of tn-o bonds ivith surface atoms; on balance the reaction is always xothermic, but since a bond is broken it generally requires an energy of activaion. I n other instances molecular adsorption occurs, but theoretical calcula-
71'4
KEITH J . L.IIDLGH
tioiis (17, 19, 20) have indic.ated that 1' cei t a i n imiouiit oi bond stretching occurs, and it is this that i* ie.pon-ible io1 the energie. of activation that are tound The kinetic ~ N \ Y Sof adsorption and desorption are different according to whether 01 not the bond beromes completely broken on adsorption, the case of adsorption I\ ithout dissociation \\ ill be considered first The process of adsorption may be envisioned (13; c j 11, 23) as a bimolecular imction between a molecule in the gas phase and an "active center" (rf 23) on the adsorbing surface; the active center may be a single surface atom or a pair or group of such stoms. If N Bis the number of molecules in the gat phase, whirti is of volume T' cc , and N, nnd N , are the respective numbers of bare bites and of adsorbed molecules at any instant on the surface, of area 5' *q c m , the ronc w t i ations may he defined as follow\: c,,
=
N,/V gas molecules per cubic centiineter
r
=
Y8/Shire sites per q u a i e centimeter
c, = S , / S adsorbed molecules per square cent m e t e r
'L'he rquilibriuni con\tant lor the prochehs
14
thus given I J ~
u here the f's are the complete partition functions for the specie*. Representing the partition function for the gas pei unit volunir ( U Z I , .fg V ) ab F,, the equilibrium cwnstaut may be expressed as
'l'his expression is seen t'o differ frorri the espressioii applicable tu a homogeneous equilibrium in that all of the partition iunctions in the latter are for unit volume of gas. Eyuat>ion3 may readily be put in the usual form of the Langmuii~isotherm (16) by rioting t'liat cy is proportional t o the gas pressure p ? m d cu and c, t u e and ( I - d ) , respectively, where 0 is the fraction of surface covered. If the zero-point cwntrihution is iwnoved fium the partition frinctioiis, equation 3 kames
Jvhere E: is the ellerg\- ul' dsorptiuii per iliulec.uk at the at)solute zero; the partition fun(tions .f,z, F g , and , f ~:IW n o \ v t>v;iluutetiwith referenve t o the zero-point level. 'I'tie above treatmerit of the equilibriurn cwiditiun nia!. ieadily be extended t L calculating the ixtes of' adsorptioii and desorptioii. Iluring adsorption a gat molecule \vi11 pass thruugh :i series u t twifiguratioiis. t h t corresponding to the
MECI-IAXISMS OF S O M E ELEMEIiTAlIT SIURSACE REACTIOSS
715
maximum free energy being the activated state for the process In the theory of absolute reaction rates, as with most theories of the rates of chemical reactions. the asbumption is made that the activated complexes are in statistical equilibrium ith the gas molecules and the surface sites, and that their concentration can be cdculated in terms of the relevant partition fiinctions. The equilibrium expression. analogous to equation 1,is
ivhere the symbol 1 denotes the activated complex; E , is now the iiicrease of energy involved in going from the gaseous state t o the activated state, i.e., i h the energy of activation for adsorption at the absolute zero The partition function f: may noli be considered. In the (Lase of chemisorption, since relatively strong bonds are formed bet\\-een the adsorbed molecules and the surface, the activated compleves will be localized on the surface and mill possess no translational or rotational freedom; the partition function is therefore the product of a number of vibrational factors. The vibrations are all of the ordinary kind except the one corresponding to the reaction coordinate; for this there is no energ- barrier, and the vibration has the characteristics of :t free translation. The partition function corresponding to this degree of freedom is the limiting value of a vibrational partition funrtion as the frequency Y of vihratiori approaches zero; it is thus given t)y
- kT hv
If the product of the remaining vibrational partition functions for the activated complex is written as f *,the equilibrium expression becomes
which rearranges to
The quantity YC'. being the product of the freqiienc? of decomposition of the tctivated complexes and their concentration, is the rate of adsorption u1 in molrw l e ~per square centimeter per second, v i z :
716
KEITH J. LAIDLER
I n an exactly similar manner it may be shown that the rate of desorption given by
At equilibrium these rates are equal; equating them and putting Ea
- El
u2
=
is
E,
one obtains, as is necessary, the adsorption isotherm (equation 4).
I I
FIG.1. Schematic representatioii of the frce energy -4,t h e energy E , and t h e entropy term - 7's as functions of the distance d of the adsorbed species from t h e surface. I n this case there is no positive energv of activation for adsorption, but there is u free energy of adsorption A i i l s oning t o t h e influence of the entropy term. T h e configuration of the activated complex, t h e free energy for n hich is a ma\imum, is denoted by 2. It is t o be noted t h a t in this case there may be il neqative energy of activation and t h a t Ebes may be less t h a n Endfl
The adsorption and desorption procedses may also be considered from a thermodynamical point of view. As the distance from the surface dilninishes the total energy of the system may decrease continuously, as indicated in figure 1, or may show an initial increase followed by a decrease to a value lower than the initial value (figure 2); the latter case corresponds t o activated adsorption. As the distance betn-een the gas molecule and the surface decreases there is also a loss of entropy, owing t o the loss of freedom; the variation in - T S is indicated schematically in the figures. The net change in A , equal to E - T S , is also shown
MECHASlSMS O F SOME ELEMESTARY SURFACE KEACTIOXS
7li
in the figures, and it is to be noted that in both cases the free energy has a maximum corresponding to a particular configuration. There is therefore always a free energy of activation for adsorption (represented on the figures as Aids) even if there is no energy of activation E i d a . There is also always a free energy of activation for desorption (Aies)and an energy of activation for desorption (EAes), which is equal to the energy of adsorption &ids plus the energy of activation for adsorption. I
1
d
f
I
00
FIG.2. Schematic representation of A , E , and - T S versus d for thc case of a positive energy of activation. S o t e t h a t the activated complex, hich corresponds to a maximum A , does not necessarily correspond t o a niaxirnum value of E .
In the original calculations of rates of adsorption (13; cf. 11,25)the assumption n-as tentatively made that the partition function f: for the activated state in both adsorption and desorption is the same as that for the adsorbed molecules, and the satisfactory agreement n-ith experiment suggests that this assumption is justified. I t is equivalent t o postulating that the entropy corresponding to the activated compIex is approximately the same as that for the adsorbed molecule; figures 1 and 2 have been constructed to agree n-ith this. Calculations of rates of adsorption and desorption, and indeed of all surface rates, can only be carried out in an approximate manner, since there must always be some doubt as to the values to assign to some of the quantities. Thus, even for the smoothest of surfaces only a rough estimate can be made of the number
718
KEITH J. LAIDLER
of adsorption sites per square centimeter; this is sometime5 taken to be the concentration of surface atoms. The partition functions f' and f q for the activate.1 complex and the .urface sites liring taken as unity, and the vibrational and rotational factors for the gas being i.eprezentetl by b,, the rate of adsorption (eqn a iion ' 11) may he written as: (13) Similarly, puttingf; antff, equal to unity, thc rate nf (!( becomes
-(it !)t
):I I I
i
(>
j i i . r + i 1.1
12)
-
Reliable experiment'ii data o:i I ,it( 01 atl-o; ptiun and desorption are scaice, but in the cases examl:,tl 11ie agi(i(ill(' i t \ \ u s quite satisfactory. This indicates that the treatment has follon-ed the right general lines, and confirms the assumption that the complex is immobilized on the burface
Mobile adsorbcti layers; accommodation coeflcien ts The rate expressions assume a different form. and the calculated velocitie, ma) be quite different, if it is po-tulatetl that the activate 1 moleciileq are mohilp on the burface. Since this a$>umption is implicit in kinetic. theory ca1culatio:i. of the number of c o l l i ~ i o non ~ a surface, the equation for th(2 rate of' adsorption oi a mobile layer \'iill be derived a n d c.omp:ircti numericaliv ith thnt ohtaine ! above. If in the activated state the molecules I w o m i i i : i L o i 1 iii tJ asburned t o have two degrees of translational freedom, and t o ! i : i \ ~ I tits wine rotational anti vihrationai freedom as in the gaseoub btate. r l i r ~~ ~ i i i i 1 1i i) li i n betneeen artivsted ant1 initial state may be represented by
where F' and F, now reft 1 I t.-;wi I \ ely to 1 sq. cm. and to unit volume. ipplication of the theory of : i l w ) l i t ~ vreaction rates give. for the rate of adsorption :
The vibrational and rotational terms in I;': and F, itre identical and thcrrforc cancel out; the ratio F ' I F , is tliw the ratio of the translational terms, I.?.,
(20) sincar. rJ;Y is equal to the pressure p if the gas is ass~iniedto be ideal. The expression p , '(2~mi;7')" is the Hertz-Kniidsen formula for the Iiumher of molec.uleh striking 1 sq. mi. of' :I surfwce per second; equation 20 is thus equivalent t o the rate of adsorption that u.ould tie given by simple cwllision theory, on the asslimption that ever;. molerule striking the surface and having an energy in w e e + of E l \Jecwn-les atlsoi.het1. I t is of inte1,est to see how this expression differs from the (]ne o l ) t a i r i c ~ t l : i h o \ - c ~ on the :is,~iiniption of 2111 inimobilt. :ictiv:ited )Inplex. 'I'he t a1t e t w i t i \.e r:i t e expression i ii ixi I Ininioldt~wmp/t>.r i c f . cyr(ntioti 13):
(*I
l'he ratio u l ( z ) / u l ( m ) , which is the ratio of the rates calculated using the theory of al)solute reavtiori r x t w to that c d c i h t e d from collision theory, is thus:
r ,
I c*o~iceritratioiic8 u s i i a ~ y1iit.i ii vallie of approximately IO'" sites per square rentimeter, ivhile (2and:T),lh' is frequently about 10". Consequently for the :ttlsorpt ion of :itonis, for \\.hich b, is unity, the ratio U ~ ( L ' ) , ; ~ ~ ( HisL )approximately 10- '; the ( d l i h i o i i theory \vould t h i s give the correct order of magnitude for the rat t' of ii(Isoi*ptioiiof atoms. IIoTrever, for more complex molecules ( 2 m n k ~ ) / h ' 1 1 1 ~ 1 \)e ~ - sonic\\.hiit larger, n,hiIe b,, \\-liic.h no\v iricludes rotational and vibrational t e i m i h . ma\- l w 10' 01's o ; the ratio c l ( i ) t , ( i r i ) maj. thus be lo-' or Ion-el.. For the :idsoi,ption of ~ i i ( ~ l e c ~ therefore, ile~, the (dollision treatment will be in error, the niow SO the more c ~ ~ n i p l ethe s mulecwle. It is interesting to note that the 5ituaI ion k1ei.e iwemblrs that for homogeneous react'ions, for which the collisiori theory is also ;trc*iirxte f o r :itonis t i t i t is less so for molecules. 111 h t h cil~esthe rwisou 11c1
720
KEITH J. LAIDLER
is that the collision theory by it5 very nature talies 110 account of the entropy losses involved in the formation of the a c t i r a t d comples, losses which are more important the more complex the reacting molecules. The ratio of the number of inolecules becoming adsorbed on the surface t o the total number striking the surface is equal t o il
This ratio is the accommoilatioii coeficient oi the surface, and the present treitment has therefore given a method of calculating this quantity. The accommodation coefficient difi'ers from the ratio L ' 1 ( Z 1 / L , 1 ( ? 7 2 ) , considered in the last paragraph, by the Boltzmann term e-F' . I t i q smaller the more complex t h P molecule and the larger the energv of activation El.
.Idsorption with dissocLatioiL I n a number of cases there is evidence that adsorption is accompanied by (lis sociation of the molecule; :vhen this occurs it is found, as will be seen, that the adsorption isotherm assumes a tlifi'erent form and involves the square root of the pressure. Mien dissociation occurs thc resiilting atoms or free radicals can form strong primary valence bonds n ith surface atom>; t\\ o bond-, are therefore formed a t the expense of the breaking of one, so that the proc'ess may be strongly exothermic and the system more stable than if dissociation did not occur. If the adsorption involves only a stretching of the valence bond, the kinetic l a w of adsorption and desorption, and the adsorption isotherm, are the same as obtained previously; it is only when the bond hecomes completely hrolien that the laws become modified. Tivo alternatire mechanisms are then posaible ; the slow and rate-determining process may be the process of separation of the atoms, the actual adsorption process being rapid, or the adsorption process may tie ratedetermining. I n the first case the activated complex consists of a single atom or radical on the surface, so that if the molerule is represented as RLthe process may be written as
in2 + 5'
11s'
RS
By application of the method outlined previously the rate of the adsorption process can readily be shown t o be
(25) while the rate of desorption is
By equating these rates the adsorption equilibrium is found t o be given by
MECHAXISMS OF SOME ELEMEKTARY SUKFhCE REACTIOSS
i21
which is equivalent t o the expression dejuce 1 in 1935 by Folvler (81 for this case. Both the expression for the rate of adsorption and that for the adsorption jsotherm are seen t o involve the square root of the pressure of the gas. VThen the adsorption of the molecule is s l o and ~ rate-determining, the actjvated complev consists of an adsorbed R2 molecule
R? +- s + m,s: biit siih~equentlyone or hoth of the atom< jump- t o another site S':
R2. I i i C Z 2 , which may obtain particularly a t low pressures; in this case
:tiid the rate of uptalx deped:, upon the gas pressure. 1'
=
If in addition, lid
lL&:L
>L~, (40'3)
and the rate of ,korption is c:liial t o t h i t of the activated adsorption, which i, therefore rate-determining. If, on the otlier h m d , l,, > lid, 1'
= i l iLhc;l
i.,
L
(
i0i))
aiid the rate oi sorption 15 c o n t i d l e J tjy the cliffusion i n the solid and by the equilibriiim constaiit k l i I;? for the adsorption. Equation 40 has h e n found to bc obeyed for the uytnlce of o\\'gen ljj- met:ds 3t very loiv pressures and fur that of hJ-drogen up to quite high presauiez; in both cascy iy = l/2. (-3) IClc:, > i 4- ?;d, lvhen v = I.*L
(41)
i.e., the rate is intlepcridcnt 01 the ga, ~ J I ~ ~ ~ L I Under I Y . these conditions, which will aln ays Le realized at sufficiently high prehwres, the adsorption is rapid enough to maintain a complete la\ of i t v m s or moiecules, and the slow step is the diffusivn tlirough tlic soiid. Beha\ ior oi this type is shonn by osygen and many rnetds at all e\eepi xery ion p i e w i i p h It is therefore to be expected that a~ io\r prebsures the rate of uptake will depend upon the gas pressure, but that a t high pressures it will become constant. This behavior has actually been observed lor a large number of systems. I t is t o be noted that the treatment given is perfectly general and is independent of the mechanism of diffusion. TIIR PHODUCTIOS FRF:T,
ASU
I I I S U O ~ I ~ I S . ~ OF ~ I OAroiis ~ LSL,
RADlCALS
-\r
SURFACES
The devdopinent 01 the e s p r e k n i s for the rates of formation arid recombination of atoms and free radicals a t surfaces follow somewhat similar lines to the treatment of adsorption and desorption with dissociation. Again two limiting
MECHASISMS OF S O l l E ELEMEXTARY SURFACE REAPTIOSS
725
cases are to be expected, the distinction betn-een them resting upon whether the activated complex consists of a single atom or radical adsorbed on the surface or of an undissociated molecule. In the former case the over-all process can be mitten as
gn, + S G s - R% s + R and the rate of the forward reaction, Le., the dissociation, is given by an equation analogous to equation 26:
The rate of the reverse reaction, the recombination of the radicals, is given by
The equilibrium condition is obtained by equating these rates, and is therefore
or
where E = 2(E1 - E,) is the energy of dissociation, at the ahsolutr zero, of the molecule Rz. I n the second case, in which the activated complex consists of an undissociated molecule on the surface, the production of atoms takes place by a subsequent rapid process; the over-all process can thus be represented by
Hz
+ S F1: SzR; 8 S2 + 2R
The rate of dissociation is noiv given by
and the rate of recombination is given by
By putting v1 equal to v2 the equilibrium condition is again given by equation 31, but the dissociation energy is now given by E = E1 - E,. The four rate equations (42, 43, 46, and 47) will now be considered n-ith reference to (1) sparsely covered surfaces and ( 2 ) fully covered surfaces.
72(i
Ij-lien the zurface I- only >paiwly covered, the concentration c of bare burface sites is rtppro=iimately t h t of tlie siirfacc ir1ic.n coniplrtely bare, \vtiich mitv br denoted h v L ; thtx rate equation5 therefore may t)e i\ ritteii a,$ ('me I (activated coniple\ containing :t ~ i n g l tatoiii ~ :
Case
I / (activated twniplr\ writaining a ixiolecule
I he equilibriiun eqiiatioii iequatioii 45)for die process it2 2li, \vhich Iiecessarily is independent of the kinetic imc.timisnis m d does not, involve the surface, can thus Le obtained on the basis of tu.o distinct mecthanisnis, tlie niaiii features of ivhirh, for a sparsel!. covered surface, i n q . t ) smimarixecl ~ :is iollo\vs : (1 j \\?ien the activated coinples corisist,s of ii single adsorbed radicd, the rate of formation of radicals is proportional t o the sciuare root of the Inoleculai~concentration and that of the recornhination to the tirst p o w r of the radical coilcentration. ( 2 ) Jl.\?len the activated cumplex is it11 ati.surbed Ill(Jlec'Llk the rate of iormatioii of radicds is proportional to the first puiver of the niolecular c.oiic*entrat,ion,and that of the recombination to the square of the radical concent,ration. It is theoretically possible t'hat in some w s e s both mechauisms \vi11 occur simultaneously, s o that intermediate 1hetic.s ]vi11 be obtained; the dissociation will t,hen have an order of betn-een one-half a,nd iinity, arid the recombination ot' betn-een unity and tiso. Ho\\-ever,it, must l)e emphasized that if the rate of dissociation varies with tlie sqiiare rooi of the pressure of the molecules R2, that of the iwornbination mwt, necessarily 1-it1-y{vitt: the tirst, poir-t'r of thc r d i c a l concentration, since ot henvise the eorrec:t equilibrium lan [voulti not, be obtnineci. Similarly. if the rate uf dissociation is of the ririt order, that of the! recornhination must be of the second order. The liiiietic measurenieiits that hl-1T-eheen carried out, oil processes ut this lcirici are \-er>-fe\s and incomplete. On the ba of the theoret'ical treatnient of this paper a detailed xnalysis of the available experimental data is being carried out by Air, Kurt E. Shuler and the author, and the coiiclusions will be published ill the near future; fur the present it, will aufice to bring out some of the inore significant points, :md to discuss one or two of the most interesting reactions. 7
,
Fiillu c o i ~ e dsurfaces
the siirfave is lull) IYIT w e t i a n d redctioi? cannot occur 011 the adborbeti la3 ei but only on the bare part of the surface, the kinetic laws assume an entirely different form and will now h r obtained. For simplicity it will be a.jbiimed that the :idsoIhed laver is compmed wlelj- of the atom< or iatiicalq R.i e., that no foreign poisons are present If the moleciilw R?are present in the svstem in excebb, a n d the protliiction of the i*arlical~ R is being studied the c.oncentration c k of hare sites 1b largely controlled hv the eqiiilihrium hetween the molecxiiles and the surface; the adsorption
isotherm (ecluatim 27) is therefore used, and ca is put equal to L ; the equation therefore becomes
(52) where E, is the erieigy of adsorption. Insertion of this espression into equation 42 gives, for the rate of dissociation \\-hen the comples contains a single radical,
(53) The rate is therefore independent of the concentration of It,. For the reverse reaction, if the concentration of radicals II is in excess of the equilibriiini concentration, one should not use the isotherm of equation 52, since the concrnt,ration of adsorbed molecules will now be controlled by the adsorption equilibrium involving radicals, the isotherm for ivhich is
for a covered surface; EL is now the energy of adsorption for the radicals. tion of this expression into equation 43 gives
Inser-
It is t o be noted that the equilibrium condition of equation 4.5 cannot now bo obtained by equating zj and uIl since i'l and v? do not represent the rates a t equilibrium; these are given by introducing the same isotherm (either 52 or 5 i ) into both rate expressions. The rate expression 33 is only valid when the molecules are present in excess of their equilibrium concentrations, while expression 53 is true when the radicals are in excess. I n a similar manner the rate evpressions for the second mechanism, in which the comples involves a molecule It2, are (36) and
(57) The kinetic eupressions obtained for the covered layer may now be c o n s i h e d from the point of view of the transformations taking place. If a supply of molecules is brought into contact nith a surface, and the surface becomes covered with a complete layer of radicals, the subsequent evaporation of the radicals into the gas phase may take place in two ways. In the first ease the slow process involves the radicals leaving the surface as individuals, and the over-all rate is independent of the pressure of R2,since this does not influence the total number
MECHAKISRIS OF SOME ELLRfESTARY SL-RFACE REACTIOKS
729
of adsorbed radicals; this is the process to which equation 53 applies. Secondly, the slonv process may be the adsorption of a molecule R2 on a vacant space, the subsequent removal of the two R radicals from the surface being rapid; this corresponds to equation 50. Similarly the reverse process, the recombination of radicals, may involve as the SIOTV process the adsorption of an atom, the surface recornbination being rapid; this corresponds to equation 55. The second mechanism for the recombination of radicals (equation 5 7 ) implies that the adsorption of the radicals is rapid, the subsequent surface recombination being slow and rate-determining. Approsimate calculations of the kind made abore indicate that except at excessively high pressure the first mechanism will be the more important in the majority of cases: zero-order kinetics for both forward and reverse react ions are therefore to be eypected. However it has been seen that reaction on a covered surface may take place on the adsorbed layer rather than on the bare part of the surface; for a covered surface, therefore, reaction may proceed according to either equation 48 or 53:
Insertion of numerical values corresponding to 1 atm. pressure gives Irl = 1 0 8 . 5 x 1015 x 1013 x 10-15.6~-E1/k?' - 102leE1/kT (1) and v1 = 1015 x 1 0 1 3 ~ - ( E i + E d i k T = 1 0 2 8 ~ - ( E l +E,) / k T (2)
I ' the values of E , in the two expressions are the same, it is seen that the rates rill be equal if equals lo', a condition realized, for example, by a value of E , = 32 kcal. per mole a t 1000°I-, and T the absolute empei~itiire. This equation has been found to lx incwnsistent \I-ith the data, in tiat thri nunieric:il cwnstnnt 2.303RT ' 2 F is onc-half ti) one-quarter of the T-alue xinil experimentally in o\-ervoltage experiments, and as ii result alterriative iechanii;ms for overvoltage have tieen proposed (4, T, I O ) . In I-ie\\-~f t tie c~oncliisioriof the present paper that recomt)iuation of hydrogen toms is actually a tiwt-order pi'ocess, it is i~learthat the 'l'del niec~hanisnineeds :>\.i,
